| license: mit |
Carlos Furuti's cubic globe #1 - http://www.progonos.com/furuti/MapProj/Normal/ProjPoly/projPoly2.html
Based on "Earth in a Cube" by Enrico Spinielli and on my research for d3-geo-projection/pull/86 and d3-geo/issues/46.
Re-incorporating Jason Davies’ clipPolygon() code into d3v4.
Code base at Fil/d3-geo:clip-polygon.
See also https://bl.ocks.org/Fil/694ba0d0bc1fc4c24eb257dc210eb01a
forked from Fil's block: Furuti 3 - projection.clipPolygon()
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| [ | |
| [ | |
| [ | |
| 34.491577, | |
| 31.593743 | |
| ], | |
| [ | |
| 34.567108, | |
| 31.538749 | |
| ], | |
| [ | |
| 34.267730, | |
| 31.226894 | |
| ], | |
| [ | |
| 34.238891, | |
| 31.286766 | |
| ], | |
| [ | |
| 34.214172, | |
| 31.320794 | |
| ], | |
| [ | |
| 34.491577, | |
| 31.593743 | |
| ] | |
| ] ] | |
| ] | |
| } | |
| }, | |
| {"type":"Feature","id":"YEM","properties":{"name":"Yemen"},"geometry":{"type":"Polygon","coordinates":[[[53.108573,16.651051],[52.385206,16.382411],[52.191729,15.938433],[52.168165,15.59742],[51.172515,15.17525],[49.574576,14.708767],[48.679231,14.003202],[48.238947,13.94809],[47.938914,14.007233],[47.354454,13.59222],[46.717076,13.399699],[45.877593,13.347764],[45.62505,13.290946],[45.406459,13.026905],[45.144356,12.953938],[44.989533,12.699587],[44.494576,12.721653],[44.175113,12.58595],[43.482959,12.6368],[43.222871,13.22095],[43.251448,13.767584],[43.087944,14.06263],[42.892245,14.802249],[42.604873,15.213335],[42.805015,15.261963],[42.702438,15.718886],[42.823671,15.911742],[42.779332,16.347891],[43.218375,16.66689],[43.115798,17.08844],[43.380794,17.579987],[43.791519,17.319977],[44.062613,17.410359],[45.216651,17.433329],[45.399999,17.333335],[46.366659,17.233315],[46.749994,17.283338],[47.000005,16.949999],[47.466695,17.116682],[48.183344,18.166669],[49.116672,18.616668],[52.00001,19.000003],[52.782184,17.349742],[53.108573,16.651051]]]}}, | |
| {"type":"Feature","id":"ZAF","properties":{"name":"South Africa"},"geometry":{"type":"Polygon","coordinates":[[[31.521001,-29.257387],[31.325561,-29.401978],[30.901763,-29.909957],[30.622813,-30.423776],[30.055716,-31.140269],[28.925553,-32.172041],[28.219756,-32.771953],[27.464608,-33.226964],[26.419452,-33.61495],[25.909664,-33.66704],[25.780628,-33.944646],[25.172862,-33.796851],[24.677853,-33.987176],[23.594043,-33.794474],[22.988189,-33.916431],[22.574157,-33.864083],[21.542799,-34.258839],[20.689053,-34.417175],[20.071261,-34.795137],[19.616405,-34.819166],[19.193278,-34.462599],[18.855315,-34.444306],[18.424643,-33.997873],[18.377411,-34.136521],[18.244499,-33.867752],[18.25008,-33.281431],[17.92519,-32.611291],[18.24791,-32.429131],[18.221762,-31.661633],[17.566918,-30.725721],[17.064416,-29.878641],[17.062918,-29.875954],[16.344977,-28.576705],[16.824017,-28.082162],[17.218929,-28.355943],[17.387497,-28.783514],[17.836152,-28.856378],[18.464899,-29.045462],[19.002127,-28.972443],[19.894734,-28.461105],[19.895768,-24.76779],[20.165726,-24.917962],[20.758609,-25.868136],[20.66647,-26.477453],[20.889609,-26.828543],[21.605896,-26.726534],[22.105969,-26.280256],[22.579532,-25.979448],[22.824271,-25.500459],[23.312097,-25.26869],[23.73357,-25.390129],[24.211267,-25.670216],[25.025171,-25.71967],[25.664666,-25.486816],[25.765849,-25.174845],[25.941652,-24.696373],[26.485753,-24.616327],[26.786407,-24.240691],[27.11941,-23.574323],[28.017236,-22.827754],[29.432188,-22.091313],[29.839037,-22.102216],[30.322883,-22.271612],[30.659865,-22.151567],[31.191409,-22.25151],[31.670398,-23.658969],[31.930589,-24.369417],[31.752408,-25.484284],[31.837778,-25.843332],[31.333158,-25.660191],[31.04408,-25.731452],[30.949667,-26.022649],[30.676609,-26.398078],[30.685962,-26.743845],[31.282773,-27.285879],[31.86806,-27.177927],[32.071665,-26.73382],[32.83012,-26.742192],[32.580265,-27.470158],[32.462133,-28.301011],[32.203389,-28.752405],[31.521001,-29.257387]],[[28.978263,-28.955597],[28.5417,-28.647502],[28.074338,-28.851469],[27.532511,-29.242711],[26.999262,-29.875954],[27.749397,-30.645106],[28.107205,-30.545732],[28.291069,-30.226217],[28.8484,-30.070051],[29.018415,-29.743766],[29.325166,-29.257387],[28.978263,-28.955597]]]}}, | |
| {"type":"Feature","id":"ZMB","properties":{"name":"Zambia"},"geometry":{"type":"Polygon","coordinates":[[[32.759375,-9.230599],[33.231388,-9.676722],[33.485688,-10.525559],[33.31531,-10.79655],[33.114289,-11.607198],[33.306422,-12.435778],[32.991764,-12.783871],[32.688165,-13.712858],[33.214025,-13.97186],[30.179481,-14.796099],[30.274256,-15.507787],[29.516834,-15.644678],[28.947463,-16.043051],[28.825869,-16.389749],[28.467906,-16.4684],[27.598243,-17.290831],[27.044427,-17.938026],[26.706773,-17.961229],[26.381935,-17.846042],[25.264226,-17.73654],[25.084443,-17.661816],[25.07695,-17.578823],[24.682349,-17.353411],[24.033862,-17.295843],[23.215048,-17.523116],[22.562478,-16.898451],[21.887843,-16.08031],[21.933886,-12.898437],[24.016137,-12.911046],[23.930922,-12.565848],[24.079905,-12.191297],[23.904154,-11.722282],[24.017894,-11.237298],[23.912215,-10.926826],[24.257155,-10.951993],[24.314516,-11.262826],[24.78317,-11.238694],[25.418118,-11.330936],[25.75231,-11.784965],[26.553088,-11.92444],[27.16442,-11.608748],[27.388799,-12.132747],[28.155109,-12.272481],[28.523562,-12.698604],[28.934286,-13.248958],[29.699614,-13.257227],[29.616001,-12.178895],[29.341548,-12.360744],[28.642417,-11.971569],[28.372253,-11.793647],[28.49607,-10.789884],[28.673682,-9.605925],[28.449871,-9.164918],[28.734867,-8.526559],[29.002912,-8.407032],[30.346086,-8.238257],[30.740015,-8.340007],[31.157751,-8.594579],[31.556348,-8.762049],[32.191865,-8.930359],[32.759375,-9.230599]]]}}, | |
| {"type":"Feature","id":"ZWE","properties":{"name":"Zimbabwe"},"geometry":{"type":"Polygon","coordinates":[[[31.191409,-22.25151],[30.659865,-22.151567],[30.322883,-22.271612],[29.839037,-22.102216],[29.432188,-22.091313],[28.794656,-21.639454],[28.02137,-21.485975],[27.727228,-20.851802],[27.724747,-20.499059],[27.296505,-20.39152],[26.164791,-19.293086],[25.850391,-18.714413],[25.649163,-18.536026],[25.264226,-17.73654],[26.381935,-17.846042],[26.706773,-17.961229],[27.044427,-17.938026],[27.598243,-17.290831],[28.467906,-16.4684],[28.825869,-16.389749],[28.947463,-16.043051],[29.516834,-15.644678],[30.274256,-15.507787],[30.338955,-15.880839],[31.173064,-15.860944],[31.636498,-16.07199],[31.852041,-16.319417],[32.328239,-16.392074],[32.847639,-16.713398],[32.849861,-17.979057],[32.654886,-18.67209],[32.611994,-19.419383],[32.772708,-19.715592],[32.659743,-20.30429],[32.508693,-20.395292],[32.244988,-21.116489],[31.191409,-22.25151]]]}} | |
| ]} |
| // https://d3js.org/d3-geo-projection/ Version 2.2.0. Copyright 2017 Mike Bostock. | |
| (function (global, factory) { | |
| typeof exports === 'object' && typeof module !== 'undefined' ? factory(exports, require('d3-geo'), require('d3-array')) : | |
| typeof define === 'function' && define.amd ? define(['exports', 'd3-geo', 'd3-array'], factory) : | |
| (factory((global.d3 = global.d3 || {}),global.d3,global.d3)); | |
| }(this, (function (exports,d3Geo,d3Array) { 'use strict'; | |
| var abs = Math.abs; | |
| var atan = Math.atan; | |
| var atan2 = Math.atan2; | |
| var cos = Math.cos; | |
| var exp = Math.exp; | |
| var floor = Math.floor; | |
| var log = Math.log; | |
| var max = Math.max; | |
| var min = Math.min; | |
| var pow = Math.pow; | |
| var round = Math.round; | |
| var sign = Math.sign || function(x) { return x > 0 ? 1 : x < 0 ? -1 : 0; }; | |
| var sin = Math.sin; | |
| var tan = Math.tan; | |
| var epsilon = 1e-6; | |
| var epsilon2 = 1e-12; | |
| var pi = Math.PI; | |
| var halfPi = pi / 2; | |
| var quarterPi = pi / 4; | |
| var sqrt1_2 = Math.SQRT1_2; | |
| var sqrt2 = sqrt(2); | |
| var sqrtPi = sqrt(pi); | |
| var tau = pi * 2; | |
| var degrees = 180 / pi; | |
| var radians = pi / 180; | |
| function sinci(x) { | |
| return x ? x / Math.sin(x) : 1; | |
| } | |
| function asin(x) { | |
| return x > 1 ? halfPi : x < -1 ? -halfPi : Math.asin(x); | |
| } | |
| function acos(x) { | |
| return x > 1 ? 0 : x < -1 ? pi : Math.acos(x); | |
| } | |
| function sqrt(x) { | |
| return x > 0 ? Math.sqrt(x) : 0; | |
| } | |
| function tanh(x) { | |
| x = exp(2 * x); | |
| return (x - 1) / (x + 1); | |
| } | |
| function sinh(x) { | |
| return (exp(x) - exp(-x)) / 2; | |
| } | |
| function cosh(x) { | |
| return (exp(x) + exp(-x)) / 2; | |
| } | |
| function arsinh(x) { | |
| return log(x + sqrt(x * x + 1)); | |
| } | |
| function arcosh(x) { | |
| return log(x + sqrt(x * x - 1)); | |
| } | |
| function airyRaw(beta) { | |
| var tanBeta_2 = tan(beta / 2), | |
| b = 2 * log(cos(beta / 2)) / (tanBeta_2 * tanBeta_2); | |
| function forward(x, y) { | |
| var cosx = cos(x), | |
| cosy = cos(y), | |
| siny = sin(y), | |
| cosz = cosy * cosx, | |
| k = -((1 - cosz ? log((1 + cosz) / 2) / (1 - cosz) : -0.5) + b / (1 + cosz)); | |
| return [k * cosy * sin(x), k * siny]; | |
| } | |
| forward.invert = function(x, y) { | |
| var r = sqrt(x * x + y * y), | |
| z = -beta / 2, | |
| i = 50, delta; | |
| if (!r) return [0, 0]; | |
| do { | |
| var z_2 = z / 2, | |
| cosz_2 = cos(z_2), | |
| sinz_2 = sin(z_2), | |
| tanz_2 = tan(z_2), | |
| lnsecz_2 = log(1 / cosz_2); | |
| z -= delta = (2 / tanz_2 * lnsecz_2 - b * tanz_2 - r) / (-lnsecz_2 / (sinz_2 * sinz_2) + 1 - b / (2 * cosz_2 * cosz_2)); | |
| } while (abs(delta) > epsilon && --i > 0); | |
| var sinz = sin(z); | |
| return [atan2(x * sinz, r * cos(z)), asin(y * sinz / r)]; | |
| }; | |
| return forward; | |
| } | |
| var airy = function() { | |
| var beta = halfPi, | |
| m = d3Geo.geoProjectionMutator(airyRaw), | |
| p = m(beta); | |
| p.radius = function(_) { | |
| return arguments.length ? m(beta = _ * radians) : beta * degrees; | |
| }; | |
| return p | |
| .scale(179.976) | |
| .clipAngle(147); | |
| }; | |
| function aitoffRaw(x, y) { | |
| var cosy = cos(y), sincia = sinci(acos(cosy * cos(x /= 2))); | |
| return [2 * cosy * sin(x) * sincia, sin(y) * sincia]; | |
| } | |
| // Abort if [x, y] is not within an ellipse centered at [0, 0] with | |
| // semi-major axis pi and semi-minor axis pi/2. | |
| aitoffRaw.invert = function(x, y) { | |
| if (x * x + 4 * y * y > pi * pi + epsilon) return; | |
| var x1 = x, y1 = y, i = 25; | |
| do { | |
| var sinx = sin(x1), | |
| sinx_2 = sin(x1 / 2), | |
| cosx_2 = cos(x1 / 2), | |
| siny = sin(y1), | |
| cosy = cos(y1), | |
| sin_2y = sin(2 * y1), | |
| sin2y = siny * siny, | |
| cos2y = cosy * cosy, | |
| sin2x_2 = sinx_2 * sinx_2, | |
| c = 1 - cos2y * cosx_2 * cosx_2, | |
| e = c ? acos(cosy * cosx_2) * sqrt(f = 1 / c) : f = 0, | |
| f, | |
| fx = 2 * e * cosy * sinx_2 - x, | |
| fy = e * siny - y, | |
| dxdx = f * (cos2y * sin2x_2 + e * cosy * cosx_2 * sin2y), | |
| dxdy = f * (0.5 * sinx * sin_2y - e * 2 * siny * sinx_2), | |
| dydx = f * 0.25 * (sin_2y * sinx_2 - e * siny * cos2y * sinx), | |
| dydy = f * (sin2y * cosx_2 + e * sin2x_2 * cosy), | |
| z = dxdy * dydx - dydy * dxdx; | |
| if (!z) break; | |
| var dx = (fy * dxdy - fx * dydy) / z, | |
| dy = (fx * dydx - fy * dxdx) / z; | |
| x1 -= dx, y1 -= dy; | |
| } while ((abs(dx) > epsilon || abs(dy) > epsilon) && --i > 0); | |
| return [x1, y1]; | |
| }; | |
| var aitoff = function() { | |
| return d3Geo.geoProjection(aitoffRaw) | |
| .scale(152.63); | |
| }; | |
| function armadilloRaw(phi0) { | |
| var sinPhi0 = sin(phi0), | |
| cosPhi0 = cos(phi0), | |
| sPhi0 = phi0 >= 0 ? 1 : -1, | |
| tanPhi0 = tan(sPhi0 * phi0), | |
| k = (1 + sinPhi0 - cosPhi0) / 2; | |
| function forward(lambda, phi) { | |
| var cosPhi = cos(phi), | |
| cosLambda = cos(lambda /= 2); | |
| return [ | |
| (1 + cosPhi) * sin(lambda), | |
| (sPhi0 * phi > -atan2(cosLambda, tanPhi0) - 1e-3 ? 0 : -sPhi0 * 10) + k + sin(phi) * cosPhi0 - (1 + cosPhi) * sinPhi0 * cosLambda // TODO D3 core should allow null or [NaN, NaN] to be returned. | |
| ]; | |
| } | |
| forward.invert = function(x, y) { | |
| var lambda = 0, | |
| phi = 0, | |
| i = 50; | |
| do { | |
| var cosLambda = cos(lambda), | |
| sinLambda = sin(lambda), | |
| cosPhi = cos(phi), | |
| sinPhi = sin(phi), | |
| A = 1 + cosPhi, | |
| fx = A * sinLambda - x, | |
| fy = k + sinPhi * cosPhi0 - A * sinPhi0 * cosLambda - y, | |
| dxdLambda = A * cosLambda / 2, | |
| dxdPhi = -sinLambda * sinPhi, | |
| dydLambda = sinPhi0 * A * sinLambda / 2, | |
| dydPhi = cosPhi0 * cosPhi + sinPhi0 * cosLambda * sinPhi, | |
| denominator = dxdPhi * dydLambda - dydPhi * dxdLambda, | |
| dLambda = (fy * dxdPhi - fx * dydPhi) / denominator / 2, | |
| dPhi = (fx * dydLambda - fy * dxdLambda) / denominator; | |
| lambda -= dLambda, phi -= dPhi; | |
| } while ((abs(dLambda) > epsilon || abs(dPhi) > epsilon) && --i > 0); | |
| return sPhi0 * phi > -atan2(cos(lambda), tanPhi0) - 1e-3 ? [lambda * 2, phi] : null; | |
| }; | |
| return forward; | |
| } | |
| var armadillo = function() { | |
| var phi0 = 20 * radians, | |
| sPhi0 = phi0 >= 0 ? 1 : -1, | |
| tanPhi0 = tan(sPhi0 * phi0), | |
| m = d3Geo.geoProjectionMutator(armadilloRaw), | |
| p = m(phi0), | |
| stream_ = p.stream; | |
| p.parallel = function(_) { | |
| if (!arguments.length) return phi0 * degrees; | |
| tanPhi0 = tan((sPhi0 = (phi0 = _ * radians) >= 0 ? 1 : -1) * phi0); | |
| return m(phi0); | |
| }; | |
| p.stream = function(stream) { | |
| var rotate = p.rotate(), | |
| rotateStream = stream_(stream), | |
| sphereStream = (p.rotate([0, 0]), stream_(stream)); | |
| p.rotate(rotate); | |
| rotateStream.sphere = function() { | |
| sphereStream.polygonStart(), sphereStream.lineStart(); | |
| for (var lambda = sPhi0 * -180; sPhi0 * lambda < 180; lambda += sPhi0 * 90) sphereStream.point(lambda, sPhi0 * 90); | |
| while (sPhi0 * (lambda -= phi0) >= -180) { // TODO precision? | |
| sphereStream.point(lambda, sPhi0 * -atan2(cos(lambda * radians / 2), tanPhi0) * degrees); | |
| } | |
| sphereStream.lineEnd(), sphereStream.polygonEnd(); | |
| }; | |
| return rotateStream; | |
| }; | |
| return p | |
| .scale(218.695) | |
| .center([0, 28.0974]); | |
| }; | |
| function augustRaw(lambda, phi) { | |
| var tanPhi = tan(phi / 2), | |
| k = sqrt(1 - tanPhi * tanPhi), | |
| c = 1 + k * cos(lambda /= 2), | |
| x = sin(lambda) * k / c, | |
| y = tanPhi / c, | |
| x2 = x * x, | |
| y2 = y * y; | |
| return [ | |
| 4 / 3 * x * (3 + x2 - 3 * y2), | |
| 4 / 3 * y * (3 + 3 * x2 - y2) | |
| ]; | |
| } | |
| augustRaw.invert = function(x, y) { | |
| x *= 3 / 8, y *= 3 / 8; | |
| if (!x && abs(y) > 1) return null; | |
| var x2 = x * x, | |
| y2 = y * y, | |
| s = 1 + x2 + y2, | |
| sin3Eta = sqrt((s - sqrt(s * s - 4 * y * y)) / 2), | |
| eta = asin(sin3Eta) / 3, | |
| xi = sin3Eta ? arcosh(abs(y / sin3Eta)) / 3 : arsinh(abs(x)) / 3, | |
| cosEta = cos(eta), | |
| coshXi = cosh(xi), | |
| d = coshXi * coshXi - cosEta * cosEta; | |
| return [ | |
| sign(x) * 2 * atan2(sinh(xi) * cosEta, 0.25 - d), | |
| sign(y) * 2 * atan2(coshXi * sin(eta), 0.25 + d) | |
| ]; | |
| }; | |
| var august = function() { | |
| return d3Geo.geoProjection(augustRaw) | |
| .scale(66.1603); | |
| }; | |
| var sqrt8 = sqrt(8); | |
| var phi0 = log(1 + sqrt2); | |
| function bakerRaw(lambda, phi) { | |
| var phi0 = abs(phi); | |
| return phi0 < quarterPi | |
| ? [lambda, log(tan(quarterPi + phi / 2))] | |
| : [lambda * cos(phi0) * (2 * sqrt2 - 1 / sin(phi0)), sign(phi) * (2 * sqrt2 * (phi0 - quarterPi) - log(tan(phi0 / 2)))]; | |
| } | |
| bakerRaw.invert = function(x, y) { | |
| if ((y0 = abs(y)) < phi0) return [x, 2 * atan(exp(y)) - halfPi]; | |
| var phi = quarterPi, i = 25, delta, y0; | |
| do { | |
| var cosPhi_2 = cos(phi / 2), tanPhi_2 = tan(phi / 2); | |
| phi -= delta = (sqrt8 * (phi - quarterPi) - log(tanPhi_2) - y0) / (sqrt8 - cosPhi_2 * cosPhi_2 / (2 * tanPhi_2)); | |
| } while (abs(delta) > epsilon2 && --i > 0); | |
| return [x / (cos(phi) * (sqrt8 - 1 / sin(phi))), sign(y) * phi]; | |
| }; | |
| var baker = function() { | |
| return d3Geo.geoProjection(bakerRaw) | |
| .scale(112.314); | |
| }; | |
| function berghausRaw(lobes) { | |
| var k = 2 * pi / lobes; | |
| function forward(lambda, phi) { | |
| var p = d3Geo.geoAzimuthalEquidistantRaw(lambda, phi); | |
| if (abs(lambda) > halfPi) { // back hemisphere | |
| var theta = atan2(p[1], p[0]), | |
| r = sqrt(p[0] * p[0] + p[1] * p[1]), | |
| theta0 = k * round((theta - halfPi) / k) + halfPi, | |
| alpha = atan2(sin(theta -= theta0), 2 - cos(theta)); // angle relative to lobe end | |
| theta = theta0 + asin(pi / r * sin(alpha)) - alpha; | |
| p[0] = r * cos(theta); | |
| p[1] = r * sin(theta); | |
| } | |
| return p; | |
| } | |
| forward.invert = function(x, y) { | |
| var r = sqrt(x * x + y * y); | |
| if (r > halfPi) { | |
| var theta = atan2(y, x), | |
| theta0 = k * round((theta - halfPi) / k) + halfPi, | |
| s = theta > theta0 ? -1 : 1, | |
| A = r * cos(theta0 - theta), | |
| cotAlpha = 1 / tan(s * acos((A - pi) / sqrt(pi * (pi - 2 * A) + r * r))); | |
| theta = theta0 + 2 * atan((cotAlpha + s * sqrt(cotAlpha * cotAlpha - 3)) / 3); | |
| x = r * cos(theta), y = r * sin(theta); | |
| } | |
| return d3Geo.geoAzimuthalEquidistantRaw.invert(x, y); | |
| }; | |
| return forward; | |
| } | |
| var berghaus = function() { | |
| var lobes = 5, | |
| m = d3Geo.geoProjectionMutator(berghausRaw), | |
| p = m(lobes), | |
| projectionStream = p.stream, | |
| epsilon$$1 = 1e-2, | |
| cr = -cos(epsilon$$1 * radians), | |
| sr = sin(epsilon$$1 * radians); | |
| p.lobes = function(_) { | |
| return arguments.length ? m(lobes = +_) : lobes; | |
| }; | |
| p.stream = function(stream) { | |
| var rotate = p.rotate(), | |
| rotateStream = projectionStream(stream), | |
| sphereStream = (p.rotate([0, 0]), projectionStream(stream)); | |
| p.rotate(rotate); | |
| rotateStream.sphere = function() { | |
| sphereStream.polygonStart(), sphereStream.lineStart(); | |
| for (var i = 0, delta = 360 / lobes, delta0 = 2 * pi / lobes, phi = 90 - 180 / lobes, phi0 = halfPi; i < lobes; ++i, phi -= delta, phi0 -= delta0) { | |
| sphereStream.point(atan2(sr * cos(phi0), cr) * degrees, asin(sr * sin(phi0)) * degrees); | |
| if (phi < -90) { | |
| sphereStream.point(-90, -180 - phi - epsilon$$1); | |
| sphereStream.point(-90, -180 - phi + epsilon$$1); | |
| } else { | |
| sphereStream.point(90, phi + epsilon$$1); | |
| sphereStream.point(90, phi - epsilon$$1); | |
| } | |
| } | |
| sphereStream.lineEnd(), sphereStream.polygonEnd(); | |
| }; | |
| return rotateStream; | |
| }; | |
| return p | |
| .scale(87.8076) | |
| .center([0, 17.1875]) | |
| .clipAngle(180 - 1e-3); | |
| }; | |
| function hammerRaw(A, B) { | |
| if (arguments.length < 2) B = A; | |
| if (B === 1) return d3Geo.geoAzimuthalEqualAreaRaw; | |
| if (B === Infinity) return hammerQuarticAuthalicRaw; | |
| function forward(lambda, phi) { | |
| var coordinates = d3Geo.geoAzimuthalEqualAreaRaw(lambda / B, phi); | |
| coordinates[0] *= A; | |
| return coordinates; | |
| } | |
| forward.invert = function(x, y) { | |
| var coordinates = d3Geo.geoAzimuthalEqualAreaRaw.invert(x / A, y); | |
| coordinates[0] *= B; | |
| return coordinates; | |
| }; | |
| return forward; | |
| } | |
| function hammerQuarticAuthalicRaw(lambda, phi) { | |
| return [ | |
| lambda * cos(phi) / cos(phi /= 2), | |
| 2 * sin(phi) | |
| ]; | |
| } | |
| hammerQuarticAuthalicRaw.invert = function(x, y) { | |
| var phi = 2 * asin(y / 2); | |
| return [ | |
| x * cos(phi / 2) / cos(phi), | |
| phi | |
| ]; | |
| }; | |
| var hammer = function() { | |
| var B = 2, | |
| m = d3Geo.geoProjectionMutator(hammerRaw), | |
| p = m(B); | |
| p.coefficient = function(_) { | |
| if (!arguments.length) return B; | |
| return m(B = +_); | |
| }; | |
| return p | |
| .scale(169.529); | |
| }; | |
| function bertin1953Raw() { | |
| var hammer$$1 = hammerRaw(1.68, 2), | |
| fu = 1.4, k = 12; | |
| return function(lambda, phi) { | |
| if (lambda + phi < -fu) { | |
| var u = (lambda - phi + 1.6) * (lambda + phi + fu) / 8; | |
| lambda += u; | |
| phi -= 0.8 * u * sin(phi + pi / 2); | |
| } | |
| var r = hammer$$1(lambda, phi); | |
| var d = (1 - cos(lambda * phi)) / k; | |
| if (r[1] < 0) { | |
| r[0] *= 1 + d; | |
| } | |
| if (r[1] > 0) { | |
| r[1] *= 1 + d / 1.5 * r[0] * r[0]; | |
| } | |
| return r; | |
| }; | |
| } | |
| var bertin = function() { | |
| var p = d3Geo.geoProjection(bertin1953Raw()); | |
| p.rotate([-16.5, -42]); | |
| delete p.rotate; | |
| return p | |
| .scale(176.57) | |
| .center([7.93, 0.09]); | |
| }; | |
| function mollweideBromleyTheta(cp, phi) { | |
| var cpsinPhi = cp * sin(phi), i = 30, delta; | |
| do phi -= delta = (phi + sin(phi) - cpsinPhi) / (1 + cos(phi)); | |
| while (abs(delta) > epsilon && --i > 0); | |
| return phi / 2; | |
| } | |
| function mollweideBromleyRaw(cx, cy, cp) { | |
| function forward(lambda, phi) { | |
| return [cx * lambda * cos(phi = mollweideBromleyTheta(cp, phi)), cy * sin(phi)]; | |
| } | |
| forward.invert = function(x, y) { | |
| return y = asin(y / cy), [x / (cx * cos(y)), asin((2 * y + sin(2 * y)) / cp)]; | |
| }; | |
| return forward; | |
| } | |
| var mollweideRaw = mollweideBromleyRaw(sqrt2 / halfPi, sqrt2, pi); | |
| var mollweide = function() { | |
| return d3Geo.geoProjection(mollweideRaw) | |
| .scale(169.529); | |
| }; | |
| var k = 2.00276; | |
| var w = 1.11072; | |
| function boggsRaw(lambda, phi) { | |
| var theta = mollweideBromleyTheta(pi, phi); | |
| return [k * lambda / (1 / cos(phi) + w / cos(theta)), (phi + sqrt2 * sin(theta)) / k]; | |
| } | |
| boggsRaw.invert = function(x, y) { | |
| var ky = k * y, theta = y < 0 ? -quarterPi : quarterPi, i = 25, delta, phi; | |
| do { | |
| phi = ky - sqrt2 * sin(theta); | |
| theta -= delta = (sin(2 * theta) + 2 * theta - pi * sin(phi)) / (2 * cos(2 * theta) + 2 + pi * cos(phi) * sqrt2 * cos(theta)); | |
| } while (abs(delta) > epsilon && --i > 0); | |
| phi = ky - sqrt2 * sin(theta); | |
| return [x * (1 / cos(phi) + w / cos(theta)) / k, phi]; | |
| }; | |
| var boggs = function() { | |
| return d3Geo.geoProjection(boggsRaw) | |
| .scale(160.857); | |
| }; | |
| var parallel1 = function(projectAt) { | |
| var phi0 = 0, | |
| m = d3Geo.geoProjectionMutator(projectAt), | |
| p = m(phi0); | |
| p.parallel = function(_) { | |
| return arguments.length ? m(phi0 = _ * radians) : phi0 * degrees; | |
| }; | |
| return p; | |
| }; | |
| function sinusoidalRaw(lambda, phi) { | |
| return [lambda * cos(phi), phi]; | |
| } | |
| sinusoidalRaw.invert = function(x, y) { | |
| return [x / cos(y), y]; | |
| }; | |
| var sinusoidal = function() { | |
| return d3Geo.geoProjection(sinusoidalRaw) | |
| .scale(152.63); | |
| }; | |
| function bonneRaw(phi0) { | |
| if (!phi0) return sinusoidalRaw; | |
| var cotPhi0 = 1 / tan(phi0); | |
| function forward(lambda, phi) { | |
| var rho = cotPhi0 + phi0 - phi, | |
| e = rho ? lambda * cos(phi) / rho : rho; | |
| return [rho * sin(e), cotPhi0 - rho * cos(e)]; | |
| } | |
| forward.invert = function(x, y) { | |
| var rho = sqrt(x * x + (y = cotPhi0 - y) * y), | |
| phi = cotPhi0 + phi0 - rho; | |
| return [rho / cos(phi) * atan2(x, y), phi]; | |
| }; | |
| return forward; | |
| } | |
| var bonne = function() { | |
| return parallel1(bonneRaw) | |
| .scale(123.082) | |
| .center([0, 26.1441]) | |
| .parallel(45); | |
| }; | |
| function bottomleyRaw(sinPsi) { | |
| function forward(lambda, phi) { | |
| var rho = halfPi - phi, | |
| eta = rho ? lambda * sinPsi * sin(rho) / rho : rho; | |
| return [rho * sin(eta) / sinPsi, halfPi - rho * cos(eta)]; | |
| } | |
| forward.invert = function(x, y) { | |
| var x1 = x * sinPsi, | |
| y1 = halfPi - y, | |
| rho = sqrt(x1 * x1 + y1 * y1), | |
| eta = atan2(x1, y1); | |
| return [(rho ? rho / sin(rho) : 1) * eta / sinPsi, halfPi - rho]; | |
| }; | |
| return forward; | |
| } | |
| var bottomley = function() { | |
| var sinPsi = 0.5, | |
| m = d3Geo.geoProjectionMutator(bottomleyRaw), | |
| p = m(sinPsi); | |
| p.fraction = function(_) { | |
| return arguments.length ? m(sinPsi = +_) : sinPsi; | |
| }; | |
| return p | |
| .scale(158.837); | |
| }; | |
| var bromleyRaw = mollweideBromleyRaw(1, 4 / pi, pi); | |
| var bromley = function() { | |
| return d3Geo.geoProjection(bromleyRaw) | |
| .scale(152.63); | |
| }; | |
| // Azimuthal distance. | |
| function distance(dPhi, c1, s1, c2, s2, dLambda) { | |
| var cosdLambda = cos(dLambda), r; | |
| if (abs(dPhi) > 1 || abs(dLambda) > 1) { | |
| r = acos(s1 * s2 + c1 * c2 * cosdLambda); | |
| } else { | |
| var sindPhi = sin(dPhi / 2), sindLambda = sin(dLambda / 2); | |
| r = 2 * asin(sqrt(sindPhi * sindPhi + c1 * c2 * sindLambda * sindLambda)); | |
| } | |
| return abs(r) > epsilon ? [r, atan2(c2 * sin(dLambda), c1 * s2 - s1 * c2 * cosdLambda)] : [0, 0]; | |
| } | |
| // Angle opposite a, and contained between sides of lengths b and c. | |
| function angle(b, c, a) { | |
| return acos((b * b + c * c - a * a) / (2 * b * c)); | |
| } | |
| // Normalize longitude. | |
| function longitude(lambda) { | |
| return lambda - 2 * pi * floor((lambda + pi) / (2 * pi)); | |
| } | |
| function chamberlinRaw(p0, p1, p2) { | |
| var points = [ | |
| [p0[0], p0[1], sin(p0[1]), cos(p0[1])], | |
| [p1[0], p1[1], sin(p1[1]), cos(p1[1])], | |
| [p2[0], p2[1], sin(p2[1]), cos(p2[1])] | |
| ]; | |
| for (var a = points[2], b, i = 0; i < 3; ++i, a = b) { | |
| b = points[i]; | |
| a.v = distance(b[1] - a[1], a[3], a[2], b[3], b[2], b[0] - a[0]); | |
| a.point = [0, 0]; | |
| } | |
| var beta0 = angle(points[0].v[0], points[2].v[0], points[1].v[0]), | |
| beta1 = angle(points[0].v[0], points[1].v[0], points[2].v[0]), | |
| beta2 = pi - beta0; | |
| points[2].point[1] = 0; | |
| points[0].point[0] = -(points[1].point[0] = points[0].v[0] / 2); | |
| var mean = [ | |
| points[2].point[0] = points[0].point[0] + points[2].v[0] * cos(beta0), | |
| 2 * (points[0].point[1] = points[1].point[1] = points[2].v[0] * sin(beta0)) | |
| ]; | |
| function forward(lambda, phi) { | |
| var sinPhi = sin(phi), | |
| cosPhi = cos(phi), | |
| v = new Array(3), i; | |
| // Compute distance and azimuth from control points. | |
| for (i = 0; i < 3; ++i) { | |
| var p = points[i]; | |
| v[i] = distance(phi - p[1], p[3], p[2], cosPhi, sinPhi, lambda - p[0]); | |
| if (!v[i][0]) return p.point; | |
| v[i][1] = longitude(v[i][1] - p.v[1]); | |
| } | |
| // Arithmetic mean of interception points. | |
| var point = mean.slice(); | |
| for (i = 0; i < 3; ++i) { | |
| var j = i == 2 ? 0 : i + 1; | |
| var a = angle(points[i].v[0], v[i][0], v[j][0]); | |
| if (v[i][1] < 0) a = -a; | |
| if (!i) { | |
| point[0] += v[i][0] * cos(a); | |
| point[1] -= v[i][0] * sin(a); | |
| } else if (i == 1) { | |
| a = beta1 - a; | |
| point[0] -= v[i][0] * cos(a); | |
| point[1] -= v[i][0] * sin(a); | |
| } else { | |
| a = beta2 - a; | |
| point[0] += v[i][0] * cos(a); | |
| point[1] += v[i][0] * sin(a); | |
| } | |
| } | |
| point[0] /= 3, point[1] /= 3; | |
| return point; | |
| } | |
| return forward; | |
| } | |
| function pointRadians(p) { | |
| return p[0] *= radians, p[1] *= radians, p; | |
| } | |
| function chamberlinAfrica() { | |
| return chamberlin([0, 22], [45, 22], [22.5, -22]) | |
| .scale(380) | |
| .center([22.5, 2]); | |
| } | |
| function chamberlin(p0, p1, p2) { // TODO order matters! | |
| var c = d3Geo.geoCentroid({type: "MultiPoint", coordinates: [p0, p1, p2]}), | |
| R = [-c[0], -c[1]], | |
| r = d3Geo.geoRotation(R), | |
| p = d3Geo.geoProjection(chamberlinRaw(pointRadians(r(p0)), pointRadians(r(p1)), pointRadians(r(p2)))).rotate(R), | |
| center = p.center; | |
| delete p.rotate; | |
| p.center = function(_) { | |
| return arguments.length ? center(r(_)) : r.invert(center()); | |
| }; | |
| return p | |
| .clipAngle(90); | |
| } | |
| function collignonRaw(lambda, phi) { | |
| var alpha = sqrt(1 - sin(phi)); | |
| return [(2 / sqrtPi) * lambda * alpha, sqrtPi * (1 - alpha)]; | |
| } | |
| collignonRaw.invert = function(x, y) { | |
| var lambda = (lambda = y / sqrtPi - 1) * lambda; | |
| return [lambda > 0 ? x * sqrt(pi / lambda) / 2 : 0, asin(1 - lambda)]; | |
| }; | |
| var collignon = function() { | |
| return d3Geo.geoProjection(collignonRaw) | |
| .scale(95.6464) | |
| .center([0, 30]); | |
| }; | |
| function lagrangeRaw(n) { | |
| function forward(lambda, phi) { | |
| if (abs(abs(phi) - halfPi) < epsilon) return [0, phi < 0 ? -2 : 2]; | |
| var sinPhi = sin(phi), | |
| v = pow((1 + sinPhi) / (1 - sinPhi), n / 2), | |
| c = 0.5 * (v + 1 / v) + cos(lambda *= n); | |
| return [ | |
| 2 * sin(lambda) / c, | |
| (v - 1 / v) / c | |
| ]; | |
| } | |
| forward.invert = function(x, y) { | |
| var y0 = abs(y); | |
| if (abs(y0 - 2) < epsilon) return x ? null : [0, sign(y) * halfPi]; | |
| if (y0 > 2) return null; | |
| x /= 2, y /= 2; | |
| var x2 = x * x, | |
| y2 = y * y, | |
| t = 2 * y / (1 + x2 + y2); // tanh(nPhi) | |
| t = pow((1 + t) / (1 - t), 1 / n); | |
| return [ | |
| atan2(2 * x, 1 - x2 - y2) / n, | |
| asin((t - 1) / (t + 1)) | |
| ]; | |
| }; | |
| return forward; | |
| } | |
| var lagrange = function() { | |
| var n = 0.5, | |
| m = d3Geo.geoProjectionMutator(lagrangeRaw), | |
| p = m(n); | |
| p.spacing = function(_) { | |
| return arguments.length ? m(n = +_) : n; | |
| }; | |
| return p | |
| .scale(124.75); | |
| }; | |
| function complexAtan(x, y) { | |
| var x2 = x * x, | |
| y_1 = y + 1, | |
| t = 1 - x2 - y * y; | |
| return [ | |
| 0.5 * ((x >= 0 ? halfPi : -halfPi) - atan2(t, 2 * x)), | |
| -0.25 * log(t * t + 4 * x2) +0.5 * log(y_1 * y_1 + x2) | |
| ]; | |
| } | |
| function complexDivide(a, b) { | |
| if (b[1]) | |
| a = complexMul(a, [b[0], -b[1]]), b = complexNorm2(b); | |
| else | |
| b = b[0]; | |
| return [ | |
| a[0] / b, | |
| a[1] / b | |
| ]; | |
| } | |
| function complexMul(a, b) { | |
| return [ | |
| a[0] * b[0] - a[1] * b[1], | |
| a[1] * b[0] + a[0] * b[1] | |
| ]; | |
| } | |
| function complexAdd(a, b) { | |
| return [ | |
| a[0] + b[0], | |
| a[1] + b[1] | |
| ]; | |
| } | |
| function complexSub(a, b) { | |
| return [ | |
| a[0] - b[0], | |
| a[1] - b[1] | |
| ]; | |
| } | |
| function complexNorm2(a) { | |
| return a[0] * a[0] + a[1] * a[1]; | |
| } | |
| function complexNorm(a) { | |
| return sqrt(complexNorm2(a)); | |
| } | |
| function complexLogHypot(a, b) { | |
| var _a = abs(a), | |
| _b = abs(b); | |
| if (a === 0) return log(_b); | |
| if (b === 0) return log(_a); | |
| if (_a < 3000 && _b < 3000) return log(a * a + b * b) * 0.5; | |
| return log(a / cos(atan2(b, a))); | |
| } | |
| // adapted from https://github.com/infusion/Complex.js | |
| function complexPow(a, n) { | |
| var b = a[1], arg, loh; | |
| a = a[0]; | |
| if (a === 0 && b === 0) return [0,0]; | |
| if (typeof n === 'number') n = [n,0]; | |
| if (!n[1]) { | |
| if (b === 0 && a >= 0) { | |
| return [pow(a, n[0]), 0]; | |
| } else if (a === 0) { | |
| switch ((n[1] % 4 + 4) % 4) { | |
| case 0: | |
| return [pow(b, n[0]), 0]; | |
| case 1: | |
| return [0, pow(b, n[0])]; | |
| case 2: | |
| return [-pow(b, n[0]), 0]; | |
| case 3: | |
| return [0, -pow(b, n[0])]; | |
| } | |
| } | |
| } | |
| arg = atan2(b, a); | |
| loh = complexLogHypot(a, b); | |
| a = exp(n[0] * loh - n[1] * arg); | |
| b = n[1] * loh + n[0] * arg; | |
| return [a * cos(b), a * sin(b)]; | |
| } | |
| // w1 = gamma(1/n) * gamma(1 - 2/n) / n / gamma(1 - 1/n) | |
| // https://bl.ocks.org/Fil/852557838117687bbd985e4b38ff77d4 | |
| var w$1 = [-1/2, sqrt(3)/2]; | |
| var w1 = [1.7666387502854533, 0]; | |
| var m = 0.3 * 0.3; | |
| // Approximate \int _0 ^sm(z) dt / (1 - t^3)^(2/3) | |
| // sm maps a triangle to a disc, sm^-1 does the opposite | |
| function sm_1(z) { | |
| var k = [0, 0]; | |
| // rotate to have s ~= 1 | |
| var rot = complexPow(w$1, d3Array.scan([0, 1, 2].map(function(i) { | |
| return -complexMul(z, complexPow(w$1, [i, 0]))[0]; | |
| }))); | |
| var y = complexMul(rot, z); | |
| y = [1 - y[0], - y[1]]; | |
| // McIlroy formula 5 p6 and table for F3 page 16 | |
| var F0 = [ | |
| 1.44224957030741, | |
| 0.240374928384568, | |
| 0.0686785509670194, | |
| 0.0178055502507087, | |
| 0.00228276285265497, | |
| -1.48379585422573e-3, | |
| -1.64287728109203e-3, | |
| -1.02583417082273e-3, | |
| -4.83607537673571e-4, | |
| -1.67030822094781e-4, | |
| -2.45024395166263e-5, | |
| 2.14092375450951e-5, | |
| 2.55897270486771e-5, | |
| 1.73086854400834e-5, | |
| 8.72756299984649e-6, | |
| 3.18304486798473e-6, | |
| 4.79323894565283e-7 | |
| -4.58968389565456e-7, | |
| -5.62970586787826e-7, | |
| -3.92135372833465e-7 | |
| ]; | |
| var F = [0, 0]; | |
| for (var i = F0.length; i--;) F = complexAdd([F0[i],0], complexMul(F, y)); | |
| k = complexMul( | |
| complexAdd(w1, | |
| complexMul([-F[0], -F[1]], complexPow(y, (1-2/3))) | |
| ), | |
| complexMul(rot, rot) | |
| ); | |
| // when we are close to [0,0] we switch to another approximation: | |
| // https://www.wolframalpha.com/input/?i=(-2%2F3+choose+k)++*+(-1)%5Ek++%2F+(k%2B1)+with+k%3D0,1,2,3,4 | |
| // the difference is _very_ tiny but necessary | |
| // if we want projection(0,0) === [0,0] | |
| var n = complexNorm2(z); | |
| if (n < m) { | |
| var H0 = [ | |
| 1, 1/3, 5/27, 10/81, 22/243 //… | |
| ]; | |
| var z3 = complexPow(z, [3,0]); | |
| var h = [0,0]; | |
| for (i = H0.length; i--;) h = complexAdd([H0[i],0], complexMul(h, z3)); | |
| h = complexMul(h, z); | |
| k = complexAdd(complexMul(k, [n / m, 0]), complexMul(h, [1 - n / m, 0])); | |
| } | |
| return k; | |
| } | |
| var lagrange1_2 = lagrangeRaw(0.5); | |
| function coxRaw(lambda, phi) { | |
| var s = lagrange1_2(lambda, phi); | |
| var t = sm_1([s[1] / 2, s[0] / 2]); | |
| return [t[1], t[0]] | |
| } | |
| // the Sphere should go *exactly* to the vertices of the triangles | |
| // because they are singular points | |
| function sphere() { | |
| var c = 2 * asin(1 / sqrt(5)) * degrees; | |
| return { | |
| type: "Polygon", | |
| coordinates: [ | |
| [ [ 0,90 ], [ -180, -c + epsilon ], [ 0, -90 ], [ 180, -c + epsilon ], [ 0,90 ] ] | |
| ] | |
| }; | |
| } | |
| var cox = function() { | |
| var p = d3Geo.geoProjection(coxRaw); | |
| var stream_ = p.stream; | |
| p.stream = function(stream) { | |
| var rotate = p.rotate(), | |
| rotateStream = stream_(stream), | |
| sphereStream = (p.rotate([0, 0]), stream_(stream)); | |
| p.rotate(rotate); | |
| rotateStream.sphere = function() { d3Geo.geoStream(sphere(), sphereStream); }; | |
| return rotateStream; | |
| }; | |
| return p | |
| .scale(188.682) | |
| .center([0, 0]) | |
| .translate([ 480, 500 * 2 /3 ]); | |
| }; | |
| function craigRaw(phi0) { | |
| var tanPhi0 = tan(phi0); | |
| function forward(lambda, phi) { | |
| return [lambda, (lambda ? lambda / sin(lambda) : 1) * (sin(phi) * cos(lambda) - tanPhi0 * cos(phi))]; | |
| } | |
| forward.invert = tanPhi0 ? function(x, y) { | |
| if (x) y *= sin(x) / x; | |
| var cosLambda = cos(x); | |
| return [x, 2 * atan2(sqrt(cosLambda * cosLambda + tanPhi0 * tanPhi0 - y * y) - cosLambda, tanPhi0 - y)]; | |
| } : function(x, y) { | |
| return [x, asin(x ? y * tan(x) / x : y)]; | |
| }; | |
| return forward; | |
| } | |
| var craig = function() { | |
| return parallel1(craigRaw) | |
| .scale(249.828) | |
| .clipAngle(90); | |
| }; | |
| var sqrt3 = sqrt(3); | |
| function crasterRaw(lambda, phi) { | |
| return [sqrt3 * lambda * (2 * cos(2 * phi / 3) - 1) / sqrtPi, sqrt3 * sqrtPi * sin(phi / 3)]; | |
| } | |
| crasterRaw.invert = function(x, y) { | |
| var phi = 3 * asin(y / (sqrt3 * sqrtPi)); | |
| return [sqrtPi * x / (sqrt3 * (2 * cos(2 * phi / 3) - 1)), phi]; | |
| }; | |
| var craster = function() { | |
| return d3Geo.geoProjection(crasterRaw) | |
| .scale(156.19); | |
| }; | |
| function cylindricalEqualAreaRaw(phi0) { | |
| var cosPhi0 = cos(phi0); | |
| function forward(lambda, phi) { | |
| return [lambda * cosPhi0, sin(phi) / cosPhi0]; | |
| } | |
| forward.invert = function(x, y) { | |
| return [x / cosPhi0, asin(y * cosPhi0)]; | |
| }; | |
| return forward; | |
| } | |
| var cylindricalEqualArea = function() { | |
| return parallel1(cylindricalEqualAreaRaw) | |
| .parallel(38.58) // acos(sqrt(width / height / pi)) * radians | |
| .scale(195.044); // width / (sqrt(width / height / pi) * 2 * pi) | |
| }; | |
| function cylindricalStereographicRaw(phi0) { | |
| var cosPhi0 = cos(phi0); | |
| function forward(lambda, phi) { | |
| return [lambda * cosPhi0, (1 + cosPhi0) * tan(phi / 2)]; | |
| } | |
| forward.invert = function(x, y) { | |
| return [x / cosPhi0, atan(y / (1 + cosPhi0)) * 2]; | |
| }; | |
| return forward; | |
| } | |
| var cylindricalStereographic = function() { | |
| return parallel1(cylindricalStereographicRaw) | |
| .scale(124.75); | |
| }; | |
| function eckert1Raw(lambda, phi) { | |
| var alpha = sqrt(8 / (3 * pi)); | |
| return [ | |
| alpha * lambda * (1 - abs(phi) / pi), | |
| alpha * phi | |
| ]; | |
| } | |
| eckert1Raw.invert = function(x, y) { | |
| var alpha = sqrt(8 / (3 * pi)), | |
| phi = y / alpha; | |
| return [ | |
| x / (alpha * (1 - abs(phi) / pi)), | |
| phi | |
| ]; | |
| }; | |
| var eckert1 = function() { | |
| return d3Geo.geoProjection(eckert1Raw) | |
| .scale(165.664); | |
| }; | |
| function eckert2Raw(lambda, phi) { | |
| var alpha = sqrt(4 - 3 * sin(abs(phi))); | |
| return [ | |
| 2 / sqrt(6 * pi) * lambda * alpha, | |
| sign(phi) * sqrt(2 * pi / 3) * (2 - alpha) | |
| ]; | |
| } | |
| eckert2Raw.invert = function(x, y) { | |
| var alpha = 2 - abs(y) / sqrt(2 * pi / 3); | |
| return [ | |
| x * sqrt(6 * pi) / (2 * alpha), | |
| sign(y) * asin((4 - alpha * alpha) / 3) | |
| ]; | |
| }; | |
| var eckert2 = function() { | |
| return d3Geo.geoProjection(eckert2Raw) | |
| .scale(165.664); | |
| }; | |
| function eckert3Raw(lambda, phi) { | |
| var k = sqrt(pi * (4 + pi)); | |
| return [ | |
| 2 / k * lambda * (1 + sqrt(1 - 4 * phi * phi / (pi * pi))), | |
| 4 / k * phi | |
| ]; | |
| } | |
| eckert3Raw.invert = function(x, y) { | |
| var k = sqrt(pi * (4 + pi)) / 2; | |
| return [ | |
| x * k / (1 + sqrt(1 - y * y * (4 + pi) / (4 * pi))), | |
| y * k / 2 | |
| ]; | |
| }; | |
| var eckert3 = function() { | |
| return d3Geo.geoProjection(eckert3Raw) | |
| .scale(180.739); | |
| }; | |
| function eckert4Raw(lambda, phi) { | |
| var k = (2 + halfPi) * sin(phi); | |
| phi /= 2; | |
| for (var i = 0, delta = Infinity; i < 10 && abs(delta) > epsilon; i++) { | |
| var cosPhi = cos(phi); | |
| phi -= delta = (phi + sin(phi) * (cosPhi + 2) - k) / (2 * cosPhi * (1 + cosPhi)); | |
| } | |
| return [ | |
| 2 / sqrt(pi * (4 + pi)) * lambda * (1 + cos(phi)), | |
| 2 * sqrt(pi / (4 + pi)) * sin(phi) | |
| ]; | |
| } | |
| eckert4Raw.invert = function(x, y) { | |
| var A = y * sqrt((4 + pi) / pi) / 2, | |
| k = asin(A), | |
| c = cos(k); | |
| return [ | |
| x / (2 / sqrt(pi * (4 + pi)) * (1 + c)), | |
| asin((k + A * (c + 2)) / (2 + halfPi)) | |
| ]; | |
| }; | |
| var eckert4 = function() { | |
| return d3Geo.geoProjection(eckert4Raw) | |
| .scale(180.739); | |
| }; | |
| function eckert5Raw(lambda, phi) { | |
| return [ | |
| lambda * (1 + cos(phi)) / sqrt(2 + pi), | |
| 2 * phi / sqrt(2 + pi) | |
| ]; | |
| } | |
| eckert5Raw.invert = function(x, y) { | |
| var k = sqrt(2 + pi), | |
| phi = y * k / 2; | |
| return [ | |
| k * x / (1 + cos(phi)), | |
| phi | |
| ]; | |
| }; | |
| var eckert5 = function() { | |
| return d3Geo.geoProjection(eckert5Raw) | |
| .scale(173.044); | |
| }; | |
| function eckert6Raw(lambda, phi) { | |
| var k = (1 + halfPi) * sin(phi); | |
| for (var i = 0, delta = Infinity; i < 10 && abs(delta) > epsilon; i++) { | |
| phi -= delta = (phi + sin(phi) - k) / (1 + cos(phi)); | |
| } | |
| k = sqrt(2 + pi); | |
| return [ | |
| lambda * (1 + cos(phi)) / k, | |
| 2 * phi / k | |
| ]; | |
| } | |
| eckert6Raw.invert = function(x, y) { | |
| var j = 1 + halfPi, | |
| k = sqrt(j / 2); | |
| return [ | |
| x * 2 * k / (1 + cos(y *= k)), | |
| asin((y + sin(y)) / j) | |
| ]; | |
| }; | |
| var eckert6 = function() { | |
| return d3Geo.geoProjection(eckert6Raw) | |
| .scale(173.044); | |
| }; | |
| var eisenlohrK = 3 + 2 * sqrt2; | |
| function eisenlohrRaw(lambda, phi) { | |
| var s0 = sin(lambda /= 2), | |
| c0 = cos(lambda), | |
| k = sqrt(cos(phi)), | |
| c1 = cos(phi /= 2), | |
| t = sin(phi) / (c1 + sqrt2 * c0 * k), | |
| c = sqrt(2 / (1 + t * t)), | |
| v = sqrt((sqrt2 * c1 + (c0 + s0) * k) / (sqrt2 * c1 + (c0 - s0) * k)); | |
| return [ | |
| eisenlohrK * (c * (v - 1 / v) - 2 * log(v)), | |
| eisenlohrK * (c * t * (v + 1 / v) - 2 * atan(t)) | |
| ]; | |
| } | |
| eisenlohrRaw.invert = function(x, y) { | |
| if (!(p = augustRaw.invert(x / 1.2, y * 1.065))) return null; | |
| var lambda = p[0], phi = p[1], i = 20, p; | |
| x /= eisenlohrK, y /= eisenlohrK; | |
| do { | |
| var _0 = lambda / 2, | |
| _1 = phi / 2, | |
| s0 = sin(_0), | |
| c0 = cos(_0), | |
| s1 = sin(_1), | |
| c1 = cos(_1), | |
| cos1 = cos(phi), | |
| k = sqrt(cos1), | |
| t = s1 / (c1 + sqrt2 * c0 * k), | |
| t2 = t * t, | |
| c = sqrt(2 / (1 + t2)), | |
| v0 = (sqrt2 * c1 + (c0 + s0) * k), | |
| v1 = (sqrt2 * c1 + (c0 - s0) * k), | |
| v2 = v0 / v1, | |
| v = sqrt(v2), | |
| vm1v = v - 1 / v, | |
| vp1v = v + 1 / v, | |
| fx = c * vm1v - 2 * log(v) - x, | |
| fy = c * t * vp1v - 2 * atan(t) - y, | |
| deltatDeltaLambda = s1 && sqrt1_2 * k * s0 * t2 / s1, | |
| deltatDeltaPhi = (sqrt2 * c0 * c1 + k) / (2 * (c1 + sqrt2 * c0 * k) * (c1 + sqrt2 * c0 * k) * k), | |
| deltacDeltat = -0.5 * t * c * c * c, | |
| deltacDeltaLambda = deltacDeltat * deltatDeltaLambda, | |
| deltacDeltaPhi = deltacDeltat * deltatDeltaPhi, | |
| A = (A = 2 * c1 + sqrt2 * k * (c0 - s0)) * A * v, | |
| deltavDeltaLambda = (sqrt2 * c0 * c1 * k + cos1) / A, | |
| deltavDeltaPhi = -(sqrt2 * s0 * s1) / (k * A), | |
| deltaxDeltaLambda = vm1v * deltacDeltaLambda - 2 * deltavDeltaLambda / v + c * (deltavDeltaLambda + deltavDeltaLambda / v2), | |
| deltaxDeltaPhi = vm1v * deltacDeltaPhi - 2 * deltavDeltaPhi / v + c * (deltavDeltaPhi + deltavDeltaPhi / v2), | |
| deltayDeltaLambda = t * vp1v * deltacDeltaLambda - 2 * deltatDeltaLambda / (1 + t2) + c * vp1v * deltatDeltaLambda + c * t * (deltavDeltaLambda - deltavDeltaLambda / v2), | |
| deltayDeltaPhi = t * vp1v * deltacDeltaPhi - 2 * deltatDeltaPhi / (1 + t2) + c * vp1v * deltatDeltaPhi + c * t * (deltavDeltaPhi - deltavDeltaPhi / v2), | |
| denominator = deltaxDeltaPhi * deltayDeltaLambda - deltayDeltaPhi * deltaxDeltaLambda; | |
| if (!denominator) break; | |
| var deltaLambda = (fy * deltaxDeltaPhi - fx * deltayDeltaPhi) / denominator, | |
| deltaPhi = (fx * deltayDeltaLambda - fy * deltaxDeltaLambda) / denominator; | |
| lambda -= deltaLambda; | |
| phi = max(-halfPi, min(halfPi, phi - deltaPhi)); | |
| } while ((abs(deltaLambda) > epsilon || abs(deltaPhi) > epsilon) && --i > 0); | |
| return abs(abs(phi) - halfPi) < epsilon ? [0, phi] : i && [lambda, phi]; | |
| }; | |
| var eisenlohr = function() { | |
| return d3Geo.geoProjection(eisenlohrRaw) | |
| .scale(62.5271); | |
| }; | |
| var faheyK = cos(35 * radians); | |
| function faheyRaw(lambda, phi) { | |
| var t = tan(phi / 2); | |
| return [lambda * faheyK * sqrt(1 - t * t), (1 + faheyK) * t]; | |
| } | |
| faheyRaw.invert = function(x, y) { | |
| var t = y / (1 + faheyK); | |
| return [x && x / (faheyK * sqrt(1 - t * t)), 2 * atan(t)]; | |
| }; | |
| var fahey = function() { | |
| return d3Geo.geoProjection(faheyRaw) | |
| .scale(137.152); | |
| }; | |
| function foucautRaw(lambda, phi) { | |
| var k = phi / 2, cosk = cos(k); | |
| return [ 2 * lambda / sqrtPi * cos(phi) * cosk * cosk, sqrtPi * tan(k)]; | |
| } | |
| foucautRaw.invert = function(x, y) { | |
| var k = atan(y / sqrtPi), cosk = cos(k), phi = 2 * k; | |
| return [x * sqrtPi / 2 / (cos(phi) * cosk * cosk), phi]; | |
| }; | |
| var foucaut = function() { | |
| return d3Geo.geoProjection(foucautRaw) | |
| .scale(135.264); | |
| }; | |
| function gilbertForward(point) { | |
| return [point[0] / 2, asin(tan(point[1] / 2 * radians)) * degrees]; | |
| } | |
| function gilbertInvert(point) { | |
| return [point[0] * 2, 2 * atan(sin(point[1] * radians)) * degrees]; | |
| } | |
| var gilbert = function(projectionType) { | |
| if (projectionType == null) projectionType = d3Geo.geoOrthographic; | |
| var projection = projectionType(), | |
| equirectangular = d3Geo.geoEquirectangular().scale(degrees).precision(0).clipAngle(null).translate([0, 0]); // antimeridian cutting | |
| function gilbert(point) { | |
| return projection(gilbertForward(point)); | |
| } | |
| if (projection.invert) gilbert.invert = function(point) { | |
| return gilbertInvert(projection.invert(point)); | |
| }; | |
| gilbert.stream = function(stream) { | |
| var s1 = projection.stream(stream), s0 = equirectangular.stream({ | |
| point: function(lambda, phi) { s1.point(lambda / 2, asin(tan(-phi / 2 * radians)) * degrees); }, | |
| lineStart: function() { s1.lineStart(); }, | |
| lineEnd: function() { s1.lineEnd(); }, | |
| polygonStart: function() { s1.polygonStart(); }, | |
| polygonEnd: function() { s1.polygonEnd(); } | |
| }); | |
| s0.sphere = s1.sphere; | |
| return s0; | |
| }; | |
| function property(name) { | |
| gilbert[name] = function(_) { | |
| return arguments.length ? (projection[name](_), gilbert) : projection[name](); | |
| }; | |
| } | |
| gilbert.rotate = function(_) { | |
| return arguments.length ? (equirectangular.rotate(_), gilbert) : equirectangular.rotate(); | |
| }; | |
| gilbert.center = function(_) { | |
| return arguments.length ? (projection.center(gilbertForward(_)), gilbert) : gilbertInvert(projection.center()); | |
| }; | |
| property("clipAngle"); | |
| property("clipExtent"); | |
| property("scale"); | |
| property("translate"); | |
| property("precision"); | |
| return gilbert | |
| .scale(249.5); | |
| }; | |
| function gingeryRaw(rho, n) { | |
| var k = 2 * pi / n, | |
| rho2 = rho * rho; | |
| function forward(lambda, phi) { | |
| var p = d3Geo.geoAzimuthalEquidistantRaw(lambda, phi), | |
| x = p[0], | |
| y = p[1], | |
| r2 = x * x + y * y; | |
| if (r2 > rho2) { | |
| var r = sqrt(r2), | |
| theta = atan2(y, x), | |
| theta0 = k * round(theta / k), | |
| alpha = theta - theta0, | |
| rhoCosAlpha = rho * cos(alpha), | |
| k_ = (rho * sin(alpha) - alpha * sin(rhoCosAlpha)) / (halfPi - rhoCosAlpha), | |
| s_ = gingeryLength(alpha, k_), | |
| e = (pi - rho) / gingeryIntegrate(s_, rhoCosAlpha, pi); | |
| x = r; | |
| var i = 50, delta; | |
| do { | |
| x -= delta = (rho + gingeryIntegrate(s_, rhoCosAlpha, x) * e - r) / (s_(x) * e); | |
| } while (abs(delta) > epsilon && --i > 0); | |
| y = alpha * sin(x); | |
| if (x < halfPi) y -= k_ * (x - halfPi); | |
| var s = sin(theta0), | |
| c = cos(theta0); | |
| p[0] = x * c - y * s; | |
| p[1] = x * s + y * c; | |
| } | |
| return p; | |
| } | |
| forward.invert = function(x, y) { | |
| var r2 = x * x + y * y; | |
| if (r2 > rho2) { | |
| var r = sqrt(r2), | |
| theta = atan2(y, x), | |
| theta0 = k * round(theta / k), | |
| dTheta = theta - theta0; | |
| x = r * cos(dTheta); | |
| y = r * sin(dTheta); | |
| var x_halfPi = x - halfPi, | |
| sinx = sin(x), | |
| alpha = y / sinx, | |
| delta = x < halfPi ? Infinity : 0, | |
| i = 10; | |
| while (true) { | |
| var rhosinAlpha = rho * sin(alpha), | |
| rhoCosAlpha = rho * cos(alpha), | |
| sinRhoCosAlpha = sin(rhoCosAlpha), | |
| halfPi_RhoCosAlpha = halfPi - rhoCosAlpha, | |
| k_ = (rhosinAlpha - alpha * sinRhoCosAlpha) / halfPi_RhoCosAlpha, | |
| s_ = gingeryLength(alpha, k_); | |
| if (abs(delta) < epsilon2 || !--i) break; | |
| alpha -= delta = (alpha * sinx - k_ * x_halfPi - y) / ( | |
| sinx - x_halfPi * 2 * ( | |
| halfPi_RhoCosAlpha * (rhoCosAlpha + alpha * rhosinAlpha * cos(rhoCosAlpha) - sinRhoCosAlpha) - | |
| rhosinAlpha * (rhosinAlpha - alpha * sinRhoCosAlpha) | |
| ) / (halfPi_RhoCosAlpha * halfPi_RhoCosAlpha)); | |
| } | |
| r = rho + gingeryIntegrate(s_, rhoCosAlpha, x) * (pi - rho) / gingeryIntegrate(s_, rhoCosAlpha, pi); | |
| theta = theta0 + alpha; | |
| x = r * cos(theta); | |
| y = r * sin(theta); | |
| } | |
| return d3Geo.geoAzimuthalEquidistantRaw.invert(x, y); | |
| }; | |
| return forward; | |
| } | |
| function gingeryLength(alpha, k) { | |
| return function(x) { | |
| var y_ = alpha * cos(x); | |
| if (x < halfPi) y_ -= k; | |
| return sqrt(1 + y_ * y_); | |
| }; | |
| } | |
| // Numerical integration: trapezoidal rule. | |
| function gingeryIntegrate(f, a, b) { | |
| var n = 50, | |
| h = (b - a) / n, | |
| s = f(a) + f(b); | |
| for (var i = 1, x = a; i < n; ++i) s += 2 * f(x += h); | |
| return s * 0.5 * h; | |
| } | |
| var gingery = function() { | |
| var n = 6, | |
| rho = 30 * radians, | |
| cRho = cos(rho), | |
| sRho = sin(rho), | |
| m = d3Geo.geoProjectionMutator(gingeryRaw), | |
| p = m(rho, n), | |
| stream_ = p.stream, | |
| epsilon$$1 = 1e-2, | |
| cr = -cos(epsilon$$1 * radians), | |
| sr = sin(epsilon$$1 * radians); | |
| p.radius = function(_) { | |
| if (!arguments.length) return rho * degrees; | |
| cRho = cos(rho = _ * radians); | |
| sRho = sin(rho); | |
| return m(rho, n); | |
| }; | |
| p.lobes = function(_) { | |
| if (!arguments.length) return n; | |
| return m(rho, n = +_); | |
| }; | |
| p.stream = function(stream) { | |
| var rotate = p.rotate(), | |
| rotateStream = stream_(stream), | |
| sphereStream = (p.rotate([0, 0]), stream_(stream)); | |
| p.rotate(rotate); | |
| rotateStream.sphere = function() { | |
| sphereStream.polygonStart(), sphereStream.lineStart(); | |
| for (var i = 0, delta = 2 * pi / n, phi = 0; i < n; ++i, phi -= delta) { | |
| sphereStream.point(atan2(sr * cos(phi), cr) * degrees, asin(sr * sin(phi)) * degrees); | |
| sphereStream.point(atan2(sRho * cos(phi - delta / 2), cRho) * degrees, asin(sRho * sin(phi - delta / 2)) * degrees); | |
| } | |
| sphereStream.lineEnd(), sphereStream.polygonEnd(); | |
| }; | |
| return rotateStream; | |
| }; | |
| return p | |
| .rotate([90, -40]) | |
| .scale(91.7095) | |
| .clipAngle(180 - 1e-3); | |
| }; | |
| var ginzburgPolyconicRaw = function(a, b, c, d, e, f, g, h) { | |
| if (arguments.length < 8) h = 0; | |
| function forward(lambda, phi) { | |
| if (!phi) return [a * lambda / pi, 0]; | |
| var phi2 = phi * phi, | |
| xB = a + phi2 * (b + phi2 * (c + phi2 * d)), | |
| yB = phi * (e - 1 + phi2 * (f - h + phi2 * g)), | |
| m = (xB * xB + yB * yB) / (2 * yB), | |
| alpha = lambda * asin(xB / m) / pi; | |
| return [m * sin(alpha), phi * (1 + phi2 * h) + m * (1 - cos(alpha))]; | |
| } | |
| forward.invert = function(x, y) { | |
| var lambda = pi * x / a, | |
| phi = y, | |
| deltaLambda, deltaPhi, i = 50; | |
| do { | |
| var phi2 = phi * phi, | |
| xB = a + phi2 * (b + phi2 * (c + phi2 * d)), | |
| yB = phi * (e - 1 + phi2 * (f - h + phi2 * g)), | |
| p = xB * xB + yB * yB, | |
| q = 2 * yB, | |
| m = p / q, | |
| m2 = m * m, | |
| dAlphadLambda = asin(xB / m) / pi, | |
| alpha = lambda * dAlphadLambda, | |
| xB2 = xB * xB, | |
| dxBdPhi = (2 * b + phi2 * (4 * c + phi2 * 6 * d)) * phi, | |
| dyBdPhi = e + phi2 * (3 * f + phi2 * 5 * g), | |
| dpdPhi = 2 * (xB * dxBdPhi + yB * (dyBdPhi - 1)), | |
| dqdPhi = 2 * (dyBdPhi - 1), | |
| dmdPhi = (dpdPhi * q - p * dqdPhi) / (q * q), | |
| cosAlpha = cos(alpha), | |
| sinAlpha = sin(alpha), | |
| mcosAlpha = m * cosAlpha, | |
| msinAlpha = m * sinAlpha, | |
| dAlphadPhi = ((lambda / pi) * (1 / sqrt(1 - xB2 / m2)) * (dxBdPhi * m - xB * dmdPhi)) / m2, | |
| fx = msinAlpha - x, | |
| fy = phi * (1 + phi2 * h) + m - mcosAlpha - y, | |
| deltaxDeltaPhi = dmdPhi * sinAlpha + mcosAlpha * dAlphadPhi, | |
| deltaxDeltaLambda = mcosAlpha * dAlphadLambda, | |
| deltayDeltaPhi = 1 + dmdPhi - (dmdPhi * cosAlpha - msinAlpha * dAlphadPhi), | |
| deltayDeltaLambda = msinAlpha * dAlphadLambda, | |
| denominator = deltaxDeltaPhi * deltayDeltaLambda - deltayDeltaPhi * deltaxDeltaLambda; | |
| if (!denominator) break; | |
| lambda -= deltaLambda = (fy * deltaxDeltaPhi - fx * deltayDeltaPhi) / denominator; | |
| phi -= deltaPhi = (fx * deltayDeltaLambda - fy * deltaxDeltaLambda) / denominator; | |
| } while ((abs(deltaLambda) > epsilon || abs(deltaPhi) > epsilon) && --i > 0); | |
| return [lambda, phi]; | |
| }; | |
| return forward; | |
| }; | |
| var ginzburg4Raw = ginzburgPolyconicRaw(2.8284, -1.6988, 0.75432, -0.18071, 1.76003, -0.38914, 0.042555); | |
| var ginzburg4 = function() { | |
| return d3Geo.geoProjection(ginzburg4Raw) | |
| .scale(149.995); | |
| }; | |
| var ginzburg5Raw = ginzburgPolyconicRaw(2.583819, -0.835827, 0.170354, -0.038094, 1.543313, -0.411435,0.082742); | |
| var ginzburg5 = function() { | |
| return d3Geo.geoProjection(ginzburg5Raw) | |
| .scale(153.93); | |
| }; | |
| var ginzburg6Raw = ginzburgPolyconicRaw(5 / 6 * pi, -0.62636, -0.0344, 0, 1.3493, -0.05524, 0, 0.045); | |
| var ginzburg6 = function() { | |
| return d3Geo.geoProjection(ginzburg6Raw) | |
| .scale(130.945); | |
| }; | |
| function ginzburg8Raw(lambda, phi) { | |
| var lambda2 = lambda * lambda, | |
| phi2 = phi * phi; | |
| return [ | |
| lambda * (1 - 0.162388 * phi2) * (0.87 - 0.000952426 * lambda2 * lambda2), | |
| phi * (1 + phi2 / 12) | |
| ]; | |
| } | |
| ginzburg8Raw.invert = function(x, y) { | |
| var lambda = x, | |
| phi = y, | |
| i = 50, delta; | |
| do { | |
| var phi2 = phi * phi; | |
| phi -= delta = (phi * (1 + phi2 / 12) - y) / (1 + phi2 / 4); | |
| } while (abs(delta) > epsilon && --i > 0); | |
| i = 50; | |
| x /= 1 -0.162388 * phi2; | |
| do { | |
| var lambda4 = (lambda4 = lambda * lambda) * lambda4; | |
| lambda -= delta = (lambda * (0.87 - 0.000952426 * lambda4) - x) / (0.87 - 0.00476213 * lambda4); | |
| } while (abs(delta) > epsilon && --i > 0); | |
| return [lambda, phi]; | |
| }; | |
| var ginzburg8 = function() { | |
| return d3Geo.geoProjection(ginzburg8Raw) | |
| .scale(131.747); | |
| }; | |
| var ginzburg9Raw = ginzburgPolyconicRaw(2.6516, -0.76534, 0.19123, -0.047094, 1.36289, -0.13965,0.031762); | |
| var ginzburg9 = function() { | |
| return d3Geo.geoProjection(ginzburg9Raw) | |
| .scale(131.087); | |
| }; | |
| var squareRaw = function(project) { | |
| var dx = project(halfPi, 0)[0] - project(-halfPi, 0)[0]; | |
| function projectSquare(lambda, phi) { | |
| var s = lambda > 0 ? -0.5 : 0.5, | |
| point = project(lambda + s * pi, phi); | |
| point[0] -= s * dx; | |
| return point; | |
| } | |
| if (project.invert) projectSquare.invert = function(x, y) { | |
| var s = x > 0 ? -0.5 : 0.5, | |
| location = project.invert(x + s * dx, y), | |
| lambda = location[0] - s * pi; | |
| if (lambda < -pi) lambda += 2 * pi; | |
| else if (lambda > pi) lambda -= 2 * pi; | |
| location[0] = lambda; | |
| return location; | |
| }; | |
| return projectSquare; | |
| }; | |
| function gringortenRaw(lambda, phi) { | |
| var sLambda = sign(lambda), | |
| sPhi = sign(phi), | |
| cosPhi = cos(phi), | |
| x = cos(lambda) * cosPhi, | |
| y = sin(lambda) * cosPhi, | |
| z = sin(sPhi * phi); | |
| lambda = abs(atan2(y, z)); | |
| phi = asin(x); | |
| if (abs(lambda - halfPi) > epsilon) lambda %= halfPi; | |
| var point = gringortenHexadecant(lambda > pi / 4 ? halfPi - lambda : lambda, phi); | |
| if (lambda > pi / 4) z = point[0], point[0] = -point[1], point[1] = -z; | |
| return (point[0] *= sLambda, point[1] *= -sPhi, point); | |
| } | |
| gringortenRaw.invert = function(x, y) { | |
| if (abs(x) > 1) x = sign(x) * 2 - x; | |
| if (abs(y) > 1) y = sign(y) * 2 - y; | |
| var sx = sign(x), | |
| sy = sign(y), | |
| x0 = -sx * x, | |
| y0 = -sy * y, | |
| t = y0 / x0 < 1, | |
| p = gringortenHexadecantInvert(t ? y0 : x0, t ? x0 : y0), | |
| lambda = p[0], | |
| phi = p[1], | |
| cosPhi = cos(phi); | |
| if (t) lambda = -halfPi - lambda; | |
| return [sx * (atan2(sin(lambda) * cosPhi, -sin(phi)) + pi), sy * asin(cos(lambda) * cosPhi)]; | |
| }; | |
| function gringortenHexadecant(lambda, phi) { | |
| if (phi === halfPi) return [0, 0]; | |
| var sinPhi = sin(phi), | |
| r = sinPhi * sinPhi, | |
| r2 = r * r, | |
| j = 1 + r2, | |
| k = 1 + 3 * r2, | |
| q = 1 - r2, | |
| z = asin(1 / sqrt(j)), | |
| v = q + r * j * z, | |
| p2 = (1 - sinPhi) / v, | |
| p = sqrt(p2), | |
| a2 = p2 * j, | |
| a = sqrt(a2), | |
| h = p * q, | |
| x, | |
| i; | |
| if (lambda === 0) return [0, -(h + r * a)]; | |
| var cosPhi = cos(phi), | |
| secPhi = 1 / cosPhi, | |
| drdPhi = 2 * sinPhi * cosPhi, | |
| dvdPhi = (-3 * r + z * k) * drdPhi, | |
| dp2dPhi = (-v * cosPhi - (1 - sinPhi) * dvdPhi) / (v * v), | |
| dpdPhi = (0.5 * dp2dPhi) / p, | |
| dhdPhi = q * dpdPhi - 2 * r * p * drdPhi, | |
| dra2dPhi = r * j * dp2dPhi + p2 * k * drdPhi, | |
| mu = -secPhi * drdPhi, | |
| nu = -secPhi * dra2dPhi, | |
| zeta = -2 * secPhi * dhdPhi, | |
| lambda1 = 4 * lambda / pi, | |
| delta; | |
| // Slower but accurate bisection method. | |
| if (lambda > 0.222 * pi || phi < pi / 4 && lambda > 0.175 * pi) { | |
| x = (h + r * sqrt(a2 * (1 + r2) - h * h)) / (1 + r2); | |
| if (lambda > pi / 4) return [x, x]; | |
| var x1 = x, x0 = 0.5 * x; | |
| x = 0.5 * (x0 + x1), i = 50; | |
| do { | |
| var g = sqrt(a2 - x * x), | |
| f = (x * (zeta + mu * g) + nu * asin(x / a)) - lambda1; | |
| if (!f) break; | |
| if (f < 0) x0 = x; | |
| else x1 = x; | |
| x = 0.5 * (x0 + x1); | |
| } while (abs(x1 - x0) > epsilon && --i > 0); | |
| } | |
| // Newton-Raphson. | |
| else { | |
| x = epsilon, i = 25; | |
| do { | |
| var x2 = x * x, | |
| g2 = sqrt(a2 - x2), | |
| zetaMug = zeta + mu * g2, | |
| f2 = x * zetaMug + nu * asin(x / a) - lambda1, | |
| df = zetaMug + (nu - mu * x2) / g2; | |
| x -= delta = g2 ? f2 / df : 0; | |
| } while (abs(delta) > epsilon && --i > 0); | |
| } | |
| return [x, -h - r * sqrt(a2 - x * x)]; | |
| } | |
| function gringortenHexadecantInvert(x, y) { | |
| var x0 = 0, | |
| x1 = 1, | |
| r = 0.5, | |
| i = 50; | |
| while (true) { | |
| var r2 = r * r, | |
| sinPhi = sqrt(r), | |
| z = asin(1 / sqrt(1 + r2)), | |
| v = (1 - r2) + r * (1 + r2) * z, | |
| p2 = (1 - sinPhi) / v, | |
| p = sqrt(p2), | |
| a2 = p2 * (1 + r2), | |
| h = p * (1 - r2), | |
| g2 = a2 - x * x, | |
| g = sqrt(g2), | |
| y0 = y + h + r * g; | |
| if (abs(x1 - x0) < epsilon2 || --i === 0 || y0 === 0) break; | |
| if (y0 > 0) x0 = r; | |
| else x1 = r; | |
| r = 0.5 * (x0 + x1); | |
| } | |
| if (!i) return null; | |
| var phi = asin(sinPhi), | |
| cosPhi = cos(phi), | |
| secPhi = 1 / cosPhi, | |
| drdPhi = 2 * sinPhi * cosPhi, | |
| dvdPhi = (-3 * r + z * (1 + 3 * r2)) * drdPhi, | |
| dp2dPhi = (-v * cosPhi - (1 - sinPhi) * dvdPhi) / (v * v), | |
| dpdPhi = 0.5 * dp2dPhi / p, | |
| dhdPhi = (1 - r2) * dpdPhi - 2 * r * p * drdPhi, | |
| zeta = -2 * secPhi * dhdPhi, | |
| mu = -secPhi * drdPhi, | |
| nu = -secPhi * (r * (1 + r2) * dp2dPhi + p2 * (1 + 3 * r2) * drdPhi); | |
| return [pi / 4 * (x * (zeta + mu * g) + nu * asin(x / sqrt(a2))), phi]; | |
| } | |
| var gringorten = function() { | |
| return d3Geo.geoProjection(squareRaw(gringortenRaw)) | |
| .scale(239.75); | |
| }; | |
| // Returns [sn, cn, dn](u + iv|m). | |
| function ellipticJi(u, v, m) { | |
| var a, b, c; | |
| if (!u) { | |
| b = ellipticJ(v, 1 - m); | |
| return [ | |
| [0, b[0] / b[1]], | |
| [1 / b[1], 0], | |
| [b[2] / b[1], 0] | |
| ]; | |
| } | |
| a = ellipticJ(u, m); | |
| if (!v) return [[a[0], 0], [a[1], 0], [a[2], 0]]; | |
| b = ellipticJ(v, 1 - m); | |
| c = b[1] * b[1] + m * a[0] * a[0] * b[0] * b[0]; | |
| return [ | |
| [a[0] * b[2] / c, a[1] * a[2] * b[0] * b[1] / c], | |
| [a[1] * b[1] / c, -a[0] * a[2] * b[0] * b[2] / c], | |
| [a[2] * b[1] * b[2] / c, -m * a[0] * a[1] * b[0] / c] | |
| ]; | |
| } | |
| // Returns [sn, cn, dn, ph](u|m). | |
| function ellipticJ(u, m) { | |
| var ai, b, phi, t, twon; | |
| if (m < epsilon) { | |
| t = sin(u); | |
| b = cos(u); | |
| ai = m * (u - t * b) / 4; | |
| return [ | |
| t - ai * b, | |
| b + ai * t, | |
| 1 - m * t * t / 2, | |
| u - ai | |
| ]; | |
| } | |
| if (m >= 1 - epsilon) { | |
| ai = (1 - m) / 4; | |
| b = cosh(u); | |
| t = tanh(u); | |
| phi = 1 / b; | |
| twon = b * sinh(u); | |
| return [ | |
| t + ai * (twon - u) / (b * b), | |
| phi - ai * t * phi * (twon - u), | |
| phi + ai * t * phi * (twon + u), | |
| 2 * atan(exp(u)) - halfPi + ai * (twon - u) / b | |
| ]; | |
| } | |
| var a = [1, 0, 0, 0, 0, 0, 0, 0, 0], | |
| c = [sqrt(m), 0, 0, 0, 0, 0, 0, 0, 0], | |
| i = 0; | |
| b = sqrt(1 - m); | |
| twon = 1; | |
| while (abs(c[i] / a[i]) > epsilon && i < 8) { | |
| ai = a[i++]; | |
| c[i] = (ai - b) / 2; | |
| a[i] = (ai + b) / 2; | |
| b = sqrt(ai * b); | |
| twon *= 2; | |
| } | |
| phi = twon * a[i] * u; | |
| do { | |
| t = c[i] * sin(b = phi) / a[i]; | |
| phi = (asin(t) + phi) / 2; | |
| } while (--i); | |
| return [sin(phi), t = cos(phi), t / cos(phi - b), phi]; | |
| } | |
| // Calculate F(phi+iPsi|m). | |
| // See Abramowitz and Stegun, 17.4.11. | |
| function ellipticFi(phi, psi, m) { | |
| var r = abs(phi), | |
| i = abs(psi), | |
| sinhPsi = sinh(i); | |
| if (r) { | |
| var cscPhi = 1 / sin(r), | |
| cotPhi2 = 1 / (tan(r) * tan(r)), | |
| b = -(cotPhi2 + m * (sinhPsi * sinhPsi * cscPhi * cscPhi) - 1 + m), | |
| c = (m - 1) * cotPhi2, | |
| cotLambda2 = (-b + sqrt(b * b - 4 * c)) / 2; | |
| return [ | |
| ellipticF(atan(1 / sqrt(cotLambda2)), m) * sign(phi), | |
| ellipticF(atan(sqrt((cotLambda2 / cotPhi2 - 1) / m)), 1 - m) * sign(psi) | |
| ]; | |
| } | |
| return [ | |
| 0, | |
| ellipticF(atan(sinhPsi), 1 - m) * sign(psi) | |
| ]; | |
| } | |
| // Calculate F(phi|m) where m = k² = sin²α. | |
| // See Abramowitz and Stegun, 17.6.7. | |
| function ellipticF(phi, m) { | |
| if (!m) return phi; | |
| if (m === 1) return log(tan(phi / 2 + quarterPi)); | |
| var a = 1, | |
| b = sqrt(1 - m), | |
| c = sqrt(m); | |
| for (var i = 0; abs(c) > epsilon; i++) { | |
| if (phi % pi) { | |
| var dPhi = atan(b * tan(phi) / a); | |
| if (dPhi < 0) dPhi += pi; | |
| phi += dPhi + ~~(phi / pi) * pi; | |
| } else phi += phi; | |
| c = (a + b) / 2; | |
| b = sqrt(a * b); | |
| c = ((a = c) - b) / 2; | |
| } | |
| return phi / (pow(2, i) * a); | |
| } | |
| function guyouRaw(lambda, phi) { | |
| var k_ = (sqrt2 - 1) / (sqrt2 + 1), | |
| k = sqrt(1 - k_ * k_), | |
| K = ellipticF(halfPi, k * k), | |
| f = -1, | |
| psi = log(tan(pi / 4 + abs(phi) / 2)), | |
| r = exp(f * psi) / sqrt(k_), | |
| at = complexAtan(r * cos(f * lambda), r * sin(f * lambda)), | |
| t = ellipticFi(at[0], at[1], k * k); | |
| return [-t[1], (phi >= 0 ? 1 : -1) * (0.5 * K - t[0])]; | |
| } | |
| guyouRaw.invert = function(x, y) { | |
| var k_ = (sqrt2 - 1) / (sqrt2 + 1), | |
| k = sqrt(1 - k_ * k_), | |
| K = ellipticF(halfPi, k * k), | |
| f = -1, | |
| j = ellipticJi(0.5 * K - y, -x, k * k), | |
| tn = complexDivide(j[0], j[1]), | |
| lambda = atan2(tn[1], tn[0]) / f; | |
| return [ | |
| lambda, | |
| 2 * atan(exp(0.5 / f * log(k_ * tn[0] * tn[0] + k_ * tn[1] * tn[1]))) - halfPi | |
| ]; | |
| }; | |
| var guyou = function() { | |
| return d3Geo.geoProjection(squareRaw(guyouRaw)) | |
| .scale(151.496); | |
| }; | |
| function hammerRetroazimuthalRaw(phi0) { | |
| var sinPhi0 = sin(phi0), | |
| cosPhi0 = cos(phi0), | |
| rotate = hammerRetroazimuthalRotation(phi0); | |
| rotate.invert = hammerRetroazimuthalRotation(-phi0); | |
| function forward(lambda, phi) { | |
| var p = rotate(lambda, phi); | |
| lambda = p[0], phi = p[1]; | |
| var sinPhi = sin(phi), | |
| cosPhi = cos(phi), | |
| cosLambda = cos(lambda), | |
| z = acos(sinPhi0 * sinPhi + cosPhi0 * cosPhi * cosLambda), | |
| sinz = sin(z), | |
| K = abs(sinz) > epsilon ? z / sinz : 1; | |
| return [ | |
| K * cosPhi0 * sin(lambda), | |
| (abs(lambda) > halfPi ? K : -K) // rotate for back hemisphere | |
| * (sinPhi0 * cosPhi - cosPhi0 * sinPhi * cosLambda) | |
| ]; | |
| } | |
| forward.invert = function(x, y) { | |
| var rho = sqrt(x * x + y * y), | |
| sinz = -sin(rho), | |
| cosz = cos(rho), | |
| a = rho * cosz, | |
| b = -y * sinz, | |
| c = rho * sinPhi0, | |
| d = sqrt(a * a + b * b - c * c), | |
| phi = atan2(a * c + b * d, b * c - a * d), | |
| lambda = (rho > halfPi ? -1 : 1) * atan2(x * sinz, rho * cos(phi) * cosz + y * sin(phi) * sinz); | |
| return rotate.invert(lambda, phi); | |
| }; | |
| return forward; | |
| } | |
| // Latitudinal rotation by phi0. | |
| // Temporary hack until D3 supports arbitrary small-circle clipping origins. | |
| function hammerRetroazimuthalRotation(phi0) { | |
| var sinPhi0 = sin(phi0), | |
| cosPhi0 = cos(phi0); | |
| return function(lambda, phi) { | |
| var cosPhi = cos(phi), | |
| x = cos(lambda) * cosPhi, | |
| y = sin(lambda) * cosPhi, | |
| z = sin(phi); | |
| return [ | |
| atan2(y, x * cosPhi0 - z * sinPhi0), | |
| asin(z * cosPhi0 + x * sinPhi0) | |
| ]; | |
| }; | |
| } | |
| var hammerRetroazimuthal = function() { | |
| var phi0 = 0, | |
| m = d3Geo.geoProjectionMutator(hammerRetroazimuthalRaw), | |
| p = m(phi0), | |
| rotate_ = p.rotate, | |
| stream_ = p.stream, | |
| circle = d3Geo.geoCircle(); | |
| p.parallel = function(_) { | |
| if (!arguments.length) return phi0 * degrees; | |
| var r = p.rotate(); | |
| return m(phi0 = _ * radians).rotate(r); | |
| }; | |
| // Temporary hack; see hammerRetroazimuthalRotation. | |
| p.rotate = function(_) { | |
| if (!arguments.length) return (_ = rotate_.call(p), _[1] += phi0 * degrees, _); | |
| rotate_.call(p, [_[0], _[1] - phi0 * degrees]); | |
| circle.center([-_[0], -_[1]]); | |
| return p; | |
| }; | |
| p.stream = function(stream) { | |
| stream = stream_(stream); | |
| stream.sphere = function() { | |
| stream.polygonStart(); | |
| var epsilon$$1 = 1e-2, | |
| ring = circle.radius(90 - epsilon$$1)().coordinates[0], | |
| n = ring.length - 1, | |
| i = -1, | |
| p; | |
| stream.lineStart(); | |
| while (++i < n) stream.point((p = ring[i])[0], p[1]); | |
| stream.lineEnd(); | |
| ring = circle.radius(90 + epsilon$$1)().coordinates[0]; | |
| n = ring.length - 1; | |
| stream.lineStart(); | |
| while (--i >= 0) stream.point((p = ring[i])[0], p[1]); | |
| stream.lineEnd(); | |
| stream.polygonEnd(); | |
| }; | |
| return stream; | |
| }; | |
| return p | |
| .scale(79.4187) | |
| .parallel(45) | |
| .clipAngle(180 - 1e-3); | |
| }; | |
| var healpixParallel = 41 + 48 / 36 + 37 / 3600; | |
| var healpixLambert = cylindricalEqualAreaRaw(0); | |
| function healpixRaw(H) { | |
| var phi0 = healpixParallel * radians, | |
| dx = collignonRaw(pi, phi0)[0] - collignonRaw(-pi, phi0)[0], | |
| y0 = healpixLambert(0, phi0)[1], | |
| y1 = collignonRaw(0, phi0)[1], | |
| dy1 = sqrtPi - y1, | |
| k = tau / H, | |
| w = 4 / tau, | |
| h = y0 + (dy1 * dy1 * 4) / tau; | |
| function forward(lambda, phi) { | |
| var point, | |
| phi2 = abs(phi); | |
| if (phi2 > phi0) { | |
| var i = min(H - 1, max(0, floor((lambda + pi) / k))); | |
| lambda += pi * (H - 1) / H - i * k; | |
| point = collignonRaw(lambda, phi2); | |
| point[0] = point[0] * tau / dx - tau * (H - 1) / (2 * H) + i * tau / H; | |
| point[1] = y0 + (point[1] - y1) * 4 * dy1 / tau; | |
| if (phi < 0) point[1] = -point[1]; | |
| } else { | |
| point = healpixLambert(lambda, phi); | |
| } | |
| point[0] *= w, point[1] /= h; | |
| return point; | |
| } | |
| forward.invert = function(x, y) { | |
| x /= w, y *= h; | |
| var y2 = abs(y); | |
| if (y2 > y0) { | |
| var i = min(H - 1, max(0, floor((x + pi) / k))); | |
| x = (x + pi * (H - 1) / H - i * k) * dx / tau; | |
| var point = collignonRaw.invert(x, 0.25 * (y2 - y0) * tau / dy1 + y1); | |
| point[0] -= pi * (H - 1) / H - i * k; | |
| if (y < 0) point[1] = -point[1]; | |
| return point; | |
| } | |
| return healpixLambert.invert(x, y); | |
| }; | |
| return forward; | |
| } | |
| function sphere$1(step) { | |
| return { | |
| type: "Polygon", | |
| coordinates: [ | |
| d3Array.range(-180, 180 + step / 2, step).map(function(x, i) { return [x, i & 1 ? 90 - 1e-6 : healpixParallel]; }) | |
| .concat(d3Array.range(180, -180 - step / 2, -step).map(function(x, i) { return [x, i & 1 ? -90 + 1e-6 : -healpixParallel]; })) | |
| ] | |
| }; | |
| } | |
| var healpix = function() { | |
| var H = 4, | |
| m = d3Geo.geoProjectionMutator(healpixRaw), | |
| p = m(H), | |
| stream_ = p.stream; | |
| p.lobes = function(_) { | |
| return arguments.length ? m(H = +_) : H; | |
| }; | |
| p.stream = function(stream) { | |
| var rotate = p.rotate(), | |
| rotateStream = stream_(stream), | |
| sphereStream = (p.rotate([0, 0]), stream_(stream)); | |
| p.rotate(rotate); | |
| rotateStream.sphere = function() { d3Geo.geoStream(sphere$1(180 / H), sphereStream); }; | |
| return rotateStream; | |
| }; | |
| return p | |
| .scale(239.75); | |
| }; | |
| function hillRaw(K) { | |
| var L = 1 + K, | |
| sinBt = sin(1 / L), | |
| Bt = asin(sinBt), | |
| A = 2 * sqrt(pi / (B = pi + 4 * Bt * L)), | |
| B, | |
| rho0 = 0.5 * A * (L + sqrt(K * (2 + K))), | |
| K2 = K * K, | |
| L2 = L * L; | |
| function forward(lambda, phi) { | |
| var t = 1 - sin(phi), | |
| rho, | |
| omega; | |
| if (t && t < 2) { | |
| var theta = halfPi - phi, i = 25, delta; | |
| do { | |
| var sinTheta = sin(theta), | |
| cosTheta = cos(theta), | |
| Bt_Bt1 = Bt + atan2(sinTheta, L - cosTheta), | |
| C = 1 + L2 - 2 * L * cosTheta; | |
| theta -= delta = (theta - K2 * Bt - L * sinTheta + C * Bt_Bt1 -0.5 * t * B) / (2 * L * sinTheta * Bt_Bt1); | |
| } while (abs(delta) > epsilon2 && --i > 0); | |
| rho = A * sqrt(C); | |
| omega = lambda * Bt_Bt1 / pi; | |
| } else { | |
| rho = A * (K + t); | |
| omega = lambda * Bt / pi; | |
| } | |
| return [ | |
| rho * sin(omega), | |
| rho0 - rho * cos(omega) | |
| ]; | |
| } | |
| forward.invert = function(x, y) { | |
| var rho2 = x * x + (y -= rho0) * y, | |
| cosTheta = (1 + L2 - rho2 / (A * A)) / (2 * L), | |
| theta = acos(cosTheta), | |
| sinTheta = sin(theta), | |
| Bt_Bt1 = Bt + atan2(sinTheta, L - cosTheta); | |
| return [ | |
| asin(x / sqrt(rho2)) * pi / Bt_Bt1, | |
| asin(1 - 2 * (theta - K2 * Bt - L * sinTheta + (1 + L2 - 2 * L * cosTheta) * Bt_Bt1) / B) | |
| ]; | |
| }; | |
| return forward; | |
| } | |
| var hill = function() { | |
| var K = 1, | |
| m = d3Geo.geoProjectionMutator(hillRaw), | |
| p = m(K); | |
| p.ratio = function(_) { | |
| return arguments.length ? m(K = +_) : K; | |
| }; | |
| return p | |
| .scale(167.774) | |
| .center([0, 18.67]); | |
| }; | |
| var sinuMollweidePhi = 0.7109889596207567; | |
| var sinuMollweideY = 0.0528035274542; | |
| function sinuMollweideRaw(lambda, phi) { | |
| return phi > -sinuMollweidePhi | |
| ? (lambda = mollweideRaw(lambda, phi), lambda[1] += sinuMollweideY, lambda) | |
| : sinusoidalRaw(lambda, phi); | |
| } | |
| sinuMollweideRaw.invert = function(x, y) { | |
| return y > -sinuMollweidePhi | |
| ? mollweideRaw.invert(x, y - sinuMollweideY) | |
| : sinusoidalRaw.invert(x, y); | |
| }; | |
| var sinuMollweide = function() { | |
| return d3Geo.geoProjection(sinuMollweideRaw) | |
| .rotate([-20, -55]) | |
| .scale(164.263) | |
| .center([0, -5.4036]); | |
| }; | |
| function homolosineRaw(lambda, phi) { | |
| return abs(phi) > sinuMollweidePhi | |
| ? (lambda = mollweideRaw(lambda, phi), lambda[1] -= phi > 0 ? sinuMollweideY : -sinuMollweideY, lambda) | |
| : sinusoidalRaw(lambda, phi); | |
| } | |
| homolosineRaw.invert = function(x, y) { | |
| return abs(y) > sinuMollweidePhi | |
| ? mollweideRaw.invert(x, y + (y > 0 ? sinuMollweideY : -sinuMollweideY)) | |
| : sinusoidalRaw.invert(x, y); | |
| }; | |
| var homolosine = function() { | |
| return d3Geo.geoProjection(homolosineRaw) | |
| .scale(152.63); | |
| }; | |
| function pointEqual(a, b) { | |
| return abs(a[0] - b[0]) < epsilon && abs(a[1] - b[1]) < epsilon; | |
| } | |
| function interpolateLine(coordinates, m) { | |
| var i = -1, | |
| n = coordinates.length, | |
| p0 = coordinates[0], | |
| p1, | |
| dx, | |
| dy, | |
| resampled = []; | |
| while (++i < n) { | |
| p1 = coordinates[i]; | |
| dx = (p1[0] - p0[0]) / m; | |
| dy = (p1[1] - p0[1]) / m; | |
| for (var j = 0; j < m; ++j) resampled.push([p0[0] + j * dx, p0[1] + j * dy]); | |
| p0 = p1; | |
| } | |
| resampled.push(p1); | |
| return resampled; | |
| } | |
| function interpolateSphere(lobes) { | |
| var coordinates = [], | |
| lobe, | |
| lambda0, phi0, phi1, | |
| lambda2, phi2, | |
| i, n = lobes[0].length; | |
| // Northern Hemisphere | |
| for (i = 0; i < n; ++i) { | |
| lobe = lobes[0][i]; | |
| lambda0 = lobe[0][0], phi0 = lobe[0][1], phi1 = lobe[1][1]; | |
| lambda2 = lobe[2][0], phi2 = lobe[2][1]; | |
| coordinates.push(interpolateLine([ | |
| [lambda0 + epsilon, phi0 + epsilon], | |
| [lambda0 + epsilon, phi1 - epsilon], | |
| [lambda2 - epsilon, phi1 - epsilon], | |
| [lambda2 - epsilon, phi2 + epsilon] | |
| ], 30)); | |
| } | |
| // Southern Hemisphere | |
| for (i = lobes[1].length - 1; i >= 0; --i) { | |
| lobe = lobes[1][i]; | |
| lambda0 = lobe[0][0], phi0 = lobe[0][1], phi1 = lobe[1][1]; | |
| lambda2 = lobe[2][0], phi2 = lobe[2][1]; | |
| coordinates.push(interpolateLine([ | |
| [lambda2 - epsilon, phi2 - epsilon], | |
| [lambda2 - epsilon, phi1 + epsilon], | |
| [lambda0 + epsilon, phi1 + epsilon], | |
| [lambda0 + epsilon, phi0 - epsilon] | |
| ], 30)); | |
| } | |
| return { | |
| type: "Polygon", | |
| coordinates: [d3Array.merge(coordinates)] | |
| }; | |
| } | |
| var interrupt = function(project, lobes) { | |
| var sphere, bounds; | |
| function forward(lambda, phi) { | |
| var sign$$1 = phi < 0 ? -1 : +1, lobe = lobes[+(phi < 0)]; | |
| for (var i = 0, n = lobe.length - 1; i < n && lambda > lobe[i][2][0]; ++i); | |
| var p = project(lambda - lobe[i][1][0], phi); | |
| p[0] += project(lobe[i][1][0], sign$$1 * phi > sign$$1 * lobe[i][0][1] ? lobe[i][0][1] : phi)[0]; | |
| return p; | |
| } | |
| // Assumes mutually exclusive bounding boxes for lobes. | |
| if (project.invert) forward.invert = function(x, y) { | |
| var bound = bounds[+(y < 0)], lobe = lobes[+(y < 0)]; | |
| for (var i = 0, n = bound.length; i < n; ++i) { | |
| var b = bound[i]; | |
| if (b[0][0] <= x && x < b[1][0] && b[0][1] <= y && y < b[1][1]) { | |
| var p = project.invert(x - project(lobe[i][1][0], 0)[0], y); | |
| p[0] += lobe[i][1][0]; | |
| return pointEqual(forward(p[0], p[1]), [x, y]) ? p : null; | |
| } | |
| } | |
| }; | |
| var p = d3Geo.geoProjection(forward), | |
| stream_ = p.stream; | |
| p.stream = function(stream) { | |
| var rotate = p.rotate(), | |
| rotateStream = stream_(stream), | |
| sphereStream = (p.rotate([0, 0]), stream_(stream)); | |
| p.rotate(rotate); | |
| rotateStream.sphere = function() { d3Geo.geoStream(sphere, sphereStream); }; | |
| return rotateStream; | |
| }; | |
| p.lobes = function(_) { | |
| if (!arguments.length) return lobes.map(function(lobe) { | |
| return lobe.map(function(l) { | |
| return [ | |
| [l[0][0] * degrees, l[0][1] * degrees], | |
| [l[1][0] * degrees, l[1][1] * degrees], | |
| [l[2][0] * degrees, l[2][1] * degrees] | |
| ]; | |
| }); | |
| }); | |
| sphere = interpolateSphere(_); | |
| lobes = _.map(function(lobe) { | |
| return lobe.map(function(l) { | |
| return [ | |
| [l[0][0] * radians, l[0][1] * radians], | |
| [l[1][0] * radians, l[1][1] * radians], | |
| [l[2][0] * radians, l[2][1] * radians] | |
| ]; | |
| }); | |
| }); | |
| bounds = lobes.map(function(lobe) { | |
| return lobe.map(function(l) { | |
| var x0 = project(l[0][0], l[0][1])[0], | |
| x1 = project(l[2][0], l[2][1])[0], | |
| y0 = project(l[1][0], l[0][1])[1], | |
| y1 = project(l[1][0], l[1][1])[1], | |
| t; | |
| if (y0 > y1) t = y0, y0 = y1, y1 = t; | |
| return [[x0, y0], [x1, y1]]; | |
| }); | |
| }); | |
| return p; | |
| }; | |
| if (lobes != null) p.lobes(lobes); | |
| return p; | |
| }; | |
| var lobes = [[ // northern hemisphere | |
| [[-180, 0], [-100, 90], [ -40, 0]], | |
| [[ -40, 0], [ 30, 90], [ 180, 0]] | |
| ], [ // southern hemisphere | |
| [[-180, 0], [-160, -90], [-100, 0]], | |
| [[-100, 0], [ -60, -90], [ -20, 0]], | |
| [[ -20, 0], [ 20, -90], [ 80, 0]], | |
| [[ 80, 0], [ 140, -90], [ 180, 0]] | |
| ]]; | |
| var boggs$1 = function() { | |
| return interrupt(boggsRaw, lobes) | |
| .scale(160.857); | |
| }; | |
| var lobes$1 = [[ // northern hemisphere | |
| [[-180, 0], [-100, 90], [ -40, 0]], | |
| [[ -40, 0], [ 30, 90], [ 180, 0]] | |
| ], [ // southern hemisphere | |
| [[-180, 0], [-160, -90], [-100, 0]], | |
| [[-100, 0], [ -60, -90], [ -20, 0]], | |
| [[ -20, 0], [ 20, -90], [ 80, 0]], | |
| [[ 80, 0], [ 140, -90], [ 180, 0]] | |
| ]]; | |
| var homolosine$1 = function() { | |
| return interrupt(homolosineRaw, lobes$1) | |
| .scale(152.63); | |
| }; | |
| var lobes$2 = [[ // northern hemisphere | |
| [[-180, 0], [-100, 90], [ -40, 0]], | |
| [[ -40, 0], [ 30, 90], [ 180, 0]] | |
| ], [ // southern hemisphere | |
| [[-180, 0], [-160, -90], [-100, 0]], | |
| [[-100, 0], [ -60, -90], [ -20, 0]], | |
| [[ -20, 0], [ 20, -90], [ 80, 0]], | |
| [[ 80, 0], [ 140, -90], [ 180, 0]] | |
| ]]; | |
| var mollweide$1 = function() { | |
| return interrupt(mollweideRaw, lobes$2) | |
| .scale(169.529); | |
| }; | |
| var lobes$3 = [[ // northern hemisphere | |
| [[-180, 0], [ -90, 90], [ 0, 0]], | |
| [[ 0, 0], [ 90, 90], [ 180, 0]] | |
| ], [ // southern hemisphere | |
| [[-180, 0], [ -90, -90], [ 0, 0]], | |
| [[ 0, 0], [ 90, -90], [ 180, 0]] | |
| ]]; | |
| var mollweideHemispheres = function() { | |
| return interrupt(mollweideRaw, lobes$3) | |
| .scale(169.529) | |
| .rotate([20, 0]); | |
| }; | |
| var lobes$4 = [[ // northern hemisphere | |
| [[-180, 35], [ -30, 90], [ 0, 35]], | |
| [[ 0, 35], [ 30, 90], [ 180, 35]] | |
| ], [ // southern hemisphere | |
| [[-180, -10], [-102, -90], [ -65, -10]], | |
| [[ -65, -10], [ 5, -90], [ 77, -10]], | |
| [[ 77, -10], [ 103, -90], [ 180, -10]] | |
| ]]; | |
| var sinuMollweide$1 = function() { | |
| return interrupt(sinuMollweideRaw, lobes$4) | |
| .rotate([-20, -55]) | |
| .scale(164.263) | |
| .center([0, -5.4036]); | |
| }; | |
| var lobes$5 = [[ // northern hemisphere | |
| [[-180, 0], [-110, 90], [ -40, 0]], | |
| [[ -40, 0], [ 0, 90], [ 40, 0]], | |
| [[ 40, 0], [ 110, 90], [ 180, 0]] | |
| ], [ // southern hemisphere | |
| [[-180, 0], [-110, -90], [ -40, 0]], | |
| [[ -40, 0], [ 0, -90], [ 40, 0]], | |
| [[ 40, 0], [ 110, -90], [ 180, 0]] | |
| ]]; | |
| var sinusoidal$1 = function() { | |
| return interrupt(sinusoidalRaw, lobes$5) | |
| .scale(152.63) | |
| .rotate([-20, 0]); | |
| }; | |
| function kavrayskiy7Raw(lambda, phi) { | |
| return [3 / tau * lambda * sqrt(pi * pi / 3 - phi * phi), phi]; | |
| } | |
| kavrayskiy7Raw.invert = function(x, y) { | |
| return [tau / 3 * x / sqrt(pi * pi / 3 - y * y), y]; | |
| }; | |
| var kavrayskiy7 = function() { | |
| return d3Geo.geoProjection(kavrayskiy7Raw) | |
| .scale(158.837); | |
| }; | |
| var pi_sqrt2 = pi / sqrt2; | |
| function larriveeRaw(lambda, phi) { | |
| return [ | |
| lambda * (1 + sqrt(cos(phi))) / 2, | |
| phi / (cos(phi / 2) * cos(lambda / 6)) | |
| ]; | |
| } | |
| larriveeRaw.invert = function(x, y) { | |
| var x0 = abs(x), | |
| y0 = abs(y), | |
| lambda = epsilon, | |
| phi = halfPi; | |
| if (y0 < pi_sqrt2) phi *= y0 / pi_sqrt2; | |
| else lambda += 6 * acos(pi_sqrt2 / y0); | |
| for (var i = 0; i < 25; i++) { | |
| var sinPhi = sin(phi), | |
| sqrtcosPhi = sqrt(cos(phi)), | |
| sinPhi_2 = sin(phi / 2), | |
| cosPhi_2 = cos(phi / 2), | |
| sinLambda_6 = sin(lambda / 6), | |
| cosLambda_6 = cos(lambda / 6), | |
| f0 = 0.5 * lambda * (1 + sqrtcosPhi) - x0, | |
| f1 = phi / (cosPhi_2 * cosLambda_6) - y0, | |
| df0dPhi = sqrtcosPhi ? -0.25 * lambda * sinPhi / sqrtcosPhi : 0, | |
| df0dLambda = 0.5 * (1 + sqrtcosPhi), | |
| df1dPhi = (1 +0.5 * phi * sinPhi_2 / cosPhi_2) / (cosPhi_2 * cosLambda_6), | |
| df1dLambda = (phi / cosPhi_2) * (sinLambda_6 / 6) / (cosLambda_6 * cosLambda_6), | |
| denom = df0dPhi * df1dLambda - df1dPhi * df0dLambda, | |
| dPhi = (f0 * df1dLambda - f1 * df0dLambda) / denom, | |
| dLambda = (f1 * df0dPhi - f0 * df1dPhi) / denom; | |
| phi -= dPhi; | |
| lambda -= dLambda; | |
| if (abs(dPhi) < epsilon && abs(dLambda) < epsilon) break; | |
| } | |
| return [x < 0 ? -lambda : lambda, y < 0 ? -phi : phi]; | |
| }; | |
| var larrivee = function() { | |
| return d3Geo.geoProjection(larriveeRaw) | |
| .scale(97.2672); | |
| }; | |
| function laskowskiRaw(lambda, phi) { | |
| var lambda2 = lambda * lambda, phi2 = phi * phi; | |
| return [ | |
| lambda * (0.975534 + phi2 * (-0.119161 + lambda2 * -0.0143059 + phi2 * -0.0547009)), | |
| phi * (1.00384 + lambda2 * (0.0802894 + phi2 * -0.02855 + lambda2 * 0.000199025) + phi2 * (0.0998909 + phi2 * -0.0491032)) | |
| ]; | |
| } | |
| laskowskiRaw.invert = function(x, y) { | |
| var lambda = sign(x) * pi, | |
| phi = y / 2, | |
| i = 50; | |
| do { | |
| var lambda2 = lambda * lambda, | |
| phi2 = phi * phi, | |
| lambdaPhi = lambda * phi, | |
| fx = lambda * (0.975534 + phi2 * (-0.119161 + lambda2 * -0.0143059 + phi2 * -0.0547009)) - x, | |
| fy = phi * (1.00384 + lambda2 * (0.0802894 + phi2 * -0.02855 + lambda2 * 0.000199025) + phi2 * (0.0998909 + phi2 * -0.0491032)) - y, | |
| deltaxDeltaLambda = 0.975534 - phi2 * (0.119161 + 3 * lambda2 * 0.0143059 + phi2 * 0.0547009), | |
| deltaxDeltaPhi = -lambdaPhi * (2 * 0.119161 + 4 * 0.0547009 * phi2 + 2 * 0.0143059 * lambda2), | |
| deltayDeltaLambda = lambdaPhi * (2 * 0.0802894 + 4 * 0.000199025 * lambda2 + 2 * -0.02855 * phi2), | |
| deltayDeltaPhi = 1.00384 + lambda2 * (0.0802894 + 0.000199025 * lambda2) + phi2 * (3 * (0.0998909 - 0.02855 * lambda2) - 5 * 0.0491032 * phi2), | |
| denominator = deltaxDeltaPhi * deltayDeltaLambda - deltayDeltaPhi * deltaxDeltaLambda, | |
| deltaLambda = (fy * deltaxDeltaPhi - fx * deltayDeltaPhi) / denominator, | |
| deltaPhi = (fx * deltayDeltaLambda - fy * deltaxDeltaLambda) / denominator; | |
| lambda -= deltaLambda, phi -= deltaPhi; | |
| } while ((abs(deltaLambda) > epsilon || abs(deltaPhi) > epsilon) && --i > 0); | |
| return i && [lambda, phi]; | |
| }; | |
| var laskowski = function() { | |
| return d3Geo.geoProjection(laskowskiRaw) | |
| .scale(139.98); | |
| }; | |
| function littrowRaw(lambda, phi) { | |
| return [ | |
| sin(lambda) / cos(phi), | |
| tan(phi) * cos(lambda) | |
| ]; | |
| } | |
| littrowRaw.invert = function(x, y) { | |
| var x2 = x * x, | |
| y2 = y * y, | |
| y2_1 = y2 + 1, | |
| cosPhi = x | |
| ? sqrt1_2 * sqrt((y2_1 - sqrt(x2 * x2 + 2 * x2 * (y2 - 1) + y2_1 * y2_1)) / x2 + 1) | |
| : 1 / sqrt(y2_1); | |
| return [ | |
| asin(x * cosPhi), | |
| sign(y) * acos(cosPhi) | |
| ]; | |
| }; | |
| var littrow = function() { | |
| return d3Geo.geoProjection(littrowRaw) | |
| .scale(144.049) | |
| .clipAngle(90 - 1e-3); | |
| }; | |
| function loximuthalRaw(phi0) { | |
| var cosPhi0 = cos(phi0), | |
| tanPhi0 = tan(quarterPi + phi0 / 2); | |
| function forward(lambda, phi) { | |
| var y = phi - phi0, | |
| x = abs(y) < epsilon ? lambda * cosPhi0 | |
| : abs(x = quarterPi + phi / 2) < epsilon || abs(abs(x) - halfPi) < epsilon | |
| ? 0 : lambda * y / log(tan(x) / tanPhi0); | |
| return [x, y]; | |
| } | |
| forward.invert = function(x, y) { | |
| var lambda, | |
| phi = y + phi0; | |
| return [ | |
| abs(y) < epsilon ? x / cosPhi0 | |
| : (abs(lambda = quarterPi + phi / 2) < epsilon || abs(abs(lambda) - halfPi) < epsilon) ? 0 | |
| : x * log(tan(lambda) / tanPhi0) / y, | |
| phi | |
| ]; | |
| }; | |
| return forward; | |
| } | |
| var loximuthal = function() { | |
| return parallel1(loximuthalRaw) | |
| .parallel(40) | |
| .scale(158.837); | |
| }; | |
| function millerRaw(lambda, phi) { | |
| return [lambda, 1.25 * log(tan(quarterPi + 0.4 * phi))]; | |
| } | |
| millerRaw.invert = function(x, y) { | |
| return [x, 2.5 * atan(exp(0.8 * y)) - 0.625 * pi]; | |
| }; | |
| var miller = function() { | |
| return d3Geo.geoProjection(millerRaw) | |
| .scale(108.318); | |
| }; | |
| function modifiedStereographicRaw(C) { | |
| var m = C.length - 1; | |
| function forward(lambda, phi) { | |
| var cosPhi = cos(phi), | |
| k = 2 / (1 + cosPhi * cos(lambda)), | |
| zr = k * cosPhi * sin(lambda), | |
| zi = k * sin(phi), | |
| i = m, | |
| w = C[i], | |
| ar = w[0], | |
| ai = w[1], | |
| t; | |
| while (--i >= 0) { | |
| w = C[i]; | |
| ar = w[0] + zr * (t = ar) - zi * ai; | |
| ai = w[1] + zr * ai + zi * t; | |
| } | |
| ar = zr * (t = ar) - zi * ai; | |
| ai = zr * ai + zi * t; | |
| return [ar, ai]; | |
| } | |
| forward.invert = function(x, y) { | |
| var i = 20, | |
| zr = x, | |
| zi = y; | |
| do { | |
| var j = m, | |
| w = C[j], | |
| ar = w[0], | |
| ai = w[1], | |
| br = 0, | |
| bi = 0, | |
| t; | |
| while (--j >= 0) { | |
| w = C[j]; | |
| br = ar + zr * (t = br) - zi * bi; | |
| bi = ai + zr * bi + zi * t; | |
| ar = w[0] + zr * (t = ar) - zi * ai; | |
| ai = w[1] + zr * ai + zi * t; | |
| } | |
| br = ar + zr * (t = br) - zi * bi; | |
| bi = ai + zr * bi + zi * t; | |
| ar = zr * (t = ar) - zi * ai - x; | |
| ai = zr * ai + zi * t - y; | |
| var denominator = br * br + bi * bi, deltar, deltai; | |
| zr -= deltar = (ar * br + ai * bi) / denominator; | |
| zi -= deltai = (ai * br - ar * bi) / denominator; | |
| } while (abs(deltar) + abs(deltai) > epsilon * epsilon && --i > 0); | |
| if (i) { | |
| var rho = sqrt(zr * zr + zi * zi), | |
| c = 2 * atan(rho * 0.5), | |
| sinc = sin(c); | |
| return [atan2(zr * sinc, rho * cos(c)), rho ? asin(zi * sinc / rho) : 0]; | |
| } | |
| }; | |
| return forward; | |
| } | |
| var alaska = [[0.9972523, 0], [0.0052513, -0.0041175], [0.0074606, 0.0048125], [-0.0153783, -0.1968253], [0.0636871, -0.1408027], [0.3660976, -0.2937382]]; | |
| var gs48 = [[0.98879, 0], [0, 0], [-0.050909, 0], [0, 0], [0.075528, 0]]; | |
| var gs50 = [[0.9842990, 0], [0.0211642, 0.0037608], [-0.1036018, -0.0575102], [-0.0329095, -0.0320119], [0.0499471, 0.1223335], [0.0260460, 0.0899805], [0.0007388, -0.1435792], [0.0075848, -0.1334108], [-0.0216473, 0.0776645], [-0.0225161, 0.0853673]]; | |
| var miller$1 = [[0.9245, 0], [0, 0], [0.01943, 0]]; | |
| var lee = [[0.721316, 0], [0, 0], [-0.00881625, -0.00617325]]; | |
| function modifiedStereographicAlaska() { | |
| return modifiedStereographic(alaska, [152, -64]) | |
| .scale(1500) | |
| .center([-160.908, 62.4864]) | |
| .clipAngle(25); | |
| } | |
| function modifiedStereographicGs48() { | |
| return modifiedStereographic(gs48, [95, -38]) | |
| .scale(1000) | |
| .clipAngle(55) | |
| .center([-96.5563, 38.8675]); | |
| } | |
| function modifiedStereographicGs50() { | |
| return modifiedStereographic(gs50, [120, -45]) | |
| .scale(359.513) | |
| .clipAngle(55) | |
| .center([-117.474, 53.0628]); | |
| } | |
| function modifiedStereographicMiller() { | |
| return modifiedStereographic(miller$1, [-20, -18]) | |
| .scale(209.091) | |
| .center([20, 16.7214]) | |
| .clipAngle(82); | |
| } | |
| function modifiedStereographicLee() { | |
| return modifiedStereographic(lee, [165, 10]) | |
| .scale(250) | |
| .clipAngle(130) | |
| .center([-165, -10]); | |
| } | |
| function modifiedStereographic(coefficients, rotate) { | |
| var p = d3Geo.geoProjection(modifiedStereographicRaw(coefficients)).rotate(rotate).clipAngle(90), | |
| r = d3Geo.geoRotation(rotate), | |
| center = p.center; | |
| delete p.rotate; | |
| p.center = function(_) { | |
| return arguments.length ? center(r(_)) : r.invert(center()); | |
| }; | |
| return p; | |
| } | |
| var sqrt6 = sqrt(6); | |
| var sqrt7 = sqrt(7); | |
| function mtFlatPolarParabolicRaw(lambda, phi) { | |
| var theta = asin(7 * sin(phi) / (3 * sqrt6)); | |
| return [ | |
| sqrt6 * lambda * (2 * cos(2 * theta / 3) - 1) / sqrt7, | |
| 9 * sin(theta / 3) / sqrt7 | |
| ]; | |
| } | |
| mtFlatPolarParabolicRaw.invert = function(x, y) { | |
| var theta = 3 * asin(y * sqrt7 / 9); | |
| return [ | |
| x * sqrt7 / (sqrt6 * (2 * cos(2 * theta / 3) - 1)), | |
| asin(sin(theta) * 3 * sqrt6 / 7) | |
| ]; | |
| }; | |
| var mtFlatPolarParabolic = function() { | |
| return d3Geo.geoProjection(mtFlatPolarParabolicRaw) | |
| .scale(164.859); | |
| }; | |
| function mtFlatPolarQuarticRaw(lambda, phi) { | |
| var k = (1 + sqrt1_2) * sin(phi), | |
| theta = phi; | |
| for (var i = 0, delta; i < 25; i++) { | |
| theta -= delta = (sin(theta / 2) + sin(theta) - k) / (0.5 * cos(theta / 2) + cos(theta)); | |
| if (abs(delta) < epsilon) break; | |
| } | |
| return [ | |
| lambda * (1 + 2 * cos(theta) / cos(theta / 2)) / (3 * sqrt2), | |
| 2 * sqrt(3) * sin(theta / 2) / sqrt(2 + sqrt2) | |
| ]; | |
| } | |
| mtFlatPolarQuarticRaw.invert = function(x, y) { | |
| var sinTheta_2 = y * sqrt(2 + sqrt2) / (2 * sqrt(3)), | |
| theta = 2 * asin(sinTheta_2); | |
| return [ | |
| 3 * sqrt2 * x / (1 + 2 * cos(theta) / cos(theta / 2)), | |
| asin((sinTheta_2 + sin(theta)) / (1 + sqrt1_2)) | |
| ]; | |
| }; | |
| var mtFlatPolarQuartic = function() { | |
| return d3Geo.geoProjection(mtFlatPolarQuarticRaw) | |
| .scale(188.209); | |
| }; | |
| function mtFlatPolarSinusoidalRaw(lambda, phi) { | |
| var A = sqrt(6 / (4 + pi)), | |
| k = (1 + pi / 4) * sin(phi), | |
| theta = phi / 2; | |
| for (var i = 0, delta; i < 25; i++) { | |
| theta -= delta = (theta / 2 + sin(theta) - k) / (0.5 + cos(theta)); | |
| if (abs(delta) < epsilon) break; | |
| } | |
| return [ | |
| A * (0.5 + cos(theta)) * lambda / 1.5, | |
| A * theta | |
| ]; | |
| } | |
| mtFlatPolarSinusoidalRaw.invert = function(x, y) { | |
| var A = sqrt(6 / (4 + pi)), | |
| theta = y / A; | |
| if (abs(abs(theta) - halfPi) < epsilon) theta = theta < 0 ? -halfPi : halfPi; | |
| return [ | |
| 1.5 * x / (A * (0.5 + cos(theta))), | |
| asin((theta / 2 + sin(theta)) / (1 + pi / 4)) | |
| ]; | |
| }; | |
| var mtFlatPolarSinusoidal = function() { | |
| return d3Geo.geoProjection(mtFlatPolarSinusoidalRaw) | |
| .scale(166.518); | |
| }; | |
| function naturalEarthRaw(lambda, phi) { | |
| var phi2 = phi * phi, phi4 = phi2 * phi2; | |
| return [ | |
| lambda * (0.8707 - 0.131979 * phi2 + phi4 * (-0.013791 + phi4 * (0.003971 * phi2 - 0.001529 * phi4))), | |
| phi * (1.007226 + phi2 * (0.015085 + phi4 * (-0.044475 + 0.028874 * phi2 - 0.005916 * phi4))) | |
| ]; | |
| } | |
| naturalEarthRaw.invert = function(x, y) { | |
| var phi = y, i = 25, delta; | |
| do { | |
| var phi2 = phi * phi, phi4 = phi2 * phi2; | |
| phi -= delta = (phi * (1.007226 + phi2 * (0.015085 + phi4 * (-0.044475 + 0.028874 * phi2 - 0.005916 * phi4))) - y) / | |
| (1.007226 + phi2 * (0.015085 * 3 + phi4 * (-0.044475 * 7 + 0.028874 * 9 * phi2 - 0.005916 * 11 * phi4))); | |
| } while (abs(delta) > epsilon && --i > 0); | |
| return [ | |
| x / (0.8707 + (phi2 = phi * phi) * (-0.131979 + phi2 * (-0.013791 + phi2 * phi2 * phi2 * (0.003971 - 0.001529 * phi2)))), | |
| phi | |
| ]; | |
| }; | |
| var naturalEarth = function() { | |
| return d3Geo.geoProjection(naturalEarthRaw) | |
| .scale(175.295); | |
| }; | |
| function naturalEarth2Raw(lambda, phi) { | |
| var phi2 = phi * phi, phi4 = phi2 * phi2, phi6 = phi2 * phi4; | |
| return [ | |
| lambda * (0.84719 - 0.13063 * phi2 + phi6 * phi6 * (-0.04515 + 0.05494 * phi2 - 0.02326 * phi4 + 0.00331 * phi6)), | |
| phi * (1.01183 + phi4 * phi4 * (-0.02625 + 0.01926 * phi2 - 0.00396 * phi4)) | |
| ]; | |
| } | |
| naturalEarth2Raw.invert = function(x, y) { | |
| var phi = y, i = 25, delta, phi2, phi4, phi6; | |
| do { | |
| phi2 = phi * phi; phi4 = phi2 * phi2; | |
| phi -= delta = ((phi * (1.01183 + phi4 * phi4 * (-0.02625 + 0.01926 * phi2 - 0.00396 * phi4))) - y) / | |
| (1.01183 + phi4 * phi4 * ((9 * -0.02625) + (11 * 0.01926) * phi2 + (13 * -0.00396) * phi4)); | |
| } while (abs(delta) > epsilon2 && --i > 0); | |
| phi2 = phi * phi; phi4 = phi2 * phi2; phi6 = phi2 * phi4; | |
| return [ | |
| x / (0.84719 - 0.13063 * phi2 + phi6 * phi6 * (-0.04515 + 0.05494 * phi2 - 0.02326 * phi4 + 0.00331 * phi6)), | |
| phi | |
| ]; | |
| }; | |
| var naturalEarth2 = function() { | |
| return d3Geo.geoProjection(naturalEarth2Raw) | |
| .scale(175.295); | |
| }; | |
| function nellHammerRaw(lambda, phi) { | |
| return [ | |
| lambda * (1 + cos(phi)) / 2, | |
| 2 * (phi - tan(phi / 2)) | |
| ]; | |
| } | |
| nellHammerRaw.invert = function(x, y) { | |
| var p = y / 2; | |
| for (var i = 0, delta = Infinity; i < 10 && abs(delta) > epsilon; ++i) { | |
| var c = cos(y / 2); | |
| y -= delta = (y - tan(y / 2) - p) / (1 - 0.5 / (c * c)); | |
| } | |
| return [ | |
| 2 * x / (1 + cos(y)), | |
| y | |
| ]; | |
| }; | |
| var nellHammer = function() { | |
| return d3Geo.geoProjection(nellHammerRaw) | |
| .scale(152.63); | |
| }; | |
| // Based on Java implementation by Bojan Savric. | |
| // https://github.com/OSUCartography/JMapProjLib/blob/master/src/com/jhlabs/map/proj/PattersonProjection.java | |
| var pattersonK1 = 1.0148; | |
| var pattersonK2 = 0.23185; | |
| var pattersonK3 = -0.14499; | |
| var pattersonK4 = 0.02406; | |
| var pattersonC1 = pattersonK1; | |
| var pattersonC2 = 5 * pattersonK2; | |
| var pattersonC3 = 7 * pattersonK3; | |
| var pattersonC4 = 9 * pattersonK4; | |
| var pattersonYmax = 1.790857183; | |
| function pattersonRaw(lambda, phi) { | |
| var phi2 = phi * phi; | |
| return [ | |
| lambda, | |
| phi * (pattersonK1 + phi2 * phi2 * (pattersonK2 + phi2 * (pattersonK3 + pattersonK4 * phi2))) | |
| ]; | |
| } | |
| pattersonRaw.invert = function(x, y) { | |
| if (y > pattersonYmax) y = pattersonYmax; | |
| else if (y < -pattersonYmax) y = -pattersonYmax; | |
| var yc = y, delta; | |
| do { // Newton-Raphson | |
| var y2 = yc * yc; | |
| yc -= delta = ((yc * (pattersonK1 + y2 * y2 * (pattersonK2 + y2 * (pattersonK3 + pattersonK4 * y2)))) - y) / (pattersonC1 + y2 * y2 * (pattersonC2 + y2 * (pattersonC3 + pattersonC4 * y2))); | |
| } while (abs(delta) > epsilon); | |
| return [x, yc]; | |
| }; | |
| var patterson = function() { | |
| return d3Geo.geoProjection(pattersonRaw) | |
| .scale(139.319); | |
| }; | |
| function polyconicRaw(lambda, phi) { | |
| if (abs(phi) < epsilon) return [lambda, 0]; | |
| var tanPhi = tan(phi), | |
| k = lambda * sin(phi); | |
| return [ | |
| sin(k) / tanPhi, | |
| phi + (1 - cos(k)) / tanPhi | |
| ]; | |
| } | |
| polyconicRaw.invert = function(x, y) { | |
| if (abs(y) < epsilon) return [x, 0]; | |
| var k = x * x + y * y, | |
| phi = y * 0.5, | |
| i = 10, delta; | |
| do { | |
| var tanPhi = tan(phi), | |
| secPhi = 1 / cos(phi), | |
| j = k - 2 * y * phi + phi * phi; | |
| phi -= delta = (tanPhi * j + 2 * (phi - y)) / (2 + j * secPhi * secPhi + 2 * (phi - y) * tanPhi); | |
| } while (abs(delta) > epsilon && --i > 0); | |
| tanPhi = tan(phi); | |
| return [ | |
| (abs(y) < abs(phi + 1 / tanPhi) ? asin(x * tanPhi) : sign(x) * (acos(abs(x * tanPhi)) + halfPi)) / sin(phi), | |
| phi | |
| ]; | |
| }; | |
| var polyconic = function() { | |
| return d3Geo.geoProjection(polyconicRaw) | |
| .scale(103.74); | |
| }; | |
| // Note: 6-element arrays are used to denote the 3x3 affine transform matrix: | |
| // [a, b, c, | |
| // d, e, f, | |
| // 0, 0, 1] - this redundant row is left out. | |
| // Transform matrix for [a0, a1] -> [b0, b1]. | |
| var matrix = function(a, b) { | |
| var u = subtract(a[1], a[0]), | |
| v = subtract(b[1], b[0]), | |
| phi = angle$1(u, v), | |
| s = length(u) / length(v); | |
| return multiply([ | |
| 1, 0, a[0][0], | |
| 0, 1, a[0][1] | |
| ], multiply([ | |
| s, 0, 0, | |
| 0, s, 0 | |
| ], multiply([ | |
| cos(phi), sin(phi), 0, | |
| -sin(phi), cos(phi), 0 | |
| ], [ | |
| 1, 0, -b[0][0], | |
| 0, 1, -b[0][1] | |
| ]))); | |
| }; | |
| // Inverts a transform matrix. | |
| function inverse(m) { | |
| var k = 1 / (m[0] * m[4] - m[1] * m[3]); | |
| return [ | |
| k * m[4], -k * m[1], k * (m[1] * m[5] - m[2] * m[4]), | |
| -k * m[3], k * m[0], k * (m[2] * m[3] - m[0] * m[5]) | |
| ]; | |
| } | |
| // Multiplies two 3x2 matrices. | |
| function multiply(a, b) { | |
| return [ | |
| a[0] * b[0] + a[1] * b[3], | |
| a[0] * b[1] + a[1] * b[4], | |
| a[0] * b[2] + a[1] * b[5] + a[2], | |
| a[3] * b[0] + a[4] * b[3], | |
| a[3] * b[1] + a[4] * b[4], | |
| a[3] * b[2] + a[4] * b[5] + a[5] | |
| ]; | |
| } | |
| // Subtracts 2D vectors. | |
| function subtract(a, b) { | |
| return [a[0] - b[0], a[1] - b[1]]; | |
| } | |
| // Magnitude of a 2D vector. | |
| function length(v) { | |
| return sqrt(v[0] * v[0] + v[1] * v[1]); | |
| } | |
| // Angle between two 2D vectors. | |
| function angle$1(a, b) { | |
| return atan2(a[0] * b[1] - a[1] * b[0], a[0] * b[0] + a[1] * b[1]); | |
| } | |
| // Creates a polyhedral projection. | |
| // * root: a spanning tree of polygon faces. Nodes are automatically | |
| // augmented with a transform matrix. | |
| // * face: a function that returns the appropriate node for a given {lambda, phi} | |
| // point (radians). | |
| // * r: rotation angle for final polyhedral net. Defaults to -pi / 6 (for | |
| // butterflies). | |
| var polyhedral = function(root, face, r) { | |
| r = r == null ? -pi / 6 : r; // TODO automate | |
| recurse(root, {transform: [ | |
| cos(r), sin(r), 0, | |
| -sin(r), cos(r), 0 | |
| ]}); | |
| function recurse(node, parent) { | |
| node.edges = faceEdges(node.face); | |
| // Find shared edge. | |
| if (parent.face) { | |
| var shared = node.shared = sharedEdge(node.face, parent.face), | |
| m = matrix(shared.map(parent.project), shared.map(node.project)); | |
| node.transform = parent.transform ? multiply(parent.transform, m) : m; | |
| // Replace shared edge in parent edges array. | |
| var edges = parent.edges; | |
| for (var i = 0, n = edges.length; i < n; ++i) { | |
| if (pointEqual$1(shared[0], edges[i][1]) && pointEqual$1(shared[1], edges[i][0])) edges[i] = node; | |
| if (pointEqual$1(shared[0], edges[i][0]) && pointEqual$1(shared[1], edges[i][1])) edges[i] = node; | |
| } | |
| edges = node.edges; | |
| for (i = 0, n = edges.length; i < n; ++i) { | |
| if (pointEqual$1(shared[0], edges[i][0]) && pointEqual$1(shared[1], edges[i][1])) edges[i] = parent; | |
| if (pointEqual$1(shared[0], edges[i][1]) && pointEqual$1(shared[1], edges[i][0])) edges[i] = parent; | |
| } | |
| } else { | |
| node.transform = parent.transform; | |
| } | |
| if (node.children) { | |
| node.children.forEach(function(child) { | |
| recurse(child, node); | |
| }); | |
| } | |
| return node; | |
| } | |
| function forward(lambda, phi) { | |
| var node = face(lambda, phi), | |
| point = node.project([lambda * degrees, phi * degrees]), | |
| t; | |
| if (t = node.transform) { | |
| return [ | |
| t[0] * point[0] + t[1] * point[1] + t[2], | |
| -(t[3] * point[0] + t[4] * point[1] + t[5]) | |
| ]; | |
| } | |
| point[1] = -point[1]; | |
| return point; | |
| } | |
| // Naive inverse! A faster solution would use bounding boxes, or even a | |
| // polygonal quadtree. | |
| if (hasInverse(root)) forward.invert = function(x, y) { | |
| var coordinates = faceInvert(root, [x, -y]); | |
| return coordinates && (coordinates[0] *= radians, coordinates[1] *= radians, coordinates); | |
| }; | |
| function faceInvert(node, coordinates) { | |
| var invert = node.project.invert, | |
| t = node.transform, | |
| point = coordinates; | |
| if (t) { | |
| t = inverse(t); | |
| point = [ | |
| t[0] * point[0] + t[1] * point[1] + t[2], | |
| (t[3] * point[0] + t[4] * point[1] + t[5]) | |
| ]; | |
| } | |
| if (invert && node === faceDegrees(p = invert(point))) return p; | |
| var p, | |
| children = node.children; | |
| for (var i = 0, n = children && children.length; i < n; ++i) { | |
| if (p = faceInvert(children[i], coordinates)) return p; | |
| } | |
| } | |
| function faceDegrees(coordinates) { | |
| return face(coordinates[0] * radians, coordinates[1] * radians); | |
| } | |
| var proj = d3Geo.geoProjection(forward), | |
| stream_ = proj.stream; | |
| // run around the mesh of faces and stream all vertices in order to create the clip polygon | |
| var polygon = []; | |
| outline(1e-3, {point: function(lambda, phi) { polygon.push([lambda, phi]); }}, root); | |
| polygon.push(polygon[0]); | |
| if (proj.clipPolygon) proj.clipPolygon({ type: "Polygon", coordinates: [ polygon ] }); | |
| proj.stream = function(stream) { | |
| var rotate = proj.rotate(), | |
| clipPolygon = proj.clipPolygon ? proj.clipPolygon() : null, | |
| rotateStream = stream_(stream), | |
| sphereStream = ((clipPolygon ? proj.clipPolygon(null) : proj).rotate([0, 0]), stream_(stream)); | |
| proj.rotate(rotate); | |
| if (clipPolygon) proj.clipPolygon({ type: "Polygon", coordinates: [ polygon ] }); | |
| rotateStream.sphere = function() { | |
| sphereStream.polygonStart(); | |
| sphereStream.lineStart(); | |
| outline(1e-5, sphereStream, root); | |
| sphereStream.lineEnd(); | |
| sphereStream.polygonEnd(); | |
| }; | |
| return rotateStream; | |
| }; | |
| return proj; | |
| }; | |
| function outline(eps, stream, node, parent) { | |
| var point, | |
| edges = node.edges, | |
| n = edges.length, | |
| edge, | |
| multiPoint = {type: "MultiPoint", coordinates: node.face}, | |
| notPoles = node.face.filter(function(d) { return abs(d[1]) !== 90; }), | |
| b = d3Geo.geoBounds({type: "MultiPoint", coordinates: notPoles}), | |
| inside = false, | |
| j = -1, | |
| dx = b[1][0] - b[0][0]; | |
| // TODO | |
| var c = dx === 180 || dx === 360 | |
| ? [(b[0][0] + b[1][0]) / 2, (b[0][1] + b[1][1]) / 2] | |
| : d3Geo.geoCentroid(multiPoint); | |
| // First find the shared edge… | |
| if (parent) while (++j < n) { | |
| if (edges[j] === parent) break; | |
| } | |
| ++j; | |
| for (var i = 0; i < n; ++i) { | |
| edge = edges[(i + j) % n]; | |
| if (Array.isArray(edge)) { | |
| if (!inside) { | |
| stream.point((point = d3Geo.geoInterpolate(edge[0], c)(eps))[0], point[1]); | |
| inside = true; | |
| } | |
| stream.point((point = d3Geo.geoInterpolate(edge[1], c)(eps))[0], point[1]); | |
| } else { | |
| inside = false; | |
| if (edge !== parent) outline(eps, stream, edge, node); | |
| } | |
| } | |
| } | |
| // Tests equality of two spherical points. | |
| function pointEqual$1(a, b) { | |
| return a && b && a[0] === b[0] && a[1] === b[1]; | |
| } | |
| // Finds a shared edge given two clockwise polygons. | |
| function sharedEdge(a, b) { | |
| var x, y, n = a.length, found = null; | |
| for (var i = 0; i < n; ++i) { | |
| x = a[i]; | |
| for (var j = b.length; --j >= 0;) { | |
| y = b[j]; | |
| if (x[0] === y[0] && x[1] === y[1]) { | |
| if (found) return [found, x]; | |
| found = x; | |
| } | |
| } | |
| } | |
| } | |
| // Converts an array of n face vertices to an array of n + 1 edges. | |
| function faceEdges(face) { | |
| var n = face.length, | |
| edges = []; | |
| for (var a = face[n - 1], i = 0; i < n; ++i) edges.push([a, a = face[i]]); | |
| return edges; | |
| } | |
| function hasInverse(node) { | |
| return node.project.invert || node.children && node.children.some(hasInverse); | |
| } | |
| // TODO generate on-the-fly to avoid external modification. | |
| var octahedron = [ | |
| [0, 90], | |
| [-90, 0], [0, 0], [90, 0], [180, 0], | |
| [0, -90] | |
| ]; | |
| var octahedron$1 = [ | |
| [0, 2, 1], | |
| [0, 3, 2], | |
| [5, 1, 2], | |
| [5, 2, 3], | |
| [0, 1, 4], | |
| [0, 4, 3], | |
| [5, 4, 1], | |
| [5, 3, 4] | |
| ].map(function(face) { | |
| return face.map(function(i) { | |
| return octahedron[i]; | |
| }); | |
| }); | |
| var butterfly = function(faceProjection) { | |
| faceProjection = faceProjection || function(face) { | |
| var c = d3Geo.geoCentroid({type: "MultiPoint", coordinates: face}); | |
| return d3Geo.geoGnomonic().scale(1).translate([0, 0]).rotate([-c[0], -c[1]]); | |
| }; | |
| var faces = octahedron$1.map(function(face) { | |
| return {face: face, project: faceProjection(face)}; | |
| }); | |
| [-1, 0, 0, 1, 0, 1, 4, 5].forEach(function(d, i) { | |
| var node = faces[d]; | |
| node && (node.children || (node.children = [])).push(faces[i]); | |
| }); | |
| return polyhedral(faces[0], function(lambda, phi) { | |
| return faces[lambda < -pi / 2 ? phi < 0 ? 6 : 4 | |
| : lambda < 0 ? phi < 0 ? 2 : 0 | |
| : lambda < pi / 2 ? phi < 0 ? 3 : 1 | |
| : phi < 0 ? 7 : 5]; | |
| }) | |
| .scale(101.858) | |
| .center([0, 45]); | |
| }; | |
| var kx = 2 / sqrt(3); | |
| function collignonK(a, b) { | |
| var p = collignonRaw(a, b); | |
| return [p[0] * kx, p[1]]; | |
| } | |
| collignonK.invert = function(x,y) { | |
| return collignonRaw.invert(x / kx, y); | |
| }; | |
| var collignon$1 = function(faceProjection) { | |
| faceProjection = faceProjection || function(face) { | |
| var c = d3Geo.geoCentroid({type: "MultiPoint", coordinates: face}); | |
| return d3Geo.geoProjection(collignonK).translate([0, 0]).scale(1).rotate(c[1] > 0 ? [-c[0], 0] : [180 - c[0], 180]); | |
| }; | |
| var faces = octahedron$1.map(function(face) { | |
| return {face: face, project: faceProjection(face)}; | |
| }); | |
| [-1, 0, 0, 1, 0, 1, 4, 5].forEach(function(d, i) { | |
| var node = faces[d]; | |
| node && (node.children || (node.children = [])).push(faces[i]); | |
| }); | |
| return polyhedral(faces[0], function(lambda, phi) { | |
| return faces[lambda < -pi / 2 ? phi < 0 ? 6 : 4 | |
| : lambda < 0 ? phi < 0 ? 2 : 0 | |
| : lambda < pi / 2 ? phi < 0 ? 3 : 1 | |
| : phi < 0 ? 7 : 5]; | |
| }) | |
| .scale(121.906) | |
| .center([0, 48.5904]); | |
| }; | |
| function leeRaw (lambda, phi) { | |
| // return d3.geoGnomonicRaw(...arguments); | |
| var w = [-1/2, sqrt(3)/2], | |
| k = [0, 0], | |
| h = [0, 0], | |
| i, | |
| z = complexMul(d3Geo.geoStereographicRaw(lambda, phi), [sqrt(2), 0]); | |
| // rotate to have s ~= 1 | |
| var sector = d3Array.scan([0,1,2].map( | |
| function(i) { | |
| return -complexMul(z, complexPow(w,[i,0]))[0]; | |
| })); | |
| var rot = complexPow(w, [sector, 0]); | |
| var n = complexNorm(z); | |
| if (n > 0.3) { | |
| // if |z| > 0.5, use the approx based on y = (1-z) | |
| // McIlroy formula 6 p6 and table for G page 16 | |
| var y = complexSub([1, 0], complexMul(rot, z)); | |
| // w1 = gamma(1/3) * gamma(1/2) / 3 / gamma(5/6); | |
| // https://bl.ocks.org/Fil/1aeff1cfda7188e9fbf037d8e466c95c | |
| var w1 = 1.4021821053254548; | |
| var G0 = [ | |
| 1.15470053837925, | |
| 0.192450089729875, | |
| 0.0481125224324687, | |
| 0.010309826235529, | |
| 3.34114739114366e-4, | |
| -1.50351632601465e-3, | |
| -1.23044177962310e-3, | |
| -6.75190201960282e-4, | |
| -2.84084537293856e-4, | |
| -8.21205120500051e-5, | |
| -1.59257630018706e-6, | |
| 1.91691805888369e-5, | |
| 1.73095888028726e-5, | |
| 1.03865580818367e-5, | |
| 4.70614523937179e-6, | |
| 1.4413500104181e-6, | |
| 1.92757960170179e-8, | |
| -3.82869799649063e-7, | |
| -3.57526015225576e-7, | |
| -2.2175964844211e-7 | |
| ]; | |
| var G = [0, 0]; | |
| for (i = G0.length; i--;) { | |
| G = complexAdd([G0[i], 0], complexMul(G, y)); | |
| } | |
| k = complexSub([w1, 0], complexMul(complexPow(y, 1/2), G)); | |
| k = complexMul(k, rot); k = complexMul(k, rot); | |
| } | |
| if (n < 0.5) { | |
| // if |z| < 0.3 | |
| // https://www.wolframalpha.com/input/?i=series+of+((1-z%5E3))+%5E+(-1%2F2)+at+z%3D0 (and ask for "more terms") | |
| // 1 + z^3/2 + (3 z^6)/8 + (5 z^9)/16 + (35 z^12)/128 + (63 z^15)/256 + (231 z^18)/1024 + O(z^21) | |
| // https://www.wolframalpha.com/input/?i=integral+of+1+%2B+z%5E3%2F2+%2B+(3+z%5E6)%2F8+%2B+(5+z%5E9)%2F16+%2B+(35+z%5E12)%2F128+%2B+(63+z%5E15)%2F256+%2B+(231+z%5E18)%2F1024 | |
| // (231 z^19)/19456 + (63 z^16)/4096 + (35 z^13)/1664 + z^10/32 + (3 z^7)/56 + z^4/8 + z + constant | |
| var H0 = [ | |
| 1, 1/8, 3/56, 1/32, 35/1664, 63/4096, 231/19456 | |
| ]; | |
| var z3 = complexPow(z, [3,0]); | |
| for (i = H0.length; i--;) { | |
| h = complexAdd([H0[i], 0], complexMul(h, z3)); | |
| } | |
| h = complexMul(h, z); | |
| } | |
| if (n < 0.3) return h; | |
| if (n > 0.5) return k; | |
| // in between 0.3 and 0.5, interpolate | |
| var t = (n - 0.3) / (0.5 - 0.3); | |
| return complexAdd( | |
| complexMul(k, [t, 0]), | |
| complexMul(h, [1 - t, 0]) | |
| ); | |
| } | |
| var asin1_3 = asin(1 / 3); | |
| var centers = [ | |
| [0, 90], | |
| [-180, -asin1_3 * degrees], | |
| [-60, -asin1_3 * degrees], | |
| [60, -asin1_3 * degrees] | |
| ]; | |
| var tetrahedron = [[1, 2, 3], [0, 2, 1], [0, 3, 2], [0, 1, 3]].map(function( | |
| face | |
| ) { | |
| return face.map(function(i) { | |
| return centers[i]; | |
| }); | |
| }); | |
| // geoPolyhedralLee | |
| var lee$1 = function() { | |
| var orientation = (arguments.length ? arguments[0] : 30) * radians; | |
| var faceProjection = function(face) { | |
| var c = d3Geo.geoCentroid({ type: "MultiPoint", coordinates: face }), | |
| rotate = [-c[0], -c[1], 30]; | |
| if (abs(c[1]) == 90) { | |
| rotate = [0, -c[1], -30]; | |
| } | |
| return d3Geo.geoProjection(leeRaw).scale(1).translate([0, 0]).rotate(rotate); | |
| }; | |
| var faces = tetrahedron.map(function(face) { | |
| return { face: face, project: faceProjection(face) }; | |
| }); | |
| [-1, 0, 0, 0].forEach(function(d, i) { | |
| var node = faces[d]; | |
| node && (node.children || (node.children = [])).push(faces[i]); | |
| }); | |
| return polyhedral( | |
| faces[0], | |
| function(lambda, phi) { | |
| lambda *= degrees; | |
| phi *= degrees; | |
| for (var i = 0; i < faces.length; i++) { | |
| if ( | |
| d3Geo.geoContains( | |
| { | |
| type: "Polygon", | |
| coordinates: [[tetrahedron[i][0], tetrahedron[i][1], tetrahedron[i][2], tetrahedron[i][0]]] | |
| }, | |
| [lambda, phi] | |
| ) | |
| ) { | |
| return faces[i]; | |
| } | |
| } | |
| }, | |
| orientation | |
| ) | |
| .precision(0.05) | |
| .rotate([-30, 0]) | |
| //.rotate([30, 180]) // for North Pole aspect, needs clipPolygon | |
| .scale(118.899) | |
| .center([0,-35.315]); | |
| }; | |
| var waterman = function(faceProjection) { | |
| faceProjection = faceProjection || function(face) { | |
| var c = face.length === 6 ? d3Geo.geoCentroid({type: "MultiPoint", coordinates: face}) : face[0]; | |
| return d3Geo.geoGnomonic().scale(1).translate([0, 0]).rotate([-c[0], -c[1]]); | |
| }; | |
| var w5 = octahedron$1.map(function(face) { | |
| var xyz = face.map(cartesian), | |
| n = xyz.length, | |
| a = xyz[n - 1], | |
| b, | |
| hexagon = []; | |
| for (var i = 0; i < n; ++i) { | |
| b = xyz[i]; | |
| hexagon.push(spherical([ | |
| a[0] * 0.9486832980505138 + b[0] * 0.31622776601683794, | |
| a[1] * 0.9486832980505138 + b[1] * 0.31622776601683794, | |
| a[2] * 0.9486832980505138 + b[2] * 0.31622776601683794 | |
| ]), spherical([ | |
| b[0] * 0.9486832980505138 + a[0] * 0.31622776601683794, | |
| b[1] * 0.9486832980505138 + a[1] * 0.31622776601683794, | |
| b[2] * 0.9486832980505138 + a[2] * 0.31622776601683794 | |
| ])); | |
| a = b; | |
| } | |
| return hexagon; | |
| }); | |
| var cornerNormals = []; | |
| var parents = [-1, 0, 0, 1, 0, 1, 4, 5]; | |
| w5.forEach(function(hexagon, j) { | |
| var face = octahedron$1[j], | |
| n = face.length, | |
| normals = cornerNormals[j] = []; | |
| for (var i = 0; i < n; ++i) { | |
| w5.push([ | |
| face[i], | |
| hexagon[(i * 2 + 2) % (2 * n)], | |
| hexagon[(i * 2 + 1) % (2 * n)] | |
| ]); | |
| parents.push(j); | |
| normals.push(cross( | |
| cartesian(hexagon[(i * 2 + 2) % (2 * n)]), | |
| cartesian(hexagon[(i * 2 + 1) % (2 * n)]) | |
| )); | |
| } | |
| }); | |
| var faces = w5.map(function(face) { | |
| return { | |
| project: faceProjection(face), | |
| face: face | |
| }; | |
| }); | |
| parents.forEach(function(d, i) { | |
| var parent = faces[d]; | |
| parent && (parent.children || (parent.children = [])).push(faces[i]); | |
| }); | |
| function face(lambda, phi) { | |
| var cosphi = cos(phi), | |
| p = [cosphi * cos(lambda), cosphi * sin(lambda), sin(phi)]; | |
| var hexagon = lambda < -pi / 2 ? phi < 0 ? 6 : 4 | |
| : lambda < 0 ? phi < 0 ? 2 : 0 | |
| : lambda < pi / 2 ? phi < 0 ? 3 : 1 | |
| : phi < 0 ? 7 : 5; | |
| var n = cornerNormals[hexagon]; | |
| return faces[dot(n[0], p) < 0 ? 8 + 3 * hexagon | |
| : dot(n[1], p) < 0 ? 8 + 3 * hexagon + 1 | |
| : dot(n[2], p) < 0 ? 8 + 3 * hexagon + 2 | |
| : hexagon]; | |
| } | |
| return polyhedral(faces[0], face) | |
| .scale(110.625) | |
| .center([0,45]); | |
| }; | |
| function dot(a, b) { | |
| for (var i = 0, n = a.length, s = 0; i < n; ++i) s += a[i] * b[i]; | |
| return s; | |
| } | |
| function cross(a, b) { | |
| return [ | |
| a[1] * b[2] - a[2] * b[1], | |
| a[2] * b[0] - a[0] * b[2], | |
| a[0] * b[1] - a[1] * b[0] | |
| ]; | |
| } | |
| // Converts 3D Cartesian to spherical coordinates (degrees). | |
| function spherical(cartesian) { | |
| return [ | |
| atan2(cartesian[1], cartesian[0]) * degrees, | |
| asin(max(-1, min(1, cartesian[2]))) * degrees | |
| ]; | |
| } | |
| // Converts spherical coordinates (degrees) to 3D Cartesian. | |
| function cartesian(coordinates) { | |
| var lambda = coordinates[0] * radians, | |
| phi = coordinates[1] * radians, | |
| cosphi = cos(phi); | |
| return [ | |
| cosphi * cos(lambda), | |
| cosphi * sin(lambda), | |
| sin(phi) | |
| ]; | |
| } | |
| var noop = function() {}; | |
| var clockwise = function(ring) { | |
| if ((n = ring.length) < 4) return false; | |
| var i = 0, | |
| n, | |
| area = ring[n - 1][1] * ring[0][0] - ring[n - 1][0] * ring[0][1]; | |
| while (++i < n) area += ring[i - 1][1] * ring[i][0] - ring[i - 1][0] * ring[i][1]; | |
| return area <= 0; | |
| }; | |
| var contains = function(ring, point) { | |
| var x = point[0], | |
| y = point[1], | |
| contains = false; | |
| for (var i = 0, n = ring.length, j = n - 1; i < n; j = i++) { | |
| var pi = ring[i], xi = pi[0], yi = pi[1], | |
| pj = ring[j], xj = pj[0], yj = pj[1]; | |
| if (((yi > y) ^ (yj > y)) && (x < (xj - xi) * (y - yi) / (yj - yi) + xi)) contains = !contains; | |
| } | |
| return contains; | |
| }; | |
| var index = function(object, projection) { | |
| var stream = projection.stream, project; | |
| if (!stream) throw new Error("invalid projection"); | |
| switch (object && object.type) { | |
| case "Feature": project = projectFeature; break; | |
| case "FeatureCollection": project = projectFeatureCollection; break; | |
| default: project = projectGeometry; break; | |
| } | |
| return project(object, stream); | |
| }; | |
| function projectFeatureCollection(o, stream) { | |
| return { | |
| type: "FeatureCollection", | |
| features: o.features.map(function(f) { | |
| return projectFeature(f, stream); | |
| }) | |
| }; | |
| } | |
| function projectFeature(o, stream) { | |
| return { | |
| type: "Feature", | |
| id: o.id, | |
| properties: o.properties, | |
| geometry: projectGeometry(o.geometry, stream) | |
| }; | |
| } | |
| function projectGeometryCollection(o, stream) { | |
| return { | |
| type: "GeometryCollection", | |
| geometries: o.geometries.map(function(o) { | |
| return projectGeometry(o, stream); | |
| }) | |
| }; | |
| } | |
| function projectGeometry(o, stream) { | |
| if (!o) return null; | |
| if (o.type === "GeometryCollection") return projectGeometryCollection(o, stream); | |
| var sink; | |
| switch (o.type) { | |
| case "Point": sink = sinkPoint; break; | |
| case "MultiPoint": sink = sinkPoint; break; | |
| case "LineString": sink = sinkLine; break; | |
| case "MultiLineString": sink = sinkLine; break; | |
| case "Polygon": sink = sinkPolygon; break; | |
| case "MultiPolygon": sink = sinkPolygon; break; | |
| case "Sphere": sink = sinkPolygon; break; | |
| default: return null; | |
| } | |
| d3Geo.geoStream(o, stream(sink)); | |
| return sink.result(); | |
| } | |
| var points = []; | |
| var lines = []; | |
| var sinkPoint = { | |
| point: function(x, y) { | |
| points.push([x, y]); | |
| }, | |
| result: function() { | |
| var result = !points.length ? null | |
| : points.length < 2 ? {type: "Point", coordinates: points[0]} | |
| : {type: "MultiPoint", coordinates: points}; | |
| points = []; | |
| return result; | |
| } | |
| }; | |
| var sinkLine = { | |
| lineStart: noop, | |
| point: function(x, y) { | |
| points.push([x, y]); | |
| }, | |
| lineEnd: function() { | |
| if (points.length) lines.push(points), points = []; | |
| }, | |
| result: function() { | |
| var result = !lines.length ? null | |
| : lines.length < 2 ? {type: "LineString", coordinates: lines[0]} | |
| : {type: "MultiLineString", coordinates: lines}; | |
| lines = []; | |
| return result; | |
| } | |
| }; | |
| var sinkPolygon = { | |
| polygonStart: noop, | |
| lineStart: noop, | |
| point: function(x, y) { | |
| points.push([x, y]); | |
| }, | |
| lineEnd: function() { | |
| var n = points.length; | |
| if (n) { | |
| do points.push(points[0].slice()); while (++n < 4); | |
| lines.push(points), points = []; | |
| } | |
| }, | |
| polygonEnd: noop, | |
| result: function() { | |
| if (!lines.length) return null; | |
| var polygons = [], | |
| holes = []; | |
| // https://github.com/d3/d3/issues/1558 | |
| lines.forEach(function(ring) { | |
| if (clockwise(ring)) polygons.push([ring]); | |
| else holes.push(ring); | |
| }); | |
| holes.forEach(function(hole) { | |
| var point = hole[0]; | |
| polygons.some(function(polygon) { | |
| if (contains(polygon[0], point)) { | |
| polygon.push(hole); | |
| return true; | |
| } | |
| }) || polygons.push([hole]); | |
| }); | |
| lines = []; | |
| return !polygons.length ? null | |
| : polygons.length > 1 ? {type: "MultiPolygon", coordinates: polygons} | |
| : {type: "Polygon", coordinates: polygons[0]}; | |
| } | |
| }; | |
| var quincuncial = function(project) { | |
| var dx = project(halfPi, 0)[0] - project(-halfPi, 0)[0]; | |
| function projectQuincuncial(lambda, phi) { | |
| var t = abs(lambda) < halfPi, | |
| p = project(t ? lambda : lambda > 0 ? lambda - pi : lambda + pi, phi), | |
| x = (p[0] - p[1]) * sqrt1_2, | |
| y = (p[0] + p[1]) * sqrt1_2; | |
| if (t) return [x, y]; | |
| var d = dx * sqrt1_2, | |
| s = x > 0 ^ y > 0 ? -1 : 1; | |
| return [s * x - sign(y) * d, s * y - sign(x) * d]; | |
| } | |
| if (project.invert) projectQuincuncial.invert = function(x0, y0) { | |
| var x = (x0 + y0) * sqrt1_2, | |
| y = (y0 - x0) * sqrt1_2, | |
| t = abs(x) < 0.5 * dx && abs(y) < 0.5 * dx; | |
| if (!t) { | |
| var d = dx * sqrt1_2, | |
| s = x > 0 ^ y > 0 ? -1 : 1, | |
| x1 = -s * x0 + (y > 0 ? 1 : -1) * d, | |
| y1 = -s * y0 + (x > 0 ? 1 : -1) * d; | |
| x = (-x1 - y1) * sqrt1_2; | |
| y = (x1 - y1) * sqrt1_2; | |
| } | |
| var p = project.invert(x, y); | |
| if (!t) p[0] += x > 0 ? pi : -pi; | |
| return p; | |
| }; | |
| return d3Geo.geoProjection(projectQuincuncial) | |
| .rotate([-90, -90, 45]) | |
| .clipAngle(180 - 1e-3); | |
| }; | |
| var gringorten$1 = function() { | |
| return quincuncial(gringortenRaw) | |
| .scale(176.423); | |
| }; | |
| var peirce = function() { | |
| return quincuncial(guyouRaw) | |
| .scale(111.48); | |
| }; | |
| var quantize = function(input, digits) { | |
| if (!(0 <= (digits = +digits) && digits <= 20)) throw new Error("invalid digits"); | |
| function quantizePoint(input) { | |
| var n = input.length, i = 2, output = new Array(n); | |
| output[0] = +input[0].toFixed(digits); | |
| output[1] = +input[1].toFixed(digits); | |
| while (i < n) output[i] = input[i], ++i; | |
| return output; | |
| } | |
| function quantizePoints(input) { | |
| return input.map(quantizePoint); | |
| } | |
| function quantizePolygon(input) { | |
| return input.map(quantizePoints); | |
| } | |
| function quantizeGeometry(input) { | |
| if (input == null) return input; | |
| var output; | |
| switch (input.type) { | |
| case "GeometryCollection": output = {type: "GeometryCollection", geometries: input.geometries.map(quantizeGeometry)}; break; | |
| case "Point": output = {type: "Point", coordinates: quantizePoint(input.coordinates)}; break; | |
| case "MultiPoint": case "LineString": output = {type: input.type, coordinates: quantizePoints(input.coordinates)}; break; | |
| case "MultiLineString": case "Polygon": output = {type: input.type, coordinates: quantizePolygon(input.coordinates)}; break; | |
| case "MultiPolygon": output = {type: "MultiPolygon", coordinates: input.coordinates.map(quantizePolygon)}; break; | |
| default: return input; | |
| } | |
| if (input.bbox != null) output.bbox = input.bbox; | |
| return output; | |
| } | |
| function quantizeFeature(input) { | |
| var output = {type: "Feature", properties: input.properties, geometry: quantizeGeometry(input.geometry)}; | |
| if (input.id != null) output.id = input.id; | |
| if (input.bbox != null) output.bbox = input.bbox; | |
| return output; | |
| } | |
| if (input != null) switch (input.type) { | |
| case "Feature": return quantizeFeature(input); | |
| case "FeatureCollection": { | |
| var output = {type: "FeatureCollection", features: input.features.map(quantizeFeature)}; | |
| if (input.bbox != null) output.bbox = input.bbox; | |
| return output; | |
| } | |
| default: return quantizeGeometry(input); | |
| } | |
| return input; | |
| }; | |
| function rectangularPolyconicRaw(phi0) { | |
| var sinPhi0 = sin(phi0); | |
| function forward(lambda, phi) { | |
| var A = sinPhi0 ? tan(lambda * sinPhi0 / 2) / sinPhi0 : lambda / 2; | |
| if (!phi) return [2 * A, -phi0]; | |
| var E = 2 * atan(A * sin(phi)), | |
| cotPhi = 1 / tan(phi); | |
| return [ | |
| sin(E) * cotPhi, | |
| phi + (1 - cos(E)) * cotPhi - phi0 | |
| ]; | |
| } | |
| // TODO return null for points outside outline. | |
| forward.invert = function(x, y) { | |
| if (abs(y += phi0) < epsilon) return [sinPhi0 ? 2 * atan(sinPhi0 * x / 2) / sinPhi0 : x, 0]; | |
| var k = x * x + y * y, | |
| phi = 0, | |
| i = 10, delta; | |
| do { | |
| var tanPhi = tan(phi), | |
| secPhi = 1 / cos(phi), | |
| j = k - 2 * y * phi + phi * phi; | |
| phi -= delta = (tanPhi * j + 2 * (phi - y)) / (2 + j * secPhi * secPhi + 2 * (phi - y) * tanPhi); | |
| } while (abs(delta) > epsilon && --i > 0); | |
| var E = x * (tanPhi = tan(phi)), | |
| A = tan(abs(y) < abs(phi + 1 / tanPhi) ? asin(E) * 0.5 : acos(E) * 0.5 + pi / 4) / sin(phi); | |
| return [ | |
| sinPhi0 ? 2 * atan(sinPhi0 * A) / sinPhi0 : 2 * A, | |
| phi | |
| ]; | |
| }; | |
| return forward; | |
| } | |
| var rectangularPolyconic = function() { | |
| return parallel1(rectangularPolyconicRaw) | |
| .scale(131.215); | |
| }; | |
| var K = [ | |
| [0.9986, -0.062], | |
| [1.0000, 0.0000], | |
| [0.9986, 0.0620], | |
| [0.9954, 0.1240], | |
| [0.9900, 0.1860], | |
| [0.9822, 0.2480], | |
| [0.9730, 0.3100], | |
| [0.9600, 0.3720], | |
| [0.9427, 0.4340], | |
| [0.9216, 0.4958], | |
| [0.8962, 0.5571], | |
| [0.8679, 0.6176], | |
| [0.8350, 0.6769], | |
| [0.7986, 0.7346], | |
| [0.7597, 0.7903], | |
| [0.7186, 0.8435], | |
| [0.6732, 0.8936], | |
| [0.6213, 0.9394], | |
| [0.5722, 0.9761], | |
| [0.5322, 1.0000] | |
| ]; | |
| K.forEach(function(d) { | |
| d[1] *= 1.0144; | |
| }); | |
| function robinsonRaw(lambda, phi) { | |
| var i = min(18, abs(phi) * 36 / pi), | |
| i0 = floor(i), | |
| di = i - i0, | |
| ax = (k = K[i0])[0], | |
| ay = k[1], | |
| bx = (k = K[++i0])[0], | |
| by = k[1], | |
| cx = (k = K[min(19, ++i0)])[0], | |
| cy = k[1], | |
| k; | |
| return [ | |
| lambda * (bx + di * (cx - ax) / 2 + di * di * (cx - 2 * bx + ax) / 2), | |
| (phi > 0 ? halfPi : -halfPi) * (by + di * (cy - ay) / 2 + di * di * (cy - 2 * by + ay) / 2) | |
| ]; | |
| } | |
| robinsonRaw.invert = function(x, y) { | |
| var yy = y / halfPi, | |
| phi = yy * 90, | |
| i = min(18, abs(phi / 5)), | |
| i0 = max(0, floor(i)); | |
| do { | |
| var ay = K[i0][1], | |
| by = K[i0 + 1][1], | |
| cy = K[min(19, i0 + 2)][1], | |
| u = cy - ay, | |
| v = cy - 2 * by + ay, | |
| t = 2 * (abs(yy) - by) / u, | |
| c = v / u, | |
| di = t * (1 - c * t * (1 - 2 * c * t)); | |
| if (di >= 0 || i0 === 1) { | |
| phi = (y >= 0 ? 5 : -5) * (di + i); | |
| var j = 50, delta; | |
| do { | |
| i = min(18, abs(phi) / 5); | |
| i0 = floor(i); | |
| di = i - i0; | |
| ay = K[i0][1]; | |
| by = K[i0 + 1][1]; | |
| cy = K[min(19, i0 + 2)][1]; | |
| phi -= (delta = (y >= 0 ? halfPi : -halfPi) * (by + di * (cy - ay) / 2 + di * di * (cy - 2 * by + ay) / 2) - y) * degrees; | |
| } while (abs(delta) > epsilon2 && --j > 0); | |
| break; | |
| } | |
| } while (--i0 >= 0); | |
| var ax = K[i0][0], | |
| bx = K[i0 + 1][0], | |
| cx = K[min(19, i0 + 2)][0]; | |
| return [ | |
| x / (bx + di * (cx - ax) / 2 + di * di * (cx - 2 * bx + ax) / 2), | |
| phi * radians | |
| ]; | |
| }; | |
| var robinson = function() { | |
| return d3Geo.geoProjection(robinsonRaw) | |
| .scale(152.63); | |
| }; | |
| function satelliteVerticalRaw(P) { | |
| function forward(lambda, phi) { | |
| var cosPhi = cos(phi), | |
| k = (P - 1) / (P - cosPhi * cos(lambda)); | |
| return [ | |
| k * cosPhi * sin(lambda), | |
| k * sin(phi) | |
| ]; | |
| } | |
| forward.invert = function(x, y) { | |
| var rho2 = x * x + y * y, | |
| rho = sqrt(rho2), | |
| sinc = (P - sqrt(1 - rho2 * (P + 1) / (P - 1))) / ((P - 1) / rho + rho / (P - 1)); | |
| return [ | |
| atan2(x * sinc, rho * sqrt(1 - sinc * sinc)), | |
| rho ? asin(y * sinc / rho) : 0 | |
| ]; | |
| }; | |
| return forward; | |
| } | |
| function satelliteRaw(P, omega) { | |
| var vertical = satelliteVerticalRaw(P); | |
| if (!omega) return vertical; | |
| var cosOmega = cos(omega), | |
| sinOmega = sin(omega); | |
| function forward(lambda, phi) { | |
| var coordinates = vertical(lambda, phi), | |
| y = coordinates[1], | |
| A = y * sinOmega / (P - 1) + cosOmega; | |
| return [ | |
| coordinates[0] * cosOmega / A, | |
| y / A | |
| ]; | |
| } | |
| forward.invert = function(x, y) { | |
| var k = (P - 1) / (P - 1 - y * sinOmega); | |
| return vertical.invert(k * x, k * y * cosOmega); | |
| }; | |
| return forward; | |
| } | |
| var satellite = function() { | |
| var distance = 2, | |
| omega = 0, | |
| m = d3Geo.geoProjectionMutator(satelliteRaw), | |
| p = m(distance, omega); | |
| // As a multiple of radius. | |
| p.distance = function(_) { | |
| if (!arguments.length) return distance; | |
| return m(distance = +_, omega); | |
| }; | |
| p.tilt = function(_) { | |
| if (!arguments.length) return omega * degrees; | |
| return m(distance, omega = _ * radians); | |
| }; | |
| return p | |
| .scale(432.147) | |
| .clipAngle(acos(1 / distance) * degrees - 1e-6); | |
| }; | |
| var epsilon$1 = 1e-4; | |
| var epsilonInverse = 1e4; | |
| var x0 = -180; | |
| var x0e = x0 + epsilon$1; | |
| var x1 = 180; | |
| var x1e = x1 - epsilon$1; | |
| var y0 = -90; | |
| var y0e = y0 + epsilon$1; | |
| var y1 = 90; | |
| var y1e = y1 - epsilon$1; | |
| function nonempty(coordinates) { | |
| return coordinates.length > 0; | |
| } | |
| function quantize$1(x) { | |
| return Math.floor(x * epsilonInverse) / epsilonInverse; | |
| } | |
| function normalizePoint(y) { | |
| return y === y0 || y === y1 ? [0, y] : [x0, quantize$1(y)]; // pole or antimeridian? | |
| } | |
| function clampPoint(p) { | |
| var x = p[0], y = p[1], clamped = false; | |
| if (x <= x0e) x = x0, clamped = true; | |
| else if (x >= x1e) x = x1, clamped = true; | |
| if (y <= y0e) y = y0, clamped = true; | |
| else if (y >= y1e) y = y1, clamped = true; | |
| return clamped ? [x, y] : p; | |
| } | |
| function clampPoints(points) { | |
| return points.map(clampPoint); | |
| } | |
| // For each ring, detect where it crosses the antimeridian or pole. | |
| function extractFragments(rings, polygon, fragments) { | |
| for (var j = 0, m = rings.length; j < m; ++j) { | |
| var ring = rings[j].slice(); | |
| // By default, assume that this ring doesn’t need any stitching. | |
| fragments.push({index: -1, polygon: polygon, ring: ring}); | |
| for (var i = 0, n = ring.length; i < n; ++i) { | |
| var point = ring[i], | |
| x = point[0], | |
| y = point[1]; | |
| // If this is an antimeridian or polar point… | |
| if (x <= x0e || x >= x1e || y <= y0e || y >= y1e) { | |
| ring[i] = clampPoint(point); | |
| // Advance through any antimeridian or polar points… | |
| for (var k = i + 1; k < n; ++k) { | |
| var pointk = ring[k], | |
| xk = pointk[0], | |
| yk = pointk[1]; | |
| if (xk > x0e && xk < x1e && yk > y0e && yk < y1e) break; | |
| } | |
| // If this was just a single antimeridian or polar point, | |
| // we don’t need to cut this ring into a fragment; | |
| // we can just leave it as-is. | |
| if (k === i + 1) continue; | |
| // Otherwise, if this is not the first point in the ring, | |
| // cut the current fragment so that it ends at the current point. | |
| // The current point is also normalized for later joining. | |
| if (i) { | |
| var fragmentBefore = {index: -1, polygon: polygon, ring: ring.slice(0, i + 1)}; | |
| fragmentBefore.ring[fragmentBefore.ring.length - 1] = normalizePoint(y); | |
| fragments[fragments.length - 1] = fragmentBefore; | |
| } | |
| // If the ring started with an antimeridian fragment, | |
| // we can ignore that fragment entirely. | |
| else fragments.pop(); | |
| // If the remainder of the ring is an antimeridian fragment, | |
| // move on to the next ring. | |
| if (k >= n) break; | |
| // Otherwise, add the remaining ring fragment and continue. | |
| fragments.push({index: -1, polygon: polygon, ring: ring = ring.slice(k - 1)}); | |
| ring[0] = normalizePoint(ring[0][1]); | |
| i = -1; | |
| n = ring.length; | |
| } | |
| } | |
| } | |
| } | |
| // Now stitch the fragments back together into rings. | |
| function stitchFragments(fragments) { | |
| var i, n = fragments.length; | |
| // To connect the fragments start-to-end, create a simple index by end. | |
| var fragmentByStart = {}, | |
| fragmentByEnd = {}, | |
| fragment, | |
| start, | |
| startFragment, | |
| end, | |
| endFragment; | |
| // For each fragment… | |
| for (i = 0; i < n; ++i) { | |
| fragment = fragments[i]; | |
| start = fragment.ring[0]; | |
| end = fragment.ring[fragment.ring.length - 1]; | |
| // If this fragment is closed, add it as a standalone ring. | |
| if (start[0] === end[0] && start[1] === end[1]) { | |
| fragment.polygon.push(fragment.ring); | |
| fragments[i] = null; | |
| continue; | |
| } | |
| fragment.index = i; | |
| fragmentByStart[start] = fragmentByEnd[end] = fragment; | |
| } | |
| // For each open fragment… | |
| for (i = 0; i < n; ++i) { | |
| fragment = fragments[i]; | |
| if (fragment) { | |
| start = fragment.ring[0]; | |
| end = fragment.ring[fragment.ring.length - 1]; | |
| startFragment = fragmentByEnd[start]; | |
| endFragment = fragmentByStart[end]; | |
| delete fragmentByStart[start]; | |
| delete fragmentByEnd[end]; | |
| // If this fragment is closed, add it as a standalone ring. | |
| if (start[0] === end[0] && start[1] === end[1]) { | |
| fragment.polygon.push(fragment.ring); | |
| continue; | |
| } | |
| if (startFragment) { | |
| delete fragmentByEnd[start]; | |
| delete fragmentByStart[startFragment.ring[0]]; | |
| startFragment.ring.pop(); // drop the shared coordinate | |
| fragments[startFragment.index] = null; | |
| fragment = {index: -1, polygon: startFragment.polygon, ring: startFragment.ring.concat(fragment.ring)}; | |
| if (startFragment === endFragment) { | |
| // Connect both ends to this single fragment to create a ring. | |
| fragment.polygon.push(fragment.ring); | |
| } else { | |
| fragment.index = n++; | |
| fragments.push(fragmentByStart[fragment.ring[0]] = fragmentByEnd[fragment.ring[fragment.ring.length - 1]] = fragment); | |
| } | |
| } else if (endFragment) { | |
| delete fragmentByStart[end]; | |
| delete fragmentByEnd[endFragment.ring[endFragment.ring.length - 1]]; | |
| fragment.ring.pop(); // drop the shared coordinate | |
| fragment = {index: n++, polygon: endFragment.polygon, ring: fragment.ring.concat(endFragment.ring)}; | |
| fragments[endFragment.index] = null; | |
| fragments.push(fragmentByStart[fragment.ring[0]] = fragmentByEnd[fragment.ring[fragment.ring.length - 1]] = fragment); | |
| } else { | |
| fragment.ring.push(fragment.ring[0]); // close ring | |
| fragment.polygon.push(fragment.ring); | |
| } | |
| } | |
| } | |
| } | |
| function stitchFeature(input) { | |
| var output = {type: "Feature", geometry: stitchGeometry(input.geometry)}; | |
| if (input.id != null) output.id = input.id; | |
| if (input.bbox != null) output.bbox = input.bbox; | |
| if (input.properties != null) output.properties = input.properties; | |
| return output; | |
| } | |
| function stitchGeometry(input) { | |
| if (input == null) return input; | |
| var output, fragments, i, n; | |
| switch (input.type) { | |
| case "GeometryCollection": output = {type: "GeometryCollection", geometries: input.geometries.map(stitchGeometry)}; break; | |
| case "Point": output = {type: "Point", coordinates: clampPoint(input.coordinates)}; break; | |
| case "MultiPoint": case "LineString": output = {type: input.type, coordinates: clampPoints(input.coordinates)}; break; | |
| case "MultiLineString": output = {type: "MultiLineString", coordinates: input.coordinates.map(clampPoints)}; break; | |
| case "Polygon": { | |
| var polygon = []; | |
| extractFragments(input.coordinates, polygon, fragments = []); | |
| stitchFragments(fragments); | |
| output = {type: "Polygon", coordinates: polygon}; | |
| break; | |
| } | |
| case "MultiPolygon": { | |
| fragments = [], i = -1, n = input.coordinates.length; | |
| var polygons = new Array(n); | |
| while (++i < n) extractFragments(input.coordinates[i], polygons[i] = [], fragments); | |
| stitchFragments(fragments); | |
| output = {type: "MultiPolygon", coordinates: polygons.filter(nonempty)}; | |
| break; | |
| } | |
| default: return input; | |
| } | |
| if (input.bbox != null) output.bbox = input.bbox; | |
| return output; | |
| } | |
| var stitch = function(input) { | |
| if (input == null) return input; | |
| switch (input.type) { | |
| case "Feature": return stitchFeature(input); | |
| case "FeatureCollection": { | |
| var output = {type: "FeatureCollection", features: input.features.map(stitchFeature)}; | |
| if (input.bbox != null) output.bbox = input.bbox; | |
| return output; | |
| } | |
| default: return stitchGeometry(input); | |
| } | |
| }; | |
| function timesRaw(lambda, phi) { | |
| var t = tan(phi / 2), | |
| s = sin(quarterPi * t); | |
| return [ | |
| lambda * (0.74482 - 0.34588 * s * s), | |
| 1.70711 * t | |
| ]; | |
| } | |
| timesRaw.invert = function(x, y) { | |
| var t = y / 1.70711, | |
| s = sin(quarterPi * t); | |
| return [ | |
| x / (0.74482 - 0.34588 * s * s), | |
| 2 * atan(t) | |
| ]; | |
| }; | |
| var times = function() { | |
| return d3Geo.geoProjection(timesRaw) | |
| .scale(146.153); | |
| }; | |
| // Compute the origin as the midpoint of the two reference points. | |
| // Rotate one of the reference points by the origin. | |
| // Apply the spherical law of sines to compute gamma rotation. | |
| var twoPoint = function(raw, p0, p1) { | |
| var i = d3Geo.geoInterpolate(p0, p1), | |
| o = i(0.5), | |
| a = d3Geo.geoRotation([-o[0], -o[1]])(p0), | |
| b = i.distance / 2, | |
| y = -asin(sin(a[1] * radians) / sin(b)), | |
| R = [-o[0], -o[1], -(a[0] > 0 ? pi - y : y) * degrees], | |
| p = d3Geo.geoProjection(raw(b)).rotate(R), | |
| r = d3Geo.geoRotation(R), | |
| center = p.center; | |
| delete p.rotate; | |
| p.center = function(_) { | |
| return arguments.length ? center(r(_)) : r.invert(center()); | |
| }; | |
| return p | |
| .clipAngle(90); | |
| }; | |
| function twoPointAzimuthalRaw(d) { | |
| var cosd = cos(d); | |
| function forward(lambda, phi) { | |
| var coordinates = d3Geo.geoGnomonicRaw(lambda, phi); | |
| coordinates[0] *= cosd; | |
| return coordinates; | |
| } | |
| forward.invert = function(x, y) { | |
| return d3Geo.geoGnomonicRaw.invert(x / cosd, y); | |
| }; | |
| return forward; | |
| } | |
| function twoPointAzimuthalUsa() { | |
| return twoPointAzimuthal([-158, 21.5], [-77, 39]) | |
| .clipAngle(60) | |
| .scale(400); | |
| } | |
| function twoPointAzimuthal(p0, p1) { | |
| return twoPoint(twoPointAzimuthalRaw, p0, p1); | |
| } | |
| // TODO clip to ellipse | |
| function twoPointEquidistantRaw(z0) { | |
| if (!(z0 *= 2)) return d3Geo.geoAzimuthalEquidistantRaw; | |
| var lambdaa = -z0 / 2, | |
| lambdab = -lambdaa, | |
| z02 = z0 * z0, | |
| tanLambda0 = tan(lambdab), | |
| S = 0.5 / sin(lambdab); | |
| function forward(lambda, phi) { | |
| var za = acos(cos(phi) * cos(lambda - lambdaa)), | |
| zb = acos(cos(phi) * cos(lambda - lambdab)), | |
| ys = phi < 0 ? -1 : 1; | |
| za *= za, zb *= zb; | |
| return [ | |
| (za - zb) / (2 * z0), | |
| ys * sqrt(4 * z02 * zb - (z02 - za + zb) * (z02 - za + zb)) / (2 * z0) | |
| ]; | |
| } | |
| forward.invert = function(x, y) { | |
| var y2 = y * y, | |
| cosza = cos(sqrt(y2 + (t = x + lambdaa) * t)), | |
| coszb = cos(sqrt(y2 + (t = x + lambdab) * t)), | |
| t, | |
| d; | |
| return [ | |
| atan2(d = cosza - coszb, t = (cosza + coszb) * tanLambda0), | |
| (y < 0 ? -1 : 1) * acos(sqrt(t * t + d * d) * S) | |
| ]; | |
| }; | |
| return forward; | |
| } | |
| function twoPointEquidistantUsa() { | |
| return twoPointEquidistant([-158, 21.5], [-77, 39]) | |
| .clipAngle(130) | |
| .scale(122.571); | |
| } | |
| function twoPointEquidistant(p0, p1) { | |
| return twoPoint(twoPointEquidistantRaw, p0, p1); | |
| } | |
| function vanDerGrintenRaw(lambda, phi) { | |
| if (abs(phi) < epsilon) return [lambda, 0]; | |
| var sinTheta = abs(phi / halfPi), | |
| theta = asin(sinTheta); | |
| if (abs(lambda) < epsilon || abs(abs(phi) - halfPi) < epsilon) return [0, sign(phi) * pi * tan(theta / 2)]; | |
| var cosTheta = cos(theta), | |
| A = abs(pi / lambda - lambda / pi) / 2, | |
| A2 = A * A, | |
| G = cosTheta / (sinTheta + cosTheta - 1), | |
| P = G * (2 / sinTheta - 1), | |
| P2 = P * P, | |
| P2_A2 = P2 + A2, | |
| G_P2 = G - P2, | |
| Q = A2 + G; | |
| return [ | |
| sign(lambda) * pi * (A * G_P2 + sqrt(A2 * G_P2 * G_P2 - P2_A2 * (G * G - P2))) / P2_A2, | |
| sign(phi) * pi * (P * Q - A * sqrt((A2 + 1) * P2_A2 - Q * Q)) / P2_A2 | |
| ]; | |
| } | |
| vanDerGrintenRaw.invert = function(x, y) { | |
| if (abs(y) < epsilon) return [x, 0]; | |
| if (abs(x) < epsilon) return [0, halfPi * sin(2 * atan(y / pi))]; | |
| var x2 = (x /= pi) * x, | |
| y2 = (y /= pi) * y, | |
| x2_y2 = x2 + y2, | |
| z = x2_y2 * x2_y2, | |
| c1 = -abs(y) * (1 + x2_y2), | |
| c2 = c1 - 2 * y2 + x2, | |
| c3 = -2 * c1 + 1 + 2 * y2 + z, | |
| d = y2 / c3 + (2 * c2 * c2 * c2 / (c3 * c3 * c3) - 9 * c1 * c2 / (c3 * c3)) / 27, | |
| a1 = (c1 - c2 * c2 / (3 * c3)) / c3, | |
| m1 = 2 * sqrt(-a1 / 3), | |
| theta1 = acos(3 * d / (a1 * m1)) / 3; | |
| return [ | |
| pi * (x2_y2 - 1 + sqrt(1 + 2 * (x2 - y2) + z)) / (2 * x), | |
| sign(y) * pi * (-m1 * cos(theta1 + pi / 3) - c2 / (3 * c3)) | |
| ]; | |
| }; | |
| var vanDerGrinten = function() { | |
| return d3Geo.geoProjection(vanDerGrintenRaw) | |
| .scale(79.4183); | |
| }; | |
| function vanDerGrinten2Raw(lambda, phi) { | |
| if (abs(phi) < epsilon) return [lambda, 0]; | |
| var sinTheta = abs(phi / halfPi), | |
| theta = asin(sinTheta); | |
| if (abs(lambda) < epsilon || abs(abs(phi) - halfPi) < epsilon) return [0, sign(phi) * pi * tan(theta / 2)]; | |
| var cosTheta = cos(theta), | |
| A = abs(pi / lambda - lambda / pi) / 2, | |
| A2 = A * A, | |
| x1 = cosTheta * (sqrt(1 + A2) - A * cosTheta) / (1 + A2 * sinTheta * sinTheta); | |
| return [ | |
| sign(lambda) * pi * x1, | |
| sign(phi) * pi * sqrt(1 - x1 * (2 * A + x1)) | |
| ]; | |
| } | |
| vanDerGrinten2Raw.invert = function(x, y) { | |
| if (!x) return [0, halfPi * sin(2 * atan(y / pi))]; | |
| var x1 = abs(x / pi), | |
| A = (1 - x1 * x1 - (y /= pi) * y) / (2 * x1), | |
| A2 = A * A, | |
| B = sqrt(A2 + 1); | |
| return [ | |
| sign(x) * pi * (B - A), | |
| sign(y) * halfPi * sin(2 * atan2(sqrt((1 - 2 * A * x1) * (A + B) - x1), sqrt(B + A + x1))) | |
| ]; | |
| }; | |
| var vanDerGrinten2 = function() { | |
| return d3Geo.geoProjection(vanDerGrinten2Raw) | |
| .scale(79.4183); | |
| }; | |
| function vanDerGrinten3Raw(lambda, phi) { | |
| if (abs(phi) < epsilon) return [lambda, 0]; | |
| var sinTheta = phi / halfPi, | |
| theta = asin(sinTheta); | |
| if (abs(lambda) < epsilon || abs(abs(phi) - halfPi) < epsilon) return [0, pi * tan(theta / 2)]; | |
| var A = (pi / lambda - lambda / pi) / 2, | |
| y1 = sinTheta / (1 + cos(theta)); | |
| return [ | |
| pi * (sign(lambda) * sqrt(A * A + 1 - y1 * y1) - A), | |
| pi * y1 | |
| ]; | |
| } | |
| vanDerGrinten3Raw.invert = function(x, y) { | |
| if (!y) return [x, 0]; | |
| var y1 = y / pi, | |
| A = (pi * pi * (1 - y1 * y1) - x * x) / (2 * pi * x); | |
| return [ | |
| x ? pi * (sign(x) * sqrt(A * A + 1) - A) : 0, | |
| halfPi * sin(2 * atan(y1)) | |
| ]; | |
| }; | |
| var vanDerGrinten3 = function() { | |
| return d3Geo.geoProjection(vanDerGrinten3Raw) | |
| .scale(79.4183); | |
| }; | |
| function vanDerGrinten4Raw(lambda, phi) { | |
| if (!phi) return [lambda, 0]; | |
| var phi0 = abs(phi); | |
| if (!lambda || phi0 === halfPi) return [0, phi]; | |
| var B = phi0 / halfPi, | |
| B2 = B * B, | |
| C = (8 * B - B2 * (B2 + 2) - 5) / (2 * B2 * (B - 1)), | |
| C2 = C * C, | |
| BC = B * C, | |
| B_C2 = B2 + C2 + 2 * BC, | |
| B_3C = B + 3 * C, | |
| lambda0 = lambda / halfPi, | |
| lambda1 = lambda0 + 1 / lambda0, | |
| D = sign(abs(lambda) - halfPi) * sqrt(lambda1 * lambda1 - 4), | |
| D2 = D * D, | |
| F = B_C2 * (B2 + C2 * D2 - 1) + (1 - B2) * (B2 * (B_3C * B_3C + 4 * C2) + 12 * BC * C2 + 4 * C2 * C2), | |
| x1 = (D * (B_C2 + C2 - 1) + 2 * sqrt(F)) / (4 * B_C2 + D2); | |
| return [ | |
| sign(lambda) * halfPi * x1, | |
| sign(phi) * halfPi * sqrt(1 + D * abs(x1) - x1 * x1) | |
| ]; | |
| } | |
| vanDerGrinten4Raw.invert = function(x, y) { | |
| var delta; | |
| if (!x || !y) return [x, y]; | |
| y /= pi; | |
| var x1 = sign(x) * x / halfPi, | |
| D = (x1 * x1 - 1 + 4 * y * y) / abs(x1), | |
| D2 = D * D, | |
| B = 2 * y, | |
| i = 50; | |
| do { | |
| var B2 = B * B, | |
| C = (8 * B - B2 * (B2 + 2) - 5) / (2 * B2 * (B - 1)), | |
| C_ = (3 * B - B2 * B - 10) / (2 * B2 * B), | |
| C2 = C * C, | |
| BC = B * C, | |
| B_C = B + C, | |
| B_C2 = B_C * B_C, | |
| B_3C = B + 3 * C, | |
| F = B_C2 * (B2 + C2 * D2 - 1) + (1 - B2) * (B2 * (B_3C * B_3C + 4 * C2) + C2 * (12 * BC + 4 * C2)), | |
| F_ = -2 * B_C * (4 * BC * C2 + (1 - 4 * B2 + 3 * B2 * B2) * (1 + C_) + C2 * (-6 + 14 * B2 - D2 + (-8 + 8 * B2 - 2 * D2) * C_) + BC * (-8 + 12 * B2 + (-10 + 10 * B2 - D2) * C_)), | |
| sqrtF = sqrt(F), | |
| f = D * (B_C2 + C2 - 1) + 2 * sqrtF - x1 * (4 * B_C2 + D2), | |
| f_ = D * (2 * C * C_ + 2 * B_C * (1 + C_)) + F_ / sqrtF - 8 * B_C * (D * (-1 + C2 + B_C2) + 2 * sqrtF) * (1 + C_) / (D2 + 4 * B_C2); | |
| B -= delta = f / f_; | |
| } while (delta > epsilon && --i > 0); | |
| return [ | |
| sign(x) * (sqrt(D * D + 4) + D) * pi / 4, | |
| halfPi * B | |
| ]; | |
| }; | |
| var vanDerGrinten4 = function() { | |
| return d3Geo.geoProjection(vanDerGrinten4Raw) | |
| .scale(127.16); | |
| }; | |
| var A = 4 * pi + 3 * sqrt(3); | |
| var B = 2 * sqrt(2 * pi * sqrt(3) / A); | |
| var wagner4Raw = mollweideBromleyRaw(B * sqrt(3) / pi, B, A / 6); | |
| var wagner4 = function() { | |
| return d3Geo.geoProjection(wagner4Raw) | |
| .scale(176.84); | |
| }; | |
| function wagner6Raw(lambda, phi) { | |
| return [lambda * sqrt(1 - 3 * phi * phi / (pi * pi)), phi]; | |
| } | |
| wagner6Raw.invert = function(x, y) { | |
| return [x / sqrt(1 - 3 * y * y / (pi * pi)), y]; | |
| }; | |
| var wagner6 = function() { | |
| return d3Geo.geoProjection(wagner6Raw) | |
| .scale(152.63); | |
| }; | |
| function wagner7Raw(lambda, phi) { | |
| var s = 0.90631 * sin(phi), | |
| c0 = sqrt(1 - s * s), | |
| c1 = sqrt(2 / (1 + c0 * cos(lambda /= 3))); | |
| return [ | |
| 2.66723 * c0 * c1 * sin(lambda), | |
| 1.24104 * s * c1 | |
| ]; | |
| } | |
| wagner7Raw.invert = function(x, y) { | |
| var t1 = x / 2.66723, | |
| t2 = y / 1.24104, | |
| p = sqrt(t1 * t1 + t2 * t2), | |
| c = 2 * asin(p / 2); | |
| return [ | |
| 3 * atan2(x * tan(c), 2.66723 * p), | |
| p && asin(y * sin(c) / (1.24104 * 0.90631 * p)) | |
| ]; | |
| }; | |
| var wagner7 = function() { | |
| return d3Geo.geoProjection(wagner7Raw) | |
| .scale(172.632); | |
| }; | |
| function wiechelRaw(lambda, phi) { | |
| var cosPhi = cos(phi), | |
| sinPhi = cos(lambda) * cosPhi, | |
| sin1_Phi = 1 - sinPhi, | |
| cosLambda = cos(lambda = atan2(sin(lambda) * cosPhi, -sin(phi))), | |
| sinLambda = sin(lambda); | |
| cosPhi = sqrt(1 - sinPhi * sinPhi); | |
| return [ | |
| sinLambda * cosPhi - cosLambda * sin1_Phi, | |
| -cosLambda * cosPhi - sinLambda * sin1_Phi | |
| ]; | |
| } | |
| wiechelRaw.invert = function(x, y) { | |
| var w = (x * x + y * y) / -2, | |
| k = sqrt(-w * (2 + w)), | |
| b = y * w + x * k, | |
| a = x * w - y * k, | |
| D = sqrt(a * a + b * b); | |
| return [ | |
| atan2(k * b, D * (1 + w)), | |
| D ? -asin(k * a / D) : 0 | |
| ]; | |
| }; | |
| var wiechel = function() { | |
| return d3Geo.geoProjection(wiechelRaw) | |
| .rotate([0, -90, 45]) | |
| .scale(124.75) | |
| .clipAngle(180 - 1e-3); | |
| }; | |
| function winkel3Raw(lambda, phi) { | |
| var coordinates = aitoffRaw(lambda, phi); | |
| return [ | |
| (coordinates[0] + lambda / halfPi) / 2, | |
| (coordinates[1] + phi) / 2 | |
| ]; | |
| } | |
| winkel3Raw.invert = function(x, y) { | |
| var lambda = x, phi = y, i = 25; | |
| do { | |
| var cosphi = cos(phi), | |
| sinphi = sin(phi), | |
| sin_2phi = sin(2 * phi), | |
| sin2phi = sinphi * sinphi, | |
| cos2phi = cosphi * cosphi, | |
| sinlambda = sin(lambda), | |
| coslambda_2 = cos(lambda / 2), | |
| sinlambda_2 = sin(lambda / 2), | |
| sin2lambda_2 = sinlambda_2 * sinlambda_2, | |
| C = 1 - cos2phi * coslambda_2 * coslambda_2, | |
| E = C ? acos(cosphi * coslambda_2) * sqrt(F = 1 / C) : F = 0, | |
| F, | |
| fx = 0.5 * (2 * E * cosphi * sinlambda_2 + lambda / halfPi) - x, | |
| fy = 0.5 * (E * sinphi + phi) - y, | |
| dxdlambda = 0.5 * F * (cos2phi * sin2lambda_2 + E * cosphi * coslambda_2 * sin2phi) + 0.5 / halfPi, | |
| dxdphi = F * (sinlambda * sin_2phi / 4 - E * sinphi * sinlambda_2), | |
| dydlambda = 0.125 * F * (sin_2phi * sinlambda_2 - E * sinphi * cos2phi * sinlambda), | |
| dydphi = 0.5 * F * (sin2phi * coslambda_2 + E * sin2lambda_2 * cosphi) + 0.5, | |
| denominator = dxdphi * dydlambda - dydphi * dxdlambda, | |
| dlambda = (fy * dxdphi - fx * dydphi) / denominator, | |
| dphi = (fx * dydlambda - fy * dxdlambda) / denominator; | |
| lambda -= dlambda, phi -= dphi; | |
| } while ((abs(dlambda) > epsilon || abs(dphi) > epsilon) && --i > 0); | |
| return [lambda, phi]; | |
| }; | |
| var winkel3 = function() { | |
| return d3Geo.geoProjection(winkel3Raw) | |
| .scale(158.837); | |
| }; | |
| exports.geoAiry = airy; | |
| exports.geoAiryRaw = airyRaw; | |
| exports.geoAitoff = aitoff; | |
| exports.geoAitoffRaw = aitoffRaw; | |
| exports.geoArmadillo = armadillo; | |
| exports.geoArmadilloRaw = armadilloRaw; | |
| exports.geoAugust = august; | |
| exports.geoAugustRaw = augustRaw; | |
| exports.geoBaker = baker; | |
| exports.geoBakerRaw = bakerRaw; | |
| exports.geoBerghaus = berghaus; | |
| exports.geoBerghausRaw = berghausRaw; | |
| exports.geoBertin1953 = bertin; | |
| exports.geoBertin1953Raw = bertin1953Raw; | |
| exports.geoBoggs = boggs; | |
| exports.geoBoggsRaw = boggsRaw; | |
| exports.geoBonne = bonne; | |
| exports.geoBonneRaw = bonneRaw; | |
| exports.geoBottomley = bottomley; | |
| exports.geoBottomleyRaw = bottomleyRaw; | |
| exports.geoBromley = bromley; | |
| exports.geoBromleyRaw = bromleyRaw; | |
| exports.geoChamberlin = chamberlin; | |
| exports.geoChamberlinRaw = chamberlinRaw; | |
| exports.geoChamberlinAfrica = chamberlinAfrica; | |
| exports.geoCollignon = collignon; | |
| exports.geoCollignonRaw = collignonRaw; | |
| exports.geoCox = cox; | |
| exports.geoCoxRaw = coxRaw; | |
| exports.geoCraig = craig; | |
| exports.geoCraigRaw = craigRaw; | |
| exports.geoCraster = craster; | |
| exports.geoCrasterRaw = crasterRaw; | |
| exports.geoCylindricalEqualArea = cylindricalEqualArea; | |
| exports.geoCylindricalEqualAreaRaw = cylindricalEqualAreaRaw; | |
| exports.geoCylindricalStereographic = cylindricalStereographic; | |
| exports.geoCylindricalStereographicRaw = cylindricalStereographicRaw; | |
| exports.geoEckert1 = eckert1; | |
| exports.geoEckert1Raw = eckert1Raw; | |
| exports.geoEckert2 = eckert2; | |
| exports.geoEckert2Raw = eckert2Raw; | |
| exports.geoEckert3 = eckert3; | |
| exports.geoEckert3Raw = eckert3Raw; | |
| exports.geoEckert4 = eckert4; | |
| exports.geoEckert4Raw = eckert4Raw; | |
| exports.geoEckert5 = eckert5; | |
| exports.geoEckert5Raw = eckert5Raw; | |
| exports.geoEckert6 = eckert6; | |
| exports.geoEckert6Raw = eckert6Raw; | |
| exports.geoEisenlohr = eisenlohr; | |
| exports.geoEisenlohrRaw = eisenlohrRaw; | |
| exports.geoFahey = fahey; | |
| exports.geoFaheyRaw = faheyRaw; | |
| exports.geoFoucaut = foucaut; | |
| exports.geoFoucautRaw = foucautRaw; | |
| exports.geoGilbert = gilbert; | |
| exports.geoGingery = gingery; | |
| exports.geoGingeryRaw = gingeryRaw; | |
| exports.geoGinzburg4 = ginzburg4; | |
| exports.geoGinzburg4Raw = ginzburg4Raw; | |
| exports.geoGinzburg5 = ginzburg5; | |
| exports.geoGinzburg5Raw = ginzburg5Raw; | |
| exports.geoGinzburg6 = ginzburg6; | |
| exports.geoGinzburg6Raw = ginzburg6Raw; | |
| exports.geoGinzburg8 = ginzburg8; | |
| exports.geoGinzburg8Raw = ginzburg8Raw; | |
| exports.geoGinzburg9 = ginzburg9; | |
| exports.geoGinzburg9Raw = ginzburg9Raw; | |
| exports.geoGringorten = gringorten; | |
| exports.geoGringortenRaw = gringortenRaw; | |
| exports.geoGuyou = guyou; | |
| exports.geoGuyouRaw = guyouRaw; | |
| exports.geoHammer = hammer; | |
| exports.geoHammerRaw = hammerRaw; | |
| exports.geoHammerRetroazimuthal = hammerRetroazimuthal; | |
| exports.geoHammerRetroazimuthalRaw = hammerRetroazimuthalRaw; | |
| exports.geoHealpix = healpix; | |
| exports.geoHealpixRaw = healpixRaw; | |
| exports.geoHill = hill; | |
| exports.geoHillRaw = hillRaw; | |
| exports.geoHomolosine = homolosine; | |
| exports.geoHomolosineRaw = homolosineRaw; | |
| exports.geoInterrupt = interrupt; | |
| exports.geoInterruptedBoggs = boggs$1; | |
| exports.geoInterruptedHomolosine = homolosine$1; | |
| exports.geoInterruptedMollweide = mollweide$1; | |
| exports.geoInterruptedMollweideHemispheres = mollweideHemispheres; | |
| exports.geoInterruptedSinuMollweide = sinuMollweide$1; | |
| exports.geoInterruptedSinusoidal = sinusoidal$1; | |
| exports.geoKavrayskiy7 = kavrayskiy7; | |
| exports.geoKavrayskiy7Raw = kavrayskiy7Raw; | |
| exports.geoLagrange = lagrange; | |
| exports.geoLagrangeRaw = lagrangeRaw; | |
| exports.geoLarrivee = larrivee; | |
| exports.geoLarriveeRaw = larriveeRaw; | |
| exports.geoLaskowski = laskowski; | |
| exports.geoLaskowskiRaw = laskowskiRaw; | |
| exports.geoLittrow = littrow; | |
| exports.geoLittrowRaw = littrowRaw; | |
| exports.geoLoximuthal = loximuthal; | |
| exports.geoLoximuthalRaw = loximuthalRaw; | |
| exports.geoMiller = miller; | |
| exports.geoMillerRaw = millerRaw; | |
| exports.geoModifiedStereographic = modifiedStereographic; | |
| exports.geoModifiedStereographicRaw = modifiedStereographicRaw; | |
| exports.geoModifiedStereographicAlaska = modifiedStereographicAlaska; | |
| exports.geoModifiedStereographicGs48 = modifiedStereographicGs48; | |
| exports.geoModifiedStereographicGs50 = modifiedStereographicGs50; | |
| exports.geoModifiedStereographicMiller = modifiedStereographicMiller; | |
| exports.geoModifiedStereographicLee = modifiedStereographicLee; | |
| exports.geoMollweide = mollweide; | |
| exports.geoMollweideRaw = mollweideRaw; | |
| exports.geoMtFlatPolarParabolic = mtFlatPolarParabolic; | |
| exports.geoMtFlatPolarParabolicRaw = mtFlatPolarParabolicRaw; | |
| exports.geoMtFlatPolarQuartic = mtFlatPolarQuartic; | |
| exports.geoMtFlatPolarQuarticRaw = mtFlatPolarQuarticRaw; | |
| exports.geoMtFlatPolarSinusoidal = mtFlatPolarSinusoidal; | |
| exports.geoMtFlatPolarSinusoidalRaw = mtFlatPolarSinusoidalRaw; | |
| exports.geoNaturalEarth = naturalEarth; | |
| exports.geoNaturalEarthRaw = naturalEarthRaw; | |
| exports.geoNaturalEarth2 = naturalEarth2; | |
| exports.geoNaturalEarth2Raw = naturalEarth2Raw; | |
| exports.geoNellHammer = nellHammer; | |
| exports.geoNellHammerRaw = nellHammerRaw; | |
| exports.geoPatterson = patterson; | |
| exports.geoPattersonRaw = pattersonRaw; | |
| exports.geoPolyconic = polyconic; | |
| exports.geoPolyconicRaw = polyconicRaw; | |
| exports.geoPolyhedral = polyhedral; | |
| exports.geoPolyhedralButterfly = butterfly; | |
| exports.geoPolyhedralCollignon = collignon$1; | |
| exports.geoPolyhedralLee = lee$1; | |
| exports.geoLeeRaw = leeRaw; | |
| exports.geoPolyhedralWaterman = waterman; | |
| exports.geoProject = index; | |
| exports.geoGringortenQuincuncial = gringorten$1; | |
| exports.geoPeirceQuincuncial = peirce; | |
| exports.geoPierceQuincuncial = peirce; | |
| exports.geoQuantize = quantize; | |
| exports.geoQuincuncial = quincuncial; | |
| exports.geoRectangularPolyconic = rectangularPolyconic; | |
| exports.geoRectangularPolyconicRaw = rectangularPolyconicRaw; | |
| exports.geoRobinson = robinson; | |
| exports.geoRobinsonRaw = robinsonRaw; | |
| exports.geoSatellite = satellite; | |
| exports.geoSatelliteRaw = satelliteRaw; | |
| exports.geoSinuMollweide = sinuMollweide; | |
| exports.geoSinuMollweideRaw = sinuMollweideRaw; | |
| exports.geoSinusoidal = sinusoidal; | |
| exports.geoSinusoidalRaw = sinusoidalRaw; | |
| exports.geoStitch = stitch; | |
| exports.geoTimes = times; | |
| exports.geoTimesRaw = timesRaw; | |
| exports.geoTwoPointAzimuthal = twoPointAzimuthal; | |
| exports.geoTwoPointAzimuthalRaw = twoPointAzimuthalRaw; | |
| exports.geoTwoPointAzimuthalUsa = twoPointAzimuthalUsa; | |
| exports.geoTwoPointEquidistant = twoPointEquidistant; | |
| exports.geoTwoPointEquidistantRaw = twoPointEquidistantRaw; | |
| exports.geoTwoPointEquidistantUsa = twoPointEquidistantUsa; | |
| exports.geoVanDerGrinten = vanDerGrinten; | |
| exports.geoVanDerGrintenRaw = vanDerGrintenRaw; | |
| exports.geoVanDerGrinten2 = vanDerGrinten2; | |
| exports.geoVanDerGrinten2Raw = vanDerGrinten2Raw; | |
| exports.geoVanDerGrinten3 = vanDerGrinten3; | |
| exports.geoVanDerGrinten3Raw = vanDerGrinten3Raw; | |
| exports.geoVanDerGrinten4 = vanDerGrinten4; | |
| exports.geoVanDerGrinten4Raw = vanDerGrinten4Raw; | |
| exports.geoWagner4 = wagner4; | |
| exports.geoWagner4Raw = wagner4Raw; | |
| exports.geoWagner6 = wagner6; | |
| exports.geoWagner6Raw = wagner6Raw; | |
| exports.geoWagner7 = wagner7; | |
| exports.geoWagner7Raw = wagner7Raw; | |
| exports.geoWiechel = wiechel; | |
| exports.geoWiechelRaw = wiechelRaw; | |
| exports.geoWinkel3 = winkel3; | |
| exports.geoWinkel3Raw = winkel3Raw; | |
| Object.defineProperty(exports, '__esModule', { value: true }); | |
| }))); |
| // https://d3js.org/d3-geo/ Version 1.6.4. Copyright 2017 Mike Bostock. | |
| (function (global, factory) { | |
| typeof exports === 'object' && typeof module !== 'undefined' ? factory(exports, require('d3-array')) : | |
| typeof define === 'function' && define.amd ? define(['exports', 'd3-array'], factory) : | |
| (factory((global.d3 = global.d3 || {}),global.d3)); | |
| }(this, function (exports,d3Array) { 'use strict'; | |
| // Adds floating point numbers with twice the normal precision. | |
| // Reference: J. R. Shewchuk, Adaptive Precision Floating-Point Arithmetic and | |
| // Fast Robust Geometric Predicates, Discrete & Computational Geometry 18(3) | |
| // 305–363 (1997). | |
| // Code adapted from GeographicLib by Charles F. F. Karney, | |
| // http://geographiclib.sourceforge.net/ | |
| function adder() { | |
| return new Adder; | |
| } | |
| function Adder() { | |
| this.reset(); | |
| } | |
| Adder.prototype = { | |
| constructor: Adder, | |
| reset: function() { | |
| this.s = // rounded value | |
| this.t = 0; // exact error | |
| }, | |
| add: function(y) { | |
| add(temp, y, this.t); | |
| add(this, temp.s, this.s); | |
| if (this.s) this.t += temp.t; | |
| else this.s = temp.t; | |
| }, | |
| valueOf: function() { | |
| return this.s; | |
| } | |
| }; | |
| var temp = new Adder; | |
| function add(adder, a, b) { | |
| var x = adder.s = a + b, | |
| bv = x - a, | |
| av = x - bv; | |
| adder.t = (a - av) + (b - bv); | |
| } | |
| var epsilon = 1e-6; | |
| var epsilon2 = 1e-12; | |
| var pi = Math.PI; | |
| var halfPi = pi / 2; | |
| var quarterPi = pi / 4; | |
| var tau = pi * 2; | |
| var degrees = 180 / pi; | |
| var radians = pi / 180; | |
| var abs = Math.abs; | |
| var atan = Math.atan; | |
| var atan2 = Math.atan2; | |
| var cos = Math.cos; | |
| var ceil = Math.ceil; | |
| var exp = Math.exp; | |
| var log = Math.log; | |
| var pow = Math.pow; | |
| var sin = Math.sin; | |
| var sign = Math.sign || function(x) { return x > 0 ? 1 : x < 0 ? -1 : 0; }; | |
| var sqrt = Math.sqrt; | |
| var tan = Math.tan; | |
| function acos(x) { | |
| return x > 1 ? 0 : x < -1 ? pi : Math.acos(x); | |
| } | |
| function asin(x) { | |
| return x > 1 ? halfPi : x < -1 ? -halfPi : Math.asin(x); | |
| } | |
| function haversin(x) { | |
| return (x = sin(x / 2)) * x; | |
| } | |
| function noop() {} | |
| function streamGeometry(geometry, stream) { | |
| if (geometry && streamGeometryType.hasOwnProperty(geometry.type)) { | |
| streamGeometryType[geometry.type](geometry, stream); | |
| } | |
| } | |
| var streamObjectType = { | |
| Feature: function(object, stream) { | |
| streamGeometry(object.geometry, stream); | |
| }, | |
| FeatureCollection: function(object, stream) { | |
| var features = object.features, i = -1, n = features.length; | |
| while (++i < n) streamGeometry(features[i].geometry, stream); | |
| } | |
| }; | |
| var streamGeometryType = { | |
| Sphere: function(object, stream) { | |
| stream.sphere(); | |
| }, | |
| Point: function(object, stream) { | |
| object = object.coordinates; | |
| stream.point(object[0], object[1], object[2]); | |
| }, | |
| MultiPoint: function(object, stream) { | |
| var coordinates = object.coordinates, i = -1, n = coordinates.length; | |
| while (++i < n) object = coordinates[i], stream.point(object[0], object[1], object[2]); | |
| }, | |
| LineString: function(object, stream) { | |
| streamLine(object.coordinates, stream, 0); | |
| }, | |
| MultiLineString: function(object, stream) { | |
| var coordinates = object.coordinates, i = -1, n = coordinates.length; | |
| while (++i < n) streamLine(coordinates[i], stream, 0); | |
| }, | |
| Polygon: function(object, stream) { | |
| streamPolygon(object.coordinates, stream); | |
| }, | |
| MultiPolygon: function(object, stream) { | |
| var coordinates = object.coordinates, i = -1, n = coordinates.length; | |
| while (++i < n) streamPolygon(coordinates[i], stream); | |
| }, | |
| GeometryCollection: function(object, stream) { | |
| var geometries = object.geometries, i = -1, n = geometries.length; | |
| while (++i < n) streamGeometry(geometries[i], stream); | |
| } | |
| }; | |
| function streamLine(coordinates, stream, closed) { | |
| var i = -1, n = coordinates.length - closed, coordinate; | |
| stream.lineStart(); | |
| while (++i < n) coordinate = coordinates[i], stream.point(coordinate[0], coordinate[1], coordinate[2]); | |
| stream.lineEnd(); | |
| } | |
| function streamPolygon(coordinates, stream) { | |
| var i = -1, n = coordinates.length; | |
| stream.polygonStart(); | |
| while (++i < n) streamLine(coordinates[i], stream, 1); | |
| stream.polygonEnd(); | |
| } | |
| function geoStream(object, stream) { | |
| if (object && streamObjectType.hasOwnProperty(object.type)) { | |
| streamObjectType[object.type](object, stream); | |
| } else { | |
| streamGeometry(object, stream); | |
| } | |
| } | |
| var areaRingSum = adder(); | |
| var areaSum = adder(); | |
| var lambda00; | |
| var phi00; | |
| var lambda0; | |
| var cosPhi0; | |
| var sinPhi0; | |
| var areaStream = { | |
| point: noop, | |
| lineStart: noop, | |
| lineEnd: noop, | |
| polygonStart: function() { | |
| areaRingSum.reset(); | |
| areaStream.lineStart = areaRingStart; | |
| areaStream.lineEnd = areaRingEnd; | |
| }, | |
| polygonEnd: function() { | |
| var areaRing = +areaRingSum; | |
| areaSum.add(areaRing < 0 ? tau + areaRing : areaRing); | |
| this.lineStart = this.lineEnd = this.point = noop; | |
| }, | |
| sphere: function() { | |
| areaSum.add(tau); | |
| } | |
| }; | |
| function areaRingStart() { | |
| areaStream.point = areaPointFirst; | |
| } | |
| function areaRingEnd() { | |
| areaPoint(lambda00, phi00); | |
| } | |
| function areaPointFirst(lambda, phi) { | |
| areaStream.point = areaPoint; | |
| lambda00 = lambda, phi00 = phi; | |
| lambda *= radians, phi *= radians; | |
| lambda0 = lambda, cosPhi0 = cos(phi = phi / 2 + quarterPi), sinPhi0 = sin(phi); | |
| } | |
| function areaPoint(lambda, phi) { | |
| lambda *= radians, phi *= radians; | |
| phi = phi / 2 + quarterPi; // half the angular distance from south pole | |
| // Spherical excess E for a spherical triangle with vertices: south pole, | |
| // previous point, current point. Uses a formula derived from Cagnoli’s | |
| // theorem. See Todhunter, Spherical Trig. (1871), Sec. 103, Eq. (2). | |
| var dLambda = lambda - lambda0, | |
| sdLambda = dLambda >= 0 ? 1 : -1, | |
| adLambda = sdLambda * dLambda, | |
| cosPhi = cos(phi), | |
| sinPhi = sin(phi), | |
| k = sinPhi0 * sinPhi, | |
| u = cosPhi0 * cosPhi + k * cos(adLambda), | |
| v = k * sdLambda * sin(adLambda); | |
| areaRingSum.add(atan2(v, u)); | |
| // Advance the previous points. | |
| lambda0 = lambda, cosPhi0 = cosPhi, sinPhi0 = sinPhi; | |
| } | |
| function area(object) { | |
| areaSum.reset(); | |
| geoStream(object, areaStream); | |
| return areaSum * 2; | |
| } | |
| function spherical(cartesian) { | |
| return [atan2(cartesian[1], cartesian[0]), asin(cartesian[2])]; | |
| } | |
| function cartesian(spherical) { | |
| var lambda = spherical[0], phi = spherical[1], cosPhi = cos(phi); | |
| return [cosPhi * cos(lambda), cosPhi * sin(lambda), sin(phi)]; | |
| } | |
| function cartesianDot(a, b) { | |
| return a[0] * b[0] + a[1] * b[1] + a[2] * b[2]; | |
| } | |
| function cartesianCross(a, b) { | |
| return [a[1] * b[2] - a[2] * b[1], a[2] * b[0] - a[0] * b[2], a[0] * b[1] - a[1] * b[0]]; | |
| } | |
| // TODO return a | |
| function cartesianAddInPlace(a, b) { | |
| a[0] += b[0], a[1] += b[1], a[2] += b[2]; | |
| } | |
| function cartesianScale(vector, k) { | |
| return [vector[0] * k, vector[1] * k, vector[2] * k]; | |
| } | |
| // TODO return d | |
| function cartesianNormalizeInPlace(d) { | |
| var l = sqrt(d[0] * d[0] + d[1] * d[1] + d[2] * d[2]); | |
| d[0] /= l, d[1] /= l, d[2] /= l; | |
| } | |
| function cartesianEqual(a, b) { | |
| var dx = b[0] - a[0], | |
| dy = b[1] - a[1], | |
| dz = b[2] - a[2]; | |
| return dx * dx + dy * dy + dz * dz < epsilon2 * epsilon2; | |
| } | |
| var lambda0$1; | |
| var phi0; | |
| var lambda1; | |
| var phi1; | |
| var lambda2; | |
| var lambda00$1; | |
| var phi00$1; | |
| var p0; | |
| var deltaSum = adder(); | |
| var ranges; | |
| var range$1; | |
| var boundsStream = { | |
| point: boundsPoint, | |
| lineStart: boundsLineStart, | |
| lineEnd: boundsLineEnd, | |
| polygonStart: function() { | |
| boundsStream.point = boundsRingPoint; | |
| boundsStream.lineStart = boundsRingStart; | |
| boundsStream.lineEnd = boundsRingEnd; | |
| deltaSum.reset(); | |
| areaStream.polygonStart(); | |
| }, | |
| polygonEnd: function() { | |
| areaStream.polygonEnd(); | |
| boundsStream.point = boundsPoint; | |
| boundsStream.lineStart = boundsLineStart; | |
| boundsStream.lineEnd = boundsLineEnd; | |
| if (areaRingSum < 0) lambda0$1 = -(lambda1 = 180), phi0 = -(phi1 = 90); | |
| else if (deltaSum > epsilon) phi1 = 90; | |
| else if (deltaSum < -epsilon) phi0 = -90; | |
| range$1[0] = lambda0$1, range$1[1] = lambda1; | |
| } | |
| }; | |
| function boundsPoint(lambda, phi) { | |
| ranges.push(range$1 = [lambda0$1 = lambda, lambda1 = lambda]); | |
| if (phi < phi0) phi0 = phi; | |
| if (phi > phi1) phi1 = phi; | |
| } | |
| function linePoint(lambda, phi) { | |
| var p = cartesian([lambda * radians, phi * radians]); | |
| if (p0) { | |
| var normal = cartesianCross(p0, p), | |
| equatorial = [normal[1], -normal[0], 0], | |
| inflection = cartesianCross(equatorial, normal); | |
| cartesianNormalizeInPlace(inflection); | |
| inflection = spherical(inflection); | |
| var delta = lambda - lambda2, | |
| sign = delta > 0 ? 1 : -1, | |
| lambdai = inflection[0] * degrees * sign, | |
| phii, | |
| antimeridian = abs(delta) > 180; | |
| if (antimeridian ^ (sign * lambda2 < lambdai && lambdai < sign * lambda)) { | |
| phii = inflection[1] * degrees; | |
| if (phii > phi1) phi1 = phii; | |
| } else if (lambdai = (lambdai + 360) % 360 - 180, antimeridian ^ (sign * lambda2 < lambdai && lambdai < sign * lambda)) { | |
| phii = -inflection[1] * degrees; | |
| if (phii < phi0) phi0 = phii; | |
| } else { | |
| if (phi < phi0) phi0 = phi; | |
| if (phi > phi1) phi1 = phi; | |
| } | |
| if (antimeridian) { | |
| if (lambda < lambda2) { | |
| if (angle(lambda0$1, lambda) > angle(lambda0$1, lambda1)) lambda1 = lambda; | |
| } else { | |
| if (angle(lambda, lambda1) > angle(lambda0$1, lambda1)) lambda0$1 = lambda; | |
| } | |
| } else { | |
| if (lambda1 >= lambda0$1) { | |
| if (lambda < lambda0$1) lambda0$1 = lambda; | |
| if (lambda > lambda1) lambda1 = lambda; | |
| } else { | |
| if (lambda > lambda2) { | |
| if (angle(lambda0$1, lambda) > angle(lambda0$1, lambda1)) lambda1 = lambda; | |
| } else { | |
| if (angle(lambda, lambda1) > angle(lambda0$1, lambda1)) lambda0$1 = lambda; | |
| } | |
| } | |
| } | |
| } else { | |
| ranges.push(range$1 = [lambda0$1 = lambda, lambda1 = lambda]); | |
| } | |
| if (phi < phi0) phi0 = phi; | |
| if (phi > phi1) phi1 = phi; | |
| p0 = p, lambda2 = lambda; | |
| } | |
| function boundsLineStart() { | |
| boundsStream.point = linePoint; | |
| } | |
| function boundsLineEnd() { | |
| range$1[0] = lambda0$1, range$1[1] = lambda1; | |
| boundsStream.point = boundsPoint; | |
| p0 = null; | |
| } | |
| function boundsRingPoint(lambda, phi) { | |
| if (p0) { | |
| var delta = lambda - lambda2; | |
| deltaSum.add(abs(delta) > 180 ? delta + (delta > 0 ? 360 : -360) : delta); | |
| } else { | |
| lambda00$1 = lambda, phi00$1 = phi; | |
| } | |
| areaStream.point(lambda, phi); | |
| linePoint(lambda, phi); | |
| } | |
| function boundsRingStart() { | |
| areaStream.lineStart(); | |
| } | |
| function boundsRingEnd() { | |
| boundsRingPoint(lambda00$1, phi00$1); | |
| areaStream.lineEnd(); | |
| if (abs(deltaSum) > epsilon) lambda0$1 = -(lambda1 = 180); | |
| range$1[0] = lambda0$1, range$1[1] = lambda1; | |
| p0 = null; | |
| } | |
| // Finds the left-right distance between two longitudes. | |
| // This is almost the same as (lambda1 - lambda0 + 360°) % 360°, except that we want | |
| // the distance between ±180° to be 360°. | |
| function angle(lambda0, lambda1) { | |
| return (lambda1 -= lambda0) < 0 ? lambda1 + 360 : lambda1; | |
| } | |
| function rangeCompare(a, b) { | |
| return a[0] - b[0]; | |
| } | |
| function rangeContains(range, x) { | |
| return range[0] <= range[1] ? range[0] <= x && x <= range[1] : x < range[0] || range[1] < x; | |
| } | |
| function bounds(feature) { | |
| var i, n, a, b, merged, deltaMax, delta; | |
| phi1 = lambda1 = -(lambda0$1 = phi0 = Infinity); | |
| ranges = []; | |
| geoStream(feature, boundsStream); | |
| // First, sort ranges by their minimum longitudes. | |
| if (n = ranges.length) { | |
| ranges.sort(rangeCompare); | |
| // Then, merge any ranges that overlap. | |
| for (i = 1, a = ranges[0], merged = [a]; i < n; ++i) { | |
| b = ranges[i]; | |
| if (rangeContains(a, b[0]) || rangeContains(a, b[1])) { | |
| if (angle(a[0], b[1]) > angle(a[0], a[1])) a[1] = b[1]; | |
| if (angle(b[0], a[1]) > angle(a[0], a[1])) a[0] = b[0]; | |
| } else { | |
| merged.push(a = b); | |
| } | |
| } | |
| // Finally, find the largest gap between the merged ranges. | |
| // The final bounding box will be the inverse of this gap. | |
| for (deltaMax = -Infinity, n = merged.length - 1, i = 0, a = merged[n]; i <= n; a = b, ++i) { | |
| b = merged[i]; | |
| if ((delta = angle(a[1], b[0])) > deltaMax) deltaMax = delta, lambda0$1 = b[0], lambda1 = a[1]; | |
| } | |
| } | |
| ranges = range$1 = null; | |
| return lambda0$1 === Infinity || phi0 === Infinity | |
| ? [[NaN, NaN], [NaN, NaN]] | |
| : [[lambda0$1, phi0], [lambda1, phi1]]; | |
| } | |
| var W0; | |
| var W1; | |
| var X0; | |
| var Y0; | |
| var Z0; | |
| var X1; | |
| var Y1; | |
| var Z1; | |
| var X2; | |
| var Y2; | |
| var Z2; | |
| var lambda00$2; | |
| var phi00$2; | |
| var x0; | |
| var y0; | |
| var z0; | |
| // previous point | |
| var centroidStream = { | |
| sphere: noop, | |
| point: centroidPoint, | |
| lineStart: centroidLineStart, | |
| lineEnd: centroidLineEnd, | |
| polygonStart: function() { | |
| centroidStream.lineStart = centroidRingStart; | |
| centroidStream.lineEnd = centroidRingEnd; | |
| }, | |
| polygonEnd: function() { | |
| centroidStream.lineStart = centroidLineStart; | |
| centroidStream.lineEnd = centroidLineEnd; | |
| } | |
| }; | |
| // Arithmetic mean of Cartesian vectors. | |
| function centroidPoint(lambda, phi) { | |
| lambda *= radians, phi *= radians; | |
| var cosPhi = cos(phi); | |
| centroidPointCartesian(cosPhi * cos(lambda), cosPhi * sin(lambda), sin(phi)); | |
| } | |
| function centroidPointCartesian(x, y, z) { | |
| ++W0; | |
| X0 += (x - X0) / W0; | |
| Y0 += (y - Y0) / W0; | |
| Z0 += (z - Z0) / W0; | |
| } | |
| function centroidLineStart() { | |
| centroidStream.point = centroidLinePointFirst; | |
| } | |
| function centroidLinePointFirst(lambda, phi) { | |
| lambda *= radians, phi *= radians; | |
| var cosPhi = cos(phi); | |
| x0 = cosPhi * cos(lambda); | |
| y0 = cosPhi * sin(lambda); | |
| z0 = sin(phi); | |
| centroidStream.point = centroidLinePoint; | |
| centroidPointCartesian(x0, y0, z0); | |
| } | |
| function centroidLinePoint(lambda, phi) { | |
| lambda *= radians, phi *= radians; | |
| var cosPhi = cos(phi), | |
| x = cosPhi * cos(lambda), | |
| y = cosPhi * sin(lambda), | |
| z = sin(phi), | |
| w = atan2(sqrt((w = y0 * z - z0 * y) * w + (w = z0 * x - x0 * z) * w + (w = x0 * y - y0 * x) * w), x0 * x + y0 * y + z0 * z); | |
| W1 += w; | |
| X1 += w * (x0 + (x0 = x)); | |
| Y1 += w * (y0 + (y0 = y)); | |
| Z1 += w * (z0 + (z0 = z)); | |
| centroidPointCartesian(x0, y0, z0); | |
| } | |
| function centroidLineEnd() { | |
| centroidStream.point = centroidPoint; | |
| } | |
| // See J. E. Brock, The Inertia Tensor for a Spherical Triangle, | |
| // J. Applied Mechanics 42, 239 (1975). | |
| function centroidRingStart() { | |
| centroidStream.point = centroidRingPointFirst; | |
| } | |
| function centroidRingEnd() { | |
| centroidRingPoint(lambda00$2, phi00$2); | |
| centroidStream.point = centroidPoint; | |
| } | |
| function centroidRingPointFirst(lambda, phi) { | |
| lambda00$2 = lambda, phi00$2 = phi; | |
| lambda *= radians, phi *= radians; | |
| centroidStream.point = centroidRingPoint; | |
| var cosPhi = cos(phi); | |
| x0 = cosPhi * cos(lambda); | |
| y0 = cosPhi * sin(lambda); | |
| z0 = sin(phi); | |
| centroidPointCartesian(x0, y0, z0); | |
| } | |
| function centroidRingPoint(lambda, phi) { | |
| lambda *= radians, phi *= radians; | |
| var cosPhi = cos(phi), | |
| x = cosPhi * cos(lambda), | |
| y = cosPhi * sin(lambda), | |
| z = sin(phi), | |
| cx = y0 * z - z0 * y, | |
| cy = z0 * x - x0 * z, | |
| cz = x0 * y - y0 * x, | |
| m = sqrt(cx * cx + cy * cy + cz * cz), | |
| w = asin(m), // line weight = angle | |
| v = m && -w / m; // area weight multiplier | |
| X2 += v * cx; | |
| Y2 += v * cy; | |
| Z2 += v * cz; | |
| W1 += w; | |
| X1 += w * (x0 + (x0 = x)); | |
| Y1 += w * (y0 + (y0 = y)); | |
| Z1 += w * (z0 + (z0 = z)); | |
| centroidPointCartesian(x0, y0, z0); | |
| } | |
| function centroid(object) { | |
| W0 = W1 = | |
| X0 = Y0 = Z0 = | |
| X1 = Y1 = Z1 = | |
| X2 = Y2 = Z2 = 0; | |
| geoStream(object, centroidStream); | |
| var x = X2, | |
| y = Y2, | |
| z = Z2, | |
| m = x * x + y * y + z * z; | |
| // If the area-weighted ccentroid is undefined, fall back to length-weighted ccentroid. | |
| if (m < epsilon2) { | |
| x = X1, y = Y1, z = Z1; | |
| // If the feature has zero length, fall back to arithmetic mean of point vectors. | |
| if (W1 < epsilon) x = X0, y = Y0, z = Z0; | |
| m = x * x + y * y + z * z; | |
| // If the feature still has an undefined ccentroid, then return. | |
| if (m < epsilon2) return [NaN, NaN]; | |
| } | |
| return [atan2(y, x) * degrees, asin(z / sqrt(m)) * degrees]; | |
| } | |
| function constant(x) { | |
| return function() { | |
| return x; | |
| }; | |
| } | |
| function compose(a, b) { | |
| function compose(x, y) { | |
| return x = a(x, y), b(x[0], x[1]); | |
| } | |
| if (a.invert && b.invert) compose.invert = function(x, y) { | |
| return x = b.invert(x, y), x && a.invert(x[0], x[1]); | |
| }; | |
| return compose; | |
| } | |
| function rotationIdentity(lambda, phi) { | |
| return [lambda > pi ? lambda - tau : lambda < -pi ? lambda + tau : lambda, phi]; | |
| } | |
| rotationIdentity.invert = rotationIdentity; | |
| function rotateRadians(deltaLambda, deltaPhi, deltaGamma) { | |
| return (deltaLambda %= tau) ? (deltaPhi || deltaGamma ? compose(rotationLambda(deltaLambda), rotationPhiGamma(deltaPhi, deltaGamma)) | |
| : rotationLambda(deltaLambda)) | |
| : (deltaPhi || deltaGamma ? rotationPhiGamma(deltaPhi, deltaGamma) | |
| : rotationIdentity); | |
| } | |
| function forwardRotationLambda(deltaLambda) { | |
| return function(lambda, phi) { | |
| return lambda += deltaLambda, [lambda > pi ? lambda - tau : lambda < -pi ? lambda + tau : lambda, phi]; | |
| }; | |
| } | |
| function rotationLambda(deltaLambda) { | |
| var rotation = forwardRotationLambda(deltaLambda); | |
| rotation.invert = forwardRotationLambda(-deltaLambda); | |
| return rotation; | |
| } | |
| function rotationPhiGamma(deltaPhi, deltaGamma) { | |
| var cosDeltaPhi = cos(deltaPhi), | |
| sinDeltaPhi = sin(deltaPhi), | |
| cosDeltaGamma = cos(deltaGamma), | |
| sinDeltaGamma = sin(deltaGamma); | |
| function rotation(lambda, phi) { | |
| var cosPhi = cos(phi), | |
| x = cos(lambda) * cosPhi, | |
| y = sin(lambda) * cosPhi, | |
| z = sin(phi), | |
| k = z * cosDeltaPhi + x * sinDeltaPhi; | |
| return [ | |
| atan2(y * cosDeltaGamma - k * sinDeltaGamma, x * cosDeltaPhi - z * sinDeltaPhi), | |
| asin(k * cosDeltaGamma + y * sinDeltaGamma) | |
| ]; | |
| } | |
| rotation.invert = function(lambda, phi) { | |
| var cosPhi = cos(phi), | |
| x = cos(lambda) * cosPhi, | |
| y = sin(lambda) * cosPhi, | |
| z = sin(phi), | |
| k = z * cosDeltaGamma - y * sinDeltaGamma; | |
| return [ | |
| atan2(y * cosDeltaGamma + z * sinDeltaGamma, x * cosDeltaPhi + k * sinDeltaPhi), | |
| asin(k * cosDeltaPhi - x * sinDeltaPhi) | |
| ]; | |
| }; | |
| return rotation; | |
| } | |
| function rotation(rotate) { | |
| rotate = rotateRadians(rotate[0] * radians, rotate[1] * radians, rotate.length > 2 ? rotate[2] * radians : 0); | |
| function forward(coordinates) { | |
| coordinates = rotate(coordinates[0] * radians, coordinates[1] * radians); | |
| return coordinates[0] *= degrees, coordinates[1] *= degrees, coordinates; | |
| } | |
| forward.invert = function(coordinates) { | |
| coordinates = rotate.invert(coordinates[0] * radians, coordinates[1] * radians); | |
| return coordinates[0] *= degrees, coordinates[1] *= degrees, coordinates; | |
| }; | |
| return forward; | |
| } | |
| // Generates a circle centered at [0°, 0°], with a given radius and precision. | |
| function circleStream(stream, radius, delta, direction, t0, t1) { | |
| if (!delta) return; | |
| var cosRadius = cos(radius), | |
| sinRadius = sin(radius), | |
| step = direction * delta; | |
| if (t0 == null) { | |
| t0 = radius + direction * tau; | |
| t1 = radius - step / 2; | |
| } else { | |
| t0 = circleRadius(cosRadius, t0); | |
| t1 = circleRadius(cosRadius, t1); | |
| if (direction > 0 ? t0 < t1 : t0 > t1) t0 += direction * tau; | |
| } | |
| for (var point, t = t0; direction > 0 ? t > t1 : t < t1; t -= step) { | |
| point = spherical([cosRadius, -sinRadius * cos(t), -sinRadius * sin(t)]); | |
| stream.point(point[0], point[1]); | |
| } | |
| } | |
| // Returns the signed angle of a cartesian point relative to [cosRadius, 0, 0]. | |
| function circleRadius(cosRadius, point) { | |
| point = cartesian(point), point[0] -= cosRadius; | |
| cartesianNormalizeInPlace(point); | |
| var radius = acos(-point[1]); | |
| return ((-point[2] < 0 ? -radius : radius) + tau - epsilon) % tau; | |
| } | |
| function circle() { | |
| var center = constant([0, 0]), | |
| radius = constant(90), | |
| precision = constant(6), | |
| ring, | |
| rotate, | |
| stream = {point: point}; | |
| function point(x, y) { | |
| ring.push(x = rotate(x, y)); | |
| x[0] *= degrees, x[1] *= degrees; | |
| } | |
| function circle() { | |
| var c = center.apply(this, arguments), | |
| r = radius.apply(this, arguments) * radians, | |
| p = precision.apply(this, arguments) * radians; | |
| ring = []; | |
| rotate = rotateRadians(-c[0] * radians, -c[1] * radians, 0).invert; | |
| circleStream(stream, r, p, 1); | |
| c = {type: "Polygon", coordinates: [ring]}; | |
| ring = rotate = null; | |
| return c; | |
| } | |
| circle.center = function(_) { | |
| return arguments.length ? (center = typeof _ === "function" ? _ : constant([+_[0], +_[1]]), circle) : center; | |
| }; | |
| circle.radius = function(_) { | |
| return arguments.length ? (radius = typeof _ === "function" ? _ : constant(+_), circle) : radius; | |
| }; | |
| circle.precision = function(_) { | |
| return arguments.length ? (precision = typeof _ === "function" ? _ : constant(+_), circle) : precision; | |
| }; | |
| return circle; | |
| } | |
| function clipBuffer() { | |
| var lines = [], | |
| line; | |
| return { | |
| point: function(x, y, i, t) { | |
| var point = [x, y]; | |
| // when called by clipPolygon, store index and t | |
| if (arguments.length > 2) { point.index = i; point.t = t; } | |
| line.push(point); | |
| }, | |
| lineStart: function() { | |
| lines.push(line = []); | |
| }, | |
| lineEnd: noop, | |
| rejoin: function() { | |
| if (lines.length > 1) lines.push(lines.pop().concat(lines.shift())); | |
| }, | |
| result: function() { | |
| var result = lines; | |
| lines = []; | |
| line = null; | |
| return result; | |
| } | |
| }; | |
| } | |
| function clipLine(a, b, x0, y0, x1, y1) { | |
| var ax = a[0], | |
| ay = a[1], | |
| bx = b[0], | |
| by = b[1], | |
| t0 = 0, | |
| t1 = 1, | |
| dx = bx - ax, | |
| dy = by - ay, | |
| r; | |
| r = x0 - ax; | |
| if (!dx && r > 0) return; | |
| r /= dx; | |
| if (dx < 0) { | |
| if (r < t0) return; | |
| if (r < t1) t1 = r; | |
| } else if (dx > 0) { | |
| if (r > t1) return; | |
| if (r > t0) t0 = r; | |
| } | |
| r = x1 - ax; | |
| if (!dx && r < 0) return; | |
| r /= dx; | |
| if (dx < 0) { | |
| if (r > t1) return; | |
| if (r > t0) t0 = r; | |
| } else if (dx > 0) { | |
| if (r < t0) return; | |
| if (r < t1) t1 = r; | |
| } | |
| r = y0 - ay; | |
| if (!dy && r > 0) return; | |
| r /= dy; | |
| if (dy < 0) { | |
| if (r < t0) return; | |
| if (r < t1) t1 = r; | |
| } else if (dy > 0) { | |
| if (r > t1) return; | |
| if (r > t0) t0 = r; | |
| } | |
| r = y1 - ay; | |
| if (!dy && r < 0) return; | |
| r /= dy; | |
| if (dy < 0) { | |
| if (r > t1) return; | |
| if (r > t0) t0 = r; | |
| } else if (dy > 0) { | |
| if (r < t0) return; | |
| if (r < t1) t1 = r; | |
| } | |
| if (t0 > 0) a[0] = ax + t0 * dx, a[1] = ay + t0 * dy; | |
| if (t1 < 1) b[0] = ax + t1 * dx, b[1] = ay + t1 * dy; | |
| return true; | |
| } | |
| function pointEqual(a, b) { | |
| return abs(a[0] - b[0]) < epsilon && abs(a[1] - b[1]) < epsilon; | |
| } | |
| function Intersection(point, points, other, entry) { | |
| this.x = point; | |
| this.z = points; | |
| this.o = other; // another intersection | |
| this.e = entry; // is an entry? | |
| this.v = false; // visited | |
| this.n = this.p = null; // next & previous | |
| } | |
| // A generalized polygon clipping algorithm: given a polygon that has been cut | |
| // into its visible line segments, and rejoins the segments by interpolating | |
| // along the clip edge. | |
| function clipRejoin(segments, compareIntersection, startInside, interpolate, stream) { | |
| var subject = [], | |
| clip = [], | |
| i, | |
| n; | |
| segments.forEach(function(segment) { | |
| if ((n = segment.length - 1) <= 0) return; | |
| var n, p0 = segment[0], p1 = segment[n], x; | |
| // If the first and last points of a segment are coincident, then treat as a | |
| // closed ring. TODO if all rings are closed, then the winding order of the | |
| // exterior ring should be checked. | |
| if (pointEqual(p0, p1)) { | |
| stream.lineStart(); | |
| for (i = 0; i < n; ++i) stream.point((p0 = segment[i])[0], p0[1]); | |
| stream.lineEnd(); | |
| return; | |
| } | |
| subject.push(x = new Intersection(p0, segment, null, true)); | |
| clip.push(x.o = new Intersection(p0, null, x, false)); | |
| subject.push(x = new Intersection(p1, segment, null, false)); | |
| clip.push(x.o = new Intersection(p1, null, x, true)); | |
| }); | |
| if (!subject.length) return; | |
| clip.sort(compareIntersection); | |
| link(subject); | |
| link(clip); | |
| for (i = 0, n = clip.length; i < n; ++i) { | |
| clip[i].e = startInside = !startInside; | |
| } | |
| var start = subject[0], | |
| points, | |
| point; | |
| while (1) { | |
| // Find first unvisited intersection. | |
| var current = start, | |
| isSubject = true; | |
| while (current.v) if ((current = current.n) === start) return; | |
| points = current.z; | |
| stream.lineStart(); | |
| do { | |
| current.v = current.o.v = true; | |
| if (current.e) { | |
| if (isSubject) { | |
| for (i = 0, n = points.length; i < n; ++i) stream.point((point = points[i])[0], point[1]); | |
| } else { | |
| interpolate(current.x, current.n.x, 1, stream); | |
| } | |
| current = current.n; | |
| } else { | |
| if (isSubject) { | |
| points = current.p.z; | |
| for (i = points.length - 1; i >= 0; --i) stream.point((point = points[i])[0], point[1]); | |
| } else { | |
| interpolate(current.x, current.p.x, -1, stream); | |
| } | |
| current = current.p; | |
| } | |
| current = current.o; | |
| points = current.z; | |
| isSubject = !isSubject; | |
| } while (!current.v); | |
| stream.lineEnd(); | |
| } | |
| } | |
| function link(array) { | |
| if (!(n = array.length)) return; | |
| var n, | |
| i = 0, | |
| a = array[0], | |
| b; | |
| while (++i < n) { | |
| a.n = b = array[i]; | |
| b.p = a; | |
| a = b; | |
| } | |
| a.n = b = array[0]; | |
| b.p = a; | |
| } | |
| var clipMax = 1e9; | |
| var clipMin = -clipMax; | |
| // TODO Use d3-polygon’s polygonContains here for the ring check? | |
| // TODO Eliminate duplicate buffering in clipBuffer and polygon.push? | |
| function clipExtent(x0, y0, x1, y1) { | |
| function visible(x, y) { | |
| return x0 <= x && x <= x1 && y0 <= y && y <= y1; | |
| } | |
| function interpolate(from, to, direction, stream) { | |
| var a = 0, a1 = 0; | |
| if (from == null | |
| || (a = corner(from, direction)) !== (a1 = corner(to, direction)) | |
| || comparePoint(from, to) < 0 ^ direction > 0) { | |
| do stream.point(a === 0 || a === 3 ? x0 : x1, a > 1 ? y1 : y0); | |
| while ((a = (a + direction + 4) % 4) !== a1); | |
| } else { | |
| stream.point(to[0], to[1]); | |
| } | |
| } | |
| function corner(p, direction) { | |
| return abs(p[0] - x0) < epsilon ? direction > 0 ? 0 : 3 | |
| : abs(p[0] - x1) < epsilon ? direction > 0 ? 2 : 1 | |
| : abs(p[1] - y0) < epsilon ? direction > 0 ? 1 : 0 | |
| : direction > 0 ? 3 : 2; // abs(p[1] - y1) < epsilon | |
| } | |
| function compareIntersection(a, b) { | |
| return comparePoint(a.x, b.x); | |
| } | |
| function comparePoint(a, b) { | |
| var ca = corner(a, 1), | |
| cb = corner(b, 1); | |
| return ca !== cb ? ca - cb | |
| : ca === 0 ? b[1] - a[1] | |
| : ca === 1 ? a[0] - b[0] | |
| : ca === 2 ? a[1] - b[1] | |
| : b[0] - a[0]; | |
| } | |
| return function(stream) { | |
| var activeStream = stream, | |
| bufferStream = clipBuffer(), | |
| segments, | |
| polygon, | |
| ring, | |
| x__, y__, v__, // first point | |
| x_, y_, v_, // previous point | |
| first, | |
| clean; | |
| var clipStream = { | |
| point: point, | |
| lineStart: lineStart, | |
| lineEnd: lineEnd, | |
| polygonStart: polygonStart, | |
| polygonEnd: polygonEnd | |
| }; | |
| function point(x, y) { | |
| if (visible(x, y)) activeStream.point(x, y); | |
| } | |
| function polygonInside() { | |
| var winding = 0; | |
| for (var i = 0, n = polygon.length; i < n; ++i) { | |
| for (var ring = polygon[i], j = 1, m = ring.length, point = ring[0], a0, a1, b0 = point[0], b1 = point[1]; j < m; ++j) { | |
| a0 = b0, a1 = b1, point = ring[j], b0 = point[0], b1 = point[1]; | |
| if (a1 <= y1) { if (b1 > y1 && (b0 - a0) * (y1 - a1) > (b1 - a1) * (x0 - a0)) ++winding; } | |
| else { if (b1 <= y1 && (b0 - a0) * (y1 - a1) < (b1 - a1) * (x0 - a0)) --winding; } | |
| } | |
| } | |
| return winding; | |
| } | |
| // Buffer geometry within a polygon and then clip it en masse. | |
| function polygonStart() { | |
| activeStream = bufferStream, segments = [], polygon = [], clean = true; | |
| } | |
| function polygonEnd() { | |
| var startInside = polygonInside(), | |
| cleanInside = clean && startInside, | |
| visible = (segments = d3Array.merge(segments)).length; | |
| if (cleanInside || visible) { | |
| stream.polygonStart(); | |
| if (cleanInside) { | |
| stream.lineStart(); | |
| interpolate(null, null, 1, stream); | |
| stream.lineEnd(); | |
| } | |
| if (visible) { | |
| clipRejoin(segments, compareIntersection, startInside, interpolate, stream); | |
| } | |
| stream.polygonEnd(); | |
| } | |
| activeStream = stream, segments = polygon = ring = null; | |
| } | |
| function lineStart() { | |
| clipStream.point = linePoint; | |
| if (polygon) polygon.push(ring = []); | |
| first = true; | |
| v_ = false; | |
| x_ = y_ = NaN; | |
| } | |
| // TODO rather than special-case polygons, simply handle them separately. | |
| // Ideally, coincident intersection points should be jittered to avoid | |
| // clipping issues. | |
| function lineEnd() { | |
| if (segments) { | |
| linePoint(x__, y__); | |
| if (v__ && v_) bufferStream.rejoin(); | |
| segments.push(bufferStream.result()); | |
| } | |
| clipStream.point = point; | |
| if (v_) activeStream.lineEnd(); | |
| } | |
| function linePoint(x, y) { | |
| var v = visible(x, y); | |
| if (polygon) ring.push([x, y]); | |
| if (first) { | |
| x__ = x, y__ = y, v__ = v; | |
| first = false; | |
| if (v) { | |
| activeStream.lineStart(); | |
| activeStream.point(x, y); | |
| } | |
| } else { | |
| if (v && v_) activeStream.point(x, y); | |
| else { | |
| var a = [x_ = Math.max(clipMin, Math.min(clipMax, x_)), y_ = Math.max(clipMin, Math.min(clipMax, y_))], | |
| b = [x = Math.max(clipMin, Math.min(clipMax, x)), y = Math.max(clipMin, Math.min(clipMax, y))]; | |
| if (clipLine(a, b, x0, y0, x1, y1)) { | |
| if (!v_) { | |
| activeStream.lineStart(); | |
| activeStream.point(a[0], a[1]); | |
| } | |
| activeStream.point(b[0], b[1]); | |
| if (!v) activeStream.lineEnd(); | |
| clean = false; | |
| } else if (v) { | |
| activeStream.lineStart(); | |
| activeStream.point(x, y); | |
| clean = false; | |
| } | |
| } | |
| } | |
| x_ = x, y_ = y, v_ = v; | |
| } | |
| return clipStream; | |
| }; | |
| } | |
| function extent() { | |
| var x0 = 0, | |
| y0 = 0, | |
| x1 = 960, | |
| y1 = 500, | |
| cache, | |
| cacheStream, | |
| clip; | |
| return clip = { | |
| stream: function(stream) { | |
| return cache && cacheStream === stream ? cache : cache = clipExtent(x0, y0, x1, y1)(cacheStream = stream); | |
| }, | |
| extent: function(_) { | |
| return arguments.length ? (x0 = +_[0][0], y0 = +_[0][1], x1 = +_[1][0], y1 = +_[1][1], cache = cacheStream = null, clip) : [[x0, y0], [x1, y1]]; | |
| } | |
| }; | |
| } | |
| var sum = adder(); | |
| function polygonContains(polygon, point) { | |
| var lambda = point[0], | |
| phi = point[1], | |
| normal = [sin(lambda), -cos(lambda), 0], | |
| angle = 0, | |
| winding = 0; | |
| sum.reset(); | |
| for (var i = 0, n = polygon.length; i < n; ++i) { | |
| if (!(m = (ring = polygon[i]).length)) continue; | |
| var ring, | |
| m, | |
| point0 = ring[m - 1], | |
| lambda0 = point0[0], | |
| phi0 = point0[1] / 2 + quarterPi, | |
| sinPhi0 = sin(phi0), | |
| cosPhi0 = cos(phi0); | |
| for (var j = 0; j < m; ++j, lambda0 = lambda1, sinPhi0 = sinPhi1, cosPhi0 = cosPhi1, point0 = point1) { | |
| var point1 = ring[j], | |
| lambda1 = point1[0], | |
| phi1 = point1[1] / 2 + quarterPi, | |
| sinPhi1 = sin(phi1), | |
| cosPhi1 = cos(phi1), | |
| delta = lambda1 - lambda0, | |
| sign = delta >= 0 ? 1 : -1, | |
| absDelta = sign * delta, | |
| antimeridian = absDelta > pi, | |
| k = sinPhi0 * sinPhi1; | |
| sum.add(atan2(k * sign * sin(absDelta), cosPhi0 * cosPhi1 + k * cos(absDelta))); | |
| angle += antimeridian ? delta + sign * tau : delta; | |
| // Are the longitudes either side of the point’s meridian (lambda), | |
| // and are the latitudes smaller than the parallel (phi)? | |
| if (antimeridian ^ lambda0 >= lambda ^ lambda1 >= lambda) { | |
| var arc = cartesianCross(cartesian(point0), cartesian(point1)); | |
| cartesianNormalizeInPlace(arc); | |
| var intersection = cartesianCross(normal, arc); | |
| cartesianNormalizeInPlace(intersection); | |
| var phiArc = (antimeridian ^ delta >= 0 ? -1 : 1) * asin(intersection[2]); | |
| if (phi > phiArc || phi === phiArc && (arc[0] || arc[1])) { | |
| winding += antimeridian ^ delta >= 0 ? 1 : -1; | |
| } | |
| } | |
| } | |
| } | |
| // First, determine whether the South pole is inside or outside: | |
| // | |
| // It is inside if: | |
| // * the polygon winds around it in a clockwise direction. | |
| // * the polygon does not (cumulatively) wind around it, but has a negative | |
| // (counter-clockwise) area. | |
| // | |
| // Second, count the (signed) number of times a segment crosses a lambda | |
| // from the point to the South pole. If it is zero, then the point is the | |
| // same side as the South pole. | |
| return (angle < -epsilon || angle < epsilon && sum < -epsilon) ^ (winding & 1); | |
| } | |
| var lengthSum = adder(); | |
| var lambda0$2; | |
| var sinPhi0$1; | |
| var cosPhi0$1; | |
| var lengthStream = { | |
| sphere: noop, | |
| point: noop, | |
| lineStart: lengthLineStart, | |
| lineEnd: noop, | |
| polygonStart: noop, | |
| polygonEnd: noop | |
| }; | |
| function lengthLineStart() { | |
| lengthStream.point = lengthPointFirst; | |
| lengthStream.lineEnd = lengthLineEnd; | |
| } | |
| function lengthLineEnd() { | |
| lengthStream.point = lengthStream.lineEnd = noop; | |
| } | |
| function lengthPointFirst(lambda, phi) { | |
| lambda *= radians, phi *= radians; | |
| lambda0$2 = lambda, sinPhi0$1 = sin(phi), cosPhi0$1 = cos(phi); | |
| lengthStream.point = lengthPoint; | |
| } | |
| function lengthPoint(lambda, phi) { | |
| lambda *= radians, phi *= radians; | |
| var sinPhi = sin(phi), | |
| cosPhi = cos(phi), | |
| delta = abs(lambda - lambda0$2), | |
| cosDelta = cos(delta), | |
| sinDelta = sin(delta), | |
| x = cosPhi * sinDelta, | |
| y = cosPhi0$1 * sinPhi - sinPhi0$1 * cosPhi * cosDelta, | |
| z = sinPhi0$1 * sinPhi + cosPhi0$1 * cosPhi * cosDelta; | |
| lengthSum.add(atan2(sqrt(x * x + y * y), z)); | |
| lambda0$2 = lambda, sinPhi0$1 = sinPhi, cosPhi0$1 = cosPhi; | |
| } | |
| function length(object) { | |
| lengthSum.reset(); | |
| geoStream(object, lengthStream); | |
| return +lengthSum; | |
| } | |
| var coordinates = [null, null]; | |
| var object = {type: "LineString", coordinates: coordinates}; | |
| function distance(a, b) { | |
| coordinates[0] = a; | |
| coordinates[1] = b; | |
| return length(object); | |
| } | |
| var containsObjectType = { | |
| Feature: function(object, point) { | |
| return containsGeometry(object.geometry, point); | |
| }, | |
| FeatureCollection: function(object, point) { | |
| var features = object.features, i = -1, n = features.length; | |
| while (++i < n) if (containsGeometry(features[i].geometry, point)) return true; | |
| return false; | |
| } | |
| }; | |
| var containsGeometryType = { | |
| Sphere: function() { | |
| return true; | |
| }, | |
| Point: function(object, point) { | |
| return containsPoint(object.coordinates, point); | |
| }, | |
| MultiPoint: function(object, point) { | |
| var coordinates = object.coordinates, i = -1, n = coordinates.length; | |
| while (++i < n) if (containsPoint(coordinates[i], point)) return true; | |
| return false; | |
| }, | |
| LineString: function(object, point) { | |
| return containsLine(object.coordinates, point); | |
| }, | |
| MultiLineString: function(object, point) { | |
| var coordinates = object.coordinates, i = -1, n = coordinates.length; | |
| while (++i < n) if (containsLine(coordinates[i], point)) return true; | |
| return false; | |
| }, | |
| Polygon: function(object, point) { | |
| return containsPolygon(object.coordinates, point); | |
| }, | |
| MultiPolygon: function(object, point) { | |
| var coordinates = object.coordinates, i = -1, n = coordinates.length; | |
| while (++i < n) if (containsPolygon(coordinates[i], point)) return true; | |
| return false; | |
| }, | |
| GeometryCollection: function(object, point) { | |
| var geometries = object.geometries, i = -1, n = geometries.length; | |
| while (++i < n) if (containsGeometry(geometries[i], point)) return true; | |
| return false; | |
| } | |
| }; | |
| function containsGeometry(geometry, point) { | |
| return geometry && containsGeometryType.hasOwnProperty(geometry.type) | |
| ? containsGeometryType[geometry.type](geometry, point) | |
| : false; | |
| } | |
| function containsPoint(coordinates, point) { | |
| return distance(coordinates, point) === 0; | |
| } | |
| function containsLine(coordinates, point) { | |
| var ab = distance(coordinates[0], coordinates[1]), | |
| ao = distance(coordinates[0], point), | |
| ob = distance(point, coordinates[1]); | |
| return ao + ob <= ab + epsilon; | |
| } | |
| function containsPolygon(coordinates, point) { | |
| return !!polygonContains(coordinates.map(ringRadians), pointRadians(point)); | |
| } | |
| function ringRadians(ring) { | |
| return ring = ring.map(pointRadians), ring.pop(), ring; | |
| } | |
| function pointRadians(point) { | |
| return [point[0] * radians, point[1] * radians]; | |
| } | |
| function contains(object, point) { | |
| return (object && containsObjectType.hasOwnProperty(object.type) | |
| ? containsObjectType[object.type] | |
| : containsGeometry)(object, point); | |
| } | |
| function graticuleX(y0, y1, dy) { | |
| var y = d3Array.range(y0, y1 - epsilon, dy).concat(y1); | |
| return function(x) { return y.map(function(y) { return [x, y]; }); }; | |
| } | |
| function graticuleY(x0, x1, dx) { | |
| var x = d3Array.range(x0, x1 - epsilon, dx).concat(x1); | |
| return function(y) { return x.map(function(x) { return [x, y]; }); }; | |
| } | |
| function graticule() { | |
| var x1, x0, X1, X0, | |
| y1, y0, Y1, Y0, | |
| dx = 10, dy = dx, DX = 90, DY = 360, | |
| x, y, X, Y, | |
| precision = 2.5; | |
| function graticule() { | |
| return {type: "MultiLineString", coordinates: lines()}; | |
| } | |
| function lines() { | |
| return d3Array.range(ceil(X0 / DX) * DX, X1, DX).map(X) | |
| .concat(d3Array.range(ceil(Y0 / DY) * DY, Y1, DY).map(Y)) | |
| .concat(d3Array.range(ceil(x0 / dx) * dx, x1, dx).filter(function(x) { return abs(x % DX) > epsilon; }).map(x)) | |
| .concat(d3Array.range(ceil(y0 / dy) * dy, y1, dy).filter(function(y) { return abs(y % DY) > epsilon; }).map(y)); | |
| } | |
| graticule.lines = function() { | |
| return lines().map(function(coordinates) { return {type: "LineString", coordinates: coordinates}; }); | |
| }; | |
| graticule.outline = function() { | |
| return { | |
| type: "Polygon", | |
| coordinates: [ | |
| X(X0).concat( | |
| Y(Y1).slice(1), | |
| X(X1).reverse().slice(1), | |
| Y(Y0).reverse().slice(1)) | |
| ] | |
| }; | |
| }; | |
| graticule.extent = function(_) { | |
| if (!arguments.length) return graticule.extentMinor(); | |
| return graticule.extentMajor(_).extentMinor(_); | |
| }; | |
| graticule.extentMajor = function(_) { | |
| if (!arguments.length) return [[X0, Y0], [X1, Y1]]; | |
| X0 = +_[0][0], X1 = +_[1][0]; | |
| Y0 = +_[0][1], Y1 = +_[1][1]; | |
| if (X0 > X1) _ = X0, X0 = X1, X1 = _; | |
| if (Y0 > Y1) _ = Y0, Y0 = Y1, Y1 = _; | |
| return graticule.precision(precision); | |
| }; | |
| graticule.extentMinor = function(_) { | |
| if (!arguments.length) return [[x0, y0], [x1, y1]]; | |
| x0 = +_[0][0], x1 = +_[1][0]; | |
| y0 = +_[0][1], y1 = +_[1][1]; | |
| if (x0 > x1) _ = x0, x0 = x1, x1 = _; | |
| if (y0 > y1) _ = y0, y0 = y1, y1 = _; | |
| return graticule.precision(precision); | |
| }; | |
| graticule.step = function(_) { | |
| if (!arguments.length) return graticule.stepMinor(); | |
| return graticule.stepMajor(_).stepMinor(_); | |
| }; | |
| graticule.stepMajor = function(_) { | |
| if (!arguments.length) return [DX, DY]; | |
| DX = +_[0], DY = +_[1]; | |
| return graticule; | |
| }; | |
| graticule.stepMinor = function(_) { | |
| if (!arguments.length) return [dx, dy]; | |
| dx = +_[0], dy = +_[1]; | |
| return graticule; | |
| }; | |
| graticule.precision = function(_) { | |
| if (!arguments.length) return precision; | |
| precision = +_; | |
| x = graticuleX(y0, y1, 90); | |
| y = graticuleY(x0, x1, precision); | |
| X = graticuleX(Y0, Y1, 90); | |
| Y = graticuleY(X0, X1, precision); | |
| return graticule; | |
| }; | |
| return graticule | |
| .extentMajor([[-180, -90 + epsilon], [180, 90 - epsilon]]) | |
| .extentMinor([[-180, -80 - epsilon], [180, 80 + epsilon]]); | |
| } | |
| function graticule10() { | |
| return graticule()(); | |
| } | |
| function interpolate(a, b) { | |
| var x0 = a[0] * radians, | |
| y0 = a[1] * radians, | |
| x1 = b[0] * radians, | |
| y1 = b[1] * radians, | |
| cy0 = cos(y0), | |
| sy0 = sin(y0), | |
| cy1 = cos(y1), | |
| sy1 = sin(y1), | |
| kx0 = cy0 * cos(x0), | |
| ky0 = cy0 * sin(x0), | |
| kx1 = cy1 * cos(x1), | |
| ky1 = cy1 * sin(x1), | |
| d = 2 * asin(sqrt(haversin(y1 - y0) + cy0 * cy1 * haversin(x1 - x0))), | |
| k = sin(d); | |
| var interpolate = d ? function(t) { | |
| var B = sin(t *= d) / k, | |
| A = sin(d - t) / k, | |
| x = A * kx0 + B * kx1, | |
| y = A * ky0 + B * ky1, | |
| z = A * sy0 + B * sy1; | |
| return [ | |
| atan2(y, x) * degrees, | |
| atan2(z, sqrt(x * x + y * y)) * degrees | |
| ]; | |
| } : function() { | |
| return [x0 * degrees, y0 * degrees]; | |
| }; | |
| interpolate.distance = d; | |
| return interpolate; | |
| } | |
| function identity(x) { | |
| return x; | |
| } | |
| var areaSum$1 = adder(); | |
| var areaRingSum$1 = adder(); | |
| var x00; | |
| var y00; | |
| var x0$1; | |
| var y0$1; | |
| var areaStream$1 = { | |
| point: noop, | |
| lineStart: noop, | |
| lineEnd: noop, | |
| polygonStart: function() { | |
| areaStream$1.lineStart = areaRingStart$1; | |
| areaStream$1.lineEnd = areaRingEnd$1; | |
| }, | |
| polygonEnd: function() { | |
| areaStream$1.lineStart = areaStream$1.lineEnd = areaStream$1.point = noop; | |
| areaSum$1.add(abs(areaRingSum$1)); | |
| areaRingSum$1.reset(); | |
| }, | |
| result: function() { | |
| var area = areaSum$1 / 2; | |
| areaSum$1.reset(); | |
| return area; | |
| } | |
| }; | |
| function areaRingStart$1() { | |
| areaStream$1.point = areaPointFirst$1; | |
| } | |
| function areaPointFirst$1(x, y) { | |
| areaStream$1.point = areaPoint$1; | |
| x00 = x0$1 = x, y00 = y0$1 = y; | |
| } | |
| function areaPoint$1(x, y) { | |
| areaRingSum$1.add(y0$1 * x - x0$1 * y); | |
| x0$1 = x, y0$1 = y; | |
| } | |
| function areaRingEnd$1() { | |
| areaPoint$1(x00, y00); | |
| } | |
| var x0$2 = Infinity; | |
| var y0$2 = x0$2; | |
| var x1 = -x0$2; | |
| var y1 = x1; | |
| var boundsStream$1 = { | |
| point: boundsPoint$1, | |
| lineStart: noop, | |
| lineEnd: noop, | |
| polygonStart: noop, | |
| polygonEnd: noop, | |
| result: function() { | |
| var bounds = [[x0$2, y0$2], [x1, y1]]; | |
| x1 = y1 = -(y0$2 = x0$2 = Infinity); | |
| return bounds; | |
| } | |
| }; | |
| function boundsPoint$1(x, y) { | |
| if (x < x0$2) x0$2 = x; | |
| if (x > x1) x1 = x; | |
| if (y < y0$2) y0$2 = y; | |
| if (y > y1) y1 = y; | |
| } | |
| var X0$1 = 0; | |
| var Y0$1 = 0; | |
| var Z0$1 = 0; | |
| var X1$1 = 0; | |
| var Y1$1 = 0; | |
| var Z1$1 = 0; | |
| var X2$1 = 0; | |
| var Y2$1 = 0; | |
| var Z2$1 = 0; | |
| var x00$1; | |
| var y00$1; | |
| var x0$3; | |
| var y0$3; | |
| var centroidStream$1 = { | |
| point: centroidPoint$1, | |
| lineStart: centroidLineStart$1, | |
| lineEnd: centroidLineEnd$1, | |
| polygonStart: function() { | |
| centroidStream$1.lineStart = centroidRingStart$1; | |
| centroidStream$1.lineEnd = centroidRingEnd$1; | |
| }, | |
| polygonEnd: function() { | |
| centroidStream$1.point = centroidPoint$1; | |
| centroidStream$1.lineStart = centroidLineStart$1; | |
| centroidStream$1.lineEnd = centroidLineEnd$1; | |
| }, | |
| result: function() { | |
| var centroid = Z2$1 ? [X2$1 / Z2$1, Y2$1 / Z2$1] | |
| : Z1$1 ? [X1$1 / Z1$1, Y1$1 / Z1$1] | |
| : Z0$1 ? [X0$1 / Z0$1, Y0$1 / Z0$1] | |
| : [NaN, NaN]; | |
| X0$1 = Y0$1 = Z0$1 = | |
| X1$1 = Y1$1 = Z1$1 = | |
| X2$1 = Y2$1 = Z2$1 = 0; | |
| return centroid; | |
| } | |
| }; | |
| function centroidPoint$1(x, y) { | |
| X0$1 += x; | |
| Y0$1 += y; | |
| ++Z0$1; | |
| } | |
| function centroidLineStart$1() { | |
| centroidStream$1.point = centroidPointFirstLine; | |
| } | |
| function centroidPointFirstLine(x, y) { | |
| centroidStream$1.point = centroidPointLine; | |
| centroidPoint$1(x0$3 = x, y0$3 = y); | |
| } | |
| function centroidPointLine(x, y) { | |
| var dx = x - x0$3, dy = y - y0$3, z = sqrt(dx * dx + dy * dy); | |
| X1$1 += z * (x0$3 + x) / 2; | |
| Y1$1 += z * (y0$3 + y) / 2; | |
| Z1$1 += z; | |
| centroidPoint$1(x0$3 = x, y0$3 = y); | |
| } | |
| function centroidLineEnd$1() { | |
| centroidStream$1.point = centroidPoint$1; | |
| } | |
| function centroidRingStart$1() { | |
| centroidStream$1.point = centroidPointFirstRing; | |
| } | |
| function centroidRingEnd$1() { | |
| centroidPointRing(x00$1, y00$1); | |
| } | |
| function centroidPointFirstRing(x, y) { | |
| centroidStream$1.point = centroidPointRing; | |
| centroidPoint$1(x00$1 = x0$3 = x, y00$1 = y0$3 = y); | |
| } | |
| function centroidPointRing(x, y) { | |
| var dx = x - x0$3, | |
| dy = y - y0$3, | |
| z = sqrt(dx * dx + dy * dy); | |
| X1$1 += z * (x0$3 + x) / 2; | |
| Y1$1 += z * (y0$3 + y) / 2; | |
| Z1$1 += z; | |
| z = y0$3 * x - x0$3 * y; | |
| X2$1 += z * (x0$3 + x); | |
| Y2$1 += z * (y0$3 + y); | |
| Z2$1 += z * 3; | |
| centroidPoint$1(x0$3 = x, y0$3 = y); | |
| } | |
| function PathContext(context) { | |
| this._context = context; | |
| } | |
| PathContext.prototype = { | |
| _radius: 4.5, | |
| pointRadius: function(_) { | |
| return this._radius = _, this; | |
| }, | |
| polygonStart: function() { | |
| this._line = 0; | |
| }, | |
| polygonEnd: function() { | |
| this._line = NaN; | |
| }, | |
| lineStart: function() { | |
| this._point = 0; | |
| }, | |
| lineEnd: function() { | |
| if (this._line === 0) this._context.closePath(); | |
| this._point = NaN; | |
| }, | |
| point: function(x, y) { | |
| switch (this._point) { | |
| case 0: { | |
| this._context.moveTo(x, y); | |
| this._point = 1; | |
| break; | |
| } | |
| case 1: { | |
| this._context.lineTo(x, y); | |
| break; | |
| } | |
| default: { | |
| this._context.moveTo(x + this._radius, y); | |
| this._context.arc(x, y, this._radius, 0, tau); | |
| break; | |
| } | |
| } | |
| }, | |
| result: noop | |
| }; | |
| var lengthSum$1 = adder(); | |
| var lengthRing; | |
| var x00$2; | |
| var y00$2; | |
| var x0$4; | |
| var y0$4; | |
| var lengthStream$1 = { | |
| point: noop, | |
| lineStart: function() { | |
| lengthStream$1.point = lengthPointFirst$1; | |
| }, | |
| lineEnd: function() { | |
| if (lengthRing) lengthPoint$1(x00$2, y00$2); | |
| lengthStream$1.point = noop; | |
| }, | |
| polygonStart: function() { | |
| lengthRing = true; | |
| }, | |
| polygonEnd: function() { | |
| lengthRing = null; | |
| }, | |
| result: function() { | |
| var length = +lengthSum$1; | |
| lengthSum$1.reset(); | |
| return length; | |
| } | |
| }; | |
| function lengthPointFirst$1(x, y) { | |
| lengthStream$1.point = lengthPoint$1; | |
| x00$2 = x0$4 = x, y00$2 = y0$4 = y; | |
| } | |
| function lengthPoint$1(x, y) { | |
| x0$4 -= x, y0$4 -= y; | |
| lengthSum$1.add(sqrt(x0$4 * x0$4 + y0$4 * y0$4)); | |
| x0$4 = x, y0$4 = y; | |
| } | |
| function PathString() { | |
| this._string = []; | |
| } | |
| PathString.prototype = { | |
| _radius: 4.5, | |
| _circle: circle$1(4.5), | |
| pointRadius: function(_) { | |
| if ((_ = +_) !== this._radius) this._radius = _, this._circle = null; | |
| return this; | |
| }, | |
| polygonStart: function() { | |
| this._line = 0; | |
| }, | |
| polygonEnd: function() { | |
| this._line = NaN; | |
| }, | |
| lineStart: function() { | |
| this._point = 0; | |
| }, | |
| lineEnd: function() { | |
| if (this._line === 0) this._string.push("Z"); | |
| this._point = NaN; | |
| }, | |
| point: function(x, y) { | |
| switch (this._point) { | |
| case 0: { | |
| this._string.push("M", x, ",", y); | |
| this._point = 1; | |
| break; | |
| } | |
| case 1: { | |
| this._string.push("L", x, ",", y); | |
| break; | |
| } | |
| default: { | |
| if (this._circle == null) this._circle = circle$1(this._radius); | |
| this._string.push("M", x, ",", y, this._circle); | |
| break; | |
| } | |
| } | |
| }, | |
| result: function() { | |
| if (this._string.length) { | |
| var result = this._string.join(""); | |
| this._string = []; | |
| return result; | |
| } else { | |
| return null; | |
| } | |
| } | |
| }; | |
| function circle$1(radius) { | |
| return "m0," + radius | |
| + "a" + radius + "," + radius + " 0 1,1 0," + -2 * radius | |
| + "a" + radius + "," + radius + " 0 1,1 0," + 2 * radius | |
| + "z"; | |
| } | |
| function index(projection, context) { | |
| var pointRadius = 4.5, | |
| projectionStream, | |
| contextStream; | |
| function path(object) { | |
| if (object) { | |
| if (typeof pointRadius === "function") contextStream.pointRadius(+pointRadius.apply(this, arguments)); | |
| geoStream(object, projectionStream(contextStream)); | |
| } | |
| return contextStream.result(); | |
| } | |
| path.area = function(object) { | |
| geoStream(object, projectionStream(areaStream$1)); | |
| return areaStream$1.result(); | |
| }; | |
| path.measure = function(object) { | |
| geoStream(object, projectionStream(lengthStream$1)); | |
| return lengthStream$1.result(); | |
| }; | |
| path.bounds = function(object) { | |
| geoStream(object, projectionStream(boundsStream$1)); | |
| return boundsStream$1.result(); | |
| }; | |
| path.centroid = function(object) { | |
| geoStream(object, projectionStream(centroidStream$1)); | |
| return centroidStream$1.result(); | |
| }; | |
| path.projection = function(_) { | |
| return arguments.length ? (projectionStream = _ == null ? (projection = null, identity) : (projection = _).stream, path) : projection; | |
| }; | |
| path.context = function(_) { | |
| if (!arguments.length) return context; | |
| contextStream = _ == null ? (context = null, new PathString) : new PathContext(context = _); | |
| if (typeof pointRadius !== "function") contextStream.pointRadius(pointRadius); | |
| return path; | |
| }; | |
| path.pointRadius = function(_) { | |
| if (!arguments.length) return pointRadius; | |
| pointRadius = typeof _ === "function" ? _ : (contextStream.pointRadius(+_), +_); | |
| return path; | |
| }; | |
| return path.projection(projection).context(context); | |
| } | |
| function clip(pointVisible, clipLine, interpolate, start, sort) { | |
| if (typeof sort === "undefined") sort = compareIntersection; | |
| return function(rotate, sink) { | |
| var line = clipLine(sink), | |
| rotatedStart = rotate.invert(start[0], start[1]), | |
| ringBuffer = clipBuffer(), | |
| ringSink = clipLine(ringBuffer), | |
| polygonStarted = false, | |
| polygon, | |
| segments, | |
| ring; | |
| var clip = { | |
| point: point, | |
| lineStart: lineStart, | |
| lineEnd: lineEnd, | |
| polygonStart: function() { | |
| clip.point = pointRing; | |
| clip.lineStart = ringStart; | |
| clip.lineEnd = ringEnd; | |
| segments = []; | |
| polygon = []; | |
| }, | |
| polygonEnd: function() { | |
| clip.point = point; | |
| clip.lineStart = lineStart; | |
| clip.lineEnd = lineEnd; | |
| segments = d3Array.merge(segments); | |
| var startInside = polygonContains(polygon, rotatedStart); | |
| if (segments.length) { | |
| if (!polygonStarted) sink.polygonStart(), polygonStarted = true; | |
| clipRejoin(segments, sort, startInside, interpolate, sink); | |
| } else if (startInside) { | |
| if (!polygonStarted) sink.polygonStart(), polygonStarted = true; | |
| sink.lineStart(); | |
| interpolate(null, null, 1, sink); | |
| sink.lineEnd(); | |
| } | |
| if (polygonStarted) sink.polygonEnd(), polygonStarted = false; | |
| segments = polygon = null; | |
| }, | |
| sphere: function() { | |
| sink.polygonStart(); | |
| sink.lineStart(); | |
| interpolate(null, null, 1, sink); | |
| sink.lineEnd(); | |
| sink.polygonEnd(); | |
| } | |
| }; | |
| function point(lambda, phi) { | |
| var point = rotate(lambda, phi); | |
| if (pointVisible(lambda = point[0], phi = point[1])) sink.point(lambda, phi); | |
| } | |
| function pointLine(lambda, phi) { | |
| var point = rotate(lambda, phi); | |
| line.point(point[0], point[1]); | |
| } | |
| function lineStart() { | |
| clip.point = pointLine; | |
| line.lineStart(); | |
| } | |
| function lineEnd() { | |
| clip.point = point; | |
| line.lineEnd(); | |
| } | |
| function pointRing(lambda, phi, close) { | |
| ring.push([lambda, phi]); | |
| var point = rotate(lambda, phi); | |
| ringSink.point(point[0], point[1], close); | |
| } | |
| function ringStart() { | |
| ringSink.lineStart(); | |
| ring = []; | |
| } | |
| function ringEnd() { | |
| pointRing(ring[0][0], ring[0][1], true); | |
| ringSink.lineEnd(); | |
| var clean = ringSink.clean(), | |
| ringSegments = ringBuffer.result(), | |
| i, n = ringSegments.length, m, | |
| segment, | |
| point; | |
| ring.pop(); | |
| polygon.push(ring); | |
| ring = null; | |
| if (!n) return; | |
| // No intersections. | |
| if (clean & 1) { | |
| segment = ringSegments[0]; | |
| if ((m = segment.length - 1) > 0) { | |
| if (!polygonStarted) sink.polygonStart(), polygonStarted = true; | |
| sink.lineStart(); | |
| for (i = 0; i < m; ++i) sink.point((point = segment[i])[0], point[1]); | |
| sink.lineEnd(); | |
| } | |
| return; | |
| } | |
| // Rejoin connected segments. | |
| // TODO reuse ringBuffer.rejoin()? | |
| if (n > 1 && clean & 2) ringSegments.push(ringSegments.pop().concat(ringSegments.shift())); | |
| segments.push(ringSegments.filter(validSegment)); | |
| } | |
| return clip; | |
| }; | |
| } | |
| function validSegment(segment) { | |
| return segment.length > 1; | |
| } | |
| // Intersections are sorted along the clip edge. For both antimeridian cutting | |
| // and circle clipping, the same comparison is used. | |
| function compareIntersection(a, b) { | |
| return ((a = a.x)[0] < 0 ? a[1] - halfPi - epsilon : halfPi - a[1]) | |
| - ((b = b.x)[0] < 0 ? b[1] - halfPi - epsilon : halfPi - b[1]); | |
| } | |
| function clipAntimeridian() { | |
| // Takes a line and cuts into visible segments. Return values: 0 - there were | |
| // intersections or the line was empty; 1 - no intersections; 2 - there were | |
| // intersections, and the first and last segments should be rejoined. | |
| function clipLine(stream) { | |
| var lambda0 = NaN, | |
| phi0 = NaN, | |
| sign0 = NaN, | |
| clean; // no intersections | |
| return { | |
| lineStart: function() { | |
| stream.lineStart(); | |
| clean = 1; | |
| }, | |
| point: function(lambda1, phi1) { | |
| var sign1 = lambda1 > 0 ? pi : -pi, | |
| delta = abs(lambda1 - lambda0); | |
| if (abs(delta - pi) < epsilon) { // line crosses a pole | |
| stream.point(lambda0, phi0 = (phi0 + phi1) / 2 > 0 ? halfPi : -halfPi); | |
| stream.point(sign0, phi0); | |
| stream.lineEnd(); | |
| stream.lineStart(); | |
| stream.point(sign1, phi0); | |
| stream.point(lambda1, phi0); | |
| clean = 0; | |
| } else if (sign0 !== sign1 && delta >= pi) { // line crosses antimeridian | |
| if (abs(lambda0 - sign0) < epsilon) lambda0 -= sign0 * epsilon; // handle degeneracies | |
| if (abs(lambda1 - sign1) < epsilon) lambda1 -= sign1 * epsilon; | |
| phi0 = clipAntimeridianIntersect(lambda0, phi0, lambda1, phi1); | |
| stream.point(sign0, phi0); | |
| stream.lineEnd(); | |
| stream.lineStart(); | |
| stream.point(sign1, phi0); | |
| clean = 0; | |
| } | |
| stream.point(lambda0 = lambda1, phi0 = phi1); | |
| sign0 = sign1; | |
| }, | |
| lineEnd: function() { | |
| stream.lineEnd(); | |
| lambda0 = phi0 = NaN; | |
| }, | |
| clean: function() { | |
| return 2 - clean; // if intersections, rejoin first and last segments | |
| } | |
| }; | |
| } | |
| function clipAntimeridianIntersect(lambda0, phi0, lambda1, phi1) { | |
| var cosPhi0, | |
| cosPhi1, | |
| sinLambda0Lambda1 = sin(lambda0 - lambda1); | |
| return abs(sinLambda0Lambda1) > epsilon | |
| ? atan((sin(phi0) * (cosPhi1 = cos(phi1)) * sin(lambda1) | |
| - sin(phi1) * (cosPhi0 = cos(phi0)) * sin(lambda0)) | |
| / (cosPhi0 * cosPhi1 * sinLambda0Lambda1)) | |
| : (phi0 + phi1) / 2; | |
| } | |
| function interpolate(from, to, direction, stream) { | |
| var phi; | |
| if (from == null) { | |
| phi = direction * halfPi; | |
| stream.point(-pi, phi); | |
| stream.point(0, phi); | |
| stream.point(pi, phi); | |
| stream.point(pi, 0); | |
| stream.point(pi, -phi); | |
| stream.point(0, -phi); | |
| stream.point(-pi, -phi); | |
| stream.point(-pi, 0); | |
| stream.point(-pi, phi); | |
| } else if (abs(from[0] - to[0]) > epsilon) { | |
| var lambda = from[0] < to[0] ? pi : -pi; | |
| phi = direction * lambda / 2; | |
| stream.point(-lambda, phi); | |
| stream.point(0, phi); | |
| stream.point(lambda, phi); | |
| } else { | |
| stream.point(to[0], to[1]); | |
| } | |
| } | |
| function visible() { | |
| return true; | |
| } | |
| return clip(visible, clipLine, interpolate, [-pi, -halfPi]); | |
| } | |
| function clipCircle(radius, delta) { | |
| var cr = cos(radius), | |
| smallRadius = cr > 0, | |
| notHemisphere = abs(cr) > epsilon; // TODO optimise for this common case | |
| function interpolate(from, to, direction, stream) { | |
| circleStream(stream, radius, delta, direction, from, to); | |
| } | |
| function visible(lambda, phi) { | |
| return cos(lambda) * cos(phi) > cr; | |
| } | |
| // Takes a line and cuts into visible segments. Return values used for polygon | |
| // clipping: 0 - there were intersections or the line was empty; 1 - no | |
| // intersections 2 - there were intersections, and the first and last segments | |
| // should be rejoined. | |
| function clipLine(stream) { | |
| var point0, // previous point | |
| c0, // code for previous point | |
| v0, // visibility of previous point | |
| v00, // visibility of first point | |
| clean; // no intersections | |
| return { | |
| lineStart: function() { | |
| v00 = v0 = false; | |
| clean = 1; | |
| }, | |
| point: function(lambda, phi) { | |
| var point1 = [lambda, phi], | |
| point2, | |
| v = visible(lambda, phi), | |
| c = smallRadius | |
| ? v ? 0 : code(lambda, phi) | |
| : v ? code(lambda + (lambda < 0 ? pi : -pi), phi) : 0; | |
| if (!point0 && (v00 = v0 = v)) stream.lineStart(); | |
| // Handle degeneracies. | |
| // TODO ignore if not clipping polygons. | |
| if (v !== v0) { | |
| point2 = intersect(point0, point1); | |
| if (!point2 || pointEqual(point0, point2) || pointEqual(point1, point2)) { | |
| point1[0] += epsilon; | |
| point1[1] += epsilon; | |
| v = visible(point1[0], point1[1]); | |
| } | |
| } | |
| if (v !== v0) { | |
| clean = 0; | |
| if (v) { | |
| // outside going in | |
| stream.lineStart(); | |
| point2 = intersect(point1, point0); | |
| stream.point(point2[0], point2[1]); | |
| } else { | |
| // inside going out | |
| point2 = intersect(point0, point1); | |
| stream.point(point2[0], point2[1]); | |
| stream.lineEnd(); | |
| } | |
| point0 = point2; | |
| } else if (notHemisphere && point0 && smallRadius ^ v) { | |
| var t; | |
| // If the codes for two points are different, or are both zero, | |
| // and there this segment intersects with the small circle. | |
| if (!(c & c0) && (t = intersect(point1, point0, true))) { | |
| clean = 0; | |
| if (smallRadius) { | |
| stream.lineStart(); | |
| stream.point(t[0][0], t[0][1]); | |
| stream.point(t[1][0], t[1][1]); | |
| stream.lineEnd(); | |
| } else { | |
| stream.point(t[1][0], t[1][1]); | |
| stream.lineEnd(); | |
| stream.lineStart(); | |
| stream.point(t[0][0], t[0][1]); | |
| } | |
| } | |
| } | |
| if (v && (!point0 || !pointEqual(point0, point1))) { | |
| stream.point(point1[0], point1[1]); | |
| } | |
| point0 = point1, v0 = v, c0 = c; | |
| }, | |
| lineEnd: function() { | |
| if (v0) stream.lineEnd(); | |
| point0 = null; | |
| }, | |
| // Rejoin first and last segments if there were intersections and the first | |
| // and last points were visible. | |
| clean: function() { | |
| return clean | ((v00 && v0) << 1); | |
| } | |
| }; | |
| } | |
| // Intersects the great circle between a and b with the clip circle. | |
| function intersect(a, b, two) { | |
| var pa = cartesian(a), | |
| pb = cartesian(b); | |
| // We have two planes, n1.p = d1 and n2.p = d2. | |
| // Find intersection line p(t) = c1 n1 + c2 n2 + t (n1 ⨯ n2). | |
| var n1 = [1, 0, 0], // normal | |
| n2 = cartesianCross(pa, pb), | |
| n2n2 = cartesianDot(n2, n2), | |
| n1n2 = n2[0], // cartesianDot(n1, n2), | |
| determinant = n2n2 - n1n2 * n1n2; | |
| // Two polar points. | |
| if (!determinant) return !two && a; | |
| var c1 = cr * n2n2 / determinant, | |
| c2 = -cr * n1n2 / determinant, | |
| n1xn2 = cartesianCross(n1, n2), | |
| A = cartesianScale(n1, c1), | |
| B = cartesianScale(n2, c2); | |
| cartesianAddInPlace(A, B); | |
| // Solve |p(t)|^2 = 1. | |
| var u = n1xn2, | |
| w = cartesianDot(A, u), | |
| uu = cartesianDot(u, u), | |
| t2 = w * w - uu * (cartesianDot(A, A) - 1); | |
| if (t2 < 0) return; | |
| var t = sqrt(t2), | |
| q = cartesianScale(u, (-w - t) / uu); | |
| cartesianAddInPlace(q, A); | |
| q = spherical(q); | |
| if (!two) return q; | |
| // Two intersection points. | |
| var lambda0 = a[0], | |
| lambda1 = b[0], | |
| phi0 = a[1], | |
| phi1 = b[1], | |
| z; | |
| if (lambda1 < lambda0) z = lambda0, lambda0 = lambda1, lambda1 = z; | |
| var delta = lambda1 - lambda0, | |
| polar = abs(delta - pi) < epsilon, | |
| meridian = polar || delta < epsilon; | |
| if (!polar && phi1 < phi0) z = phi0, phi0 = phi1, phi1 = z; | |
| // Check that the first point is between a and b. | |
| if (meridian | |
| ? polar | |
| ? phi0 + phi1 > 0 ^ q[1] < (abs(q[0] - lambda0) < epsilon ? phi0 : phi1) | |
| : phi0 <= q[1] && q[1] <= phi1 | |
| : delta > pi ^ (lambda0 <= q[0] && q[0] <= lambda1)) { | |
| var q1 = cartesianScale(u, (-w + t) / uu); | |
| cartesianAddInPlace(q1, A); | |
| return [q, spherical(q1)]; | |
| } | |
| } | |
| // Generates a 4-bit vector representing the location of a point relative to | |
| // the small circle's bounding box. | |
| function code(lambda, phi) { | |
| var r = smallRadius ? radius : pi - radius, | |
| code = 0; | |
| if (lambda < -r) code |= 1; // left | |
| else if (lambda > r) code |= 2; // right | |
| if (phi < -r) code |= 4; // below | |
| else if (phi > r) code |= 8; // above | |
| return code; | |
| } | |
| return clip(visible, clipLine, interpolate, smallRadius ? [0, -radius] : [-pi, radius - pi]); | |
| } | |
| /* | |
| * clipNone generates a clip function which doesn't clip | |
| * but complies with the preclip API by applying the rotation | |
| * | |
| */ | |
| function clipNone() { | |
| return function(rotate, stream) { | |
| var _stream = { | |
| point: function(x,y) { | |
| var r = rotate(x,y); | |
| return stream.point(r[0],r[1]); | |
| }, | |
| lineStart: stream.lineStart, | |
| lineEnd: stream.lineEnd, | |
| polygonStart: stream.polygonStart, | |
| polygonEnd: stream.polygonEnd, | |
| sphere: stream.sphere | |
| }; | |
| return _stream; | |
| } | |
| } | |
| /* | |
| import {halfPi, pi} from "../math"; | |
| function sphere(stream) { | |
| return function() { | |
| var phi = 1 * halfPi; | |
| stream.lineStart(); | |
| stream.point(-pi, phi); | |
| stream.point(0, phi); | |
| stream.point(pi, phi); | |
| stream.point(pi, 0); | |
| stream.point(pi, -phi); | |
| stream.point(0, -phi); | |
| stream.point(-pi, -phi); | |
| stream.point(-pi, 0); | |
| stream.point(-pi, phi); | |
| stream.lineEnd(); | |
| } | |
| } | |
| */ | |
| function intersectSegment(from, to) { | |
| this.from = from, this.to = to; | |
| this.normal = cartesianCross(from, to); | |
| this.fromNormal = cartesianCross(this.normal, from); | |
| this.toNormal = cartesianCross(this.normal, to); | |
| } | |
| // >> here a and b are segments processed by intersectSegment | |
| function intersect(a, b) { | |
| var axb = cartesianCross(a.normal, b.normal); | |
| cartesianNormalizeInPlace(axb); | |
| var a0 = cartesianDot(axb, a.fromNormal), | |
| a1 = cartesianDot(axb, a.toNormal), | |
| b0 = cartesianDot(axb, b.fromNormal), | |
| b1 = cartesianDot(axb, b.toNormal); | |
| if (a0 > -epsilon2 && a1 < epsilon2 && b0 > -epsilon2 && b1 < epsilon2) return axb; | |
| if (a0 < epsilon2 && a1 > -epsilon2 && b0 < epsilon2 && b1 > -epsilon2) { | |
| axb[0] = -axb[0], axb[1] = -axb[1], axb[2] = -axb[2]; | |
| return axb; | |
| } | |
| } | |
| function intersectPointOnLine(p, a) { | |
| var a0 = cartesianDot(p, a.fromNormal), | |
| a1 = cartesianDot(p, a.toNormal); | |
| p = cartesianDot(p, a.normal); | |
| return abs(p) < epsilon2 && (a0 > -epsilon2 && a1 < epsilon2 || a0 < epsilon2 && a1 > -epsilon2); | |
| } | |
| var intersectCoincident = {}; | |
| // todo: publicly expose d3.geoIntersect(segment0, segment1) ?? | |
| // cf. https://github.com/d3/d3/commit/3dbdf87974dc2588c29db0533a8500ccddb25daa#diff-65daf69cea7d039d72c1eca7c13326b0 | |
| // clipPolygon | |
| function clipPolygon (p) { | |
| var segments = []; | |
| if (p.type != "Polygon") return clipNone(); // todo: MultiPolygon? | |
| var polygon = p.coordinates.map(function(ring) { | |
| var c, c0; | |
| ring = ring.map(function(point, i) { | |
| c = cartesian(point = [point[0] * radians, point[1] * radians]); | |
| if (i) segments.push(new intersectSegment(c0, c)); | |
| c0 = c; | |
| return point; | |
| }); | |
| ring.pop(); | |
| return ring; | |
| }); | |
| function visible(lambda, phi) { | |
| return polygonContains(polygon, [lambda, phi]); | |
| } | |
| function clipLine(stream) { | |
| var point0, | |
| lambda00, | |
| phi00, | |
| v00, | |
| v0, | |
| clean; | |
| return { | |
| lineStart: function() { | |
| point0 = null; | |
| clean = 1; | |
| }, | |
| point: function(lambda, phi, close) { | |
| if (cos(lambda) == -1) lambda -= sign(sin(lambda)) * 1e-5; // move away from -180/180 https://github.com/d3/d3-geo/pull/108#issuecomment-323798937 | |
| if (close) lambda = lambda00, phi = phi00; | |
| var point = cartesian([lambda, phi]), | |
| v = v0, | |
| intersection, | |
| i, j, s, t; | |
| if (point0) { | |
| var segment = new intersectSegment(point0, point), | |
| intersections = []; | |
| for (i = 0, j = 100; i < segments.length && j > 0; ++i) { | |
| s = segments[i]; | |
| intersection = intersect(segment, s); | |
| if (intersection) { | |
| if (intersection === intersectCoincident || | |
| cartesianEqual(intersection, point0) || cartesianEqual(intersection, point) || | |
| cartesianEqual(intersection, s.from) || cartesianEqual(intersection, s.to)) { | |
| t = 1e-4; | |
| lambda = (lambda + 3 * pi + (Math.random() < .5 ? t : -t)) % (2 * pi) - pi; | |
| phi = Math.min(pi / 2 - 1e-4, Math.max(1e-4 - pi / 2, phi + (Math.random() < .5 ? t : -t))); | |
| segment = new intersectSegment(point0, point = cartesian([lambda, phi])); | |
| i = -1, --j; | |
| intersections.length = 0; | |
| continue; | |
| } | |
| var sph = spherical(intersection); | |
| intersection.distance = clipPolygonDistance(point0, intersection); | |
| intersection.index = i; | |
| intersection.t = clipPolygonDistance(s.from, intersection); | |
| intersection[0] = sph[0], intersection[1] = sph[1], intersection.pop(); | |
| intersections.push(intersection); | |
| } | |
| } | |
| if (intersections.length) { | |
| clean = 0; | |
| intersections.sort(function(a, b) { return a.distance - b.distance; }); | |
| for (i = 0; i < intersections.length; ++i) { | |
| intersection = intersections[i]; | |
| if (v = !v) { | |
| stream.lineStart(); | |
| stream.point(intersection[0], intersection[1], intersection.index, intersection.t); | |
| } else { | |
| stream.point(intersection[0], intersection[1], intersection.index, intersection.t); | |
| stream.lineEnd(); | |
| } | |
| } | |
| } | |
| if (v) stream.point(lambda, phi); | |
| } else { | |
| for (i = 0, j = 100; i < segments.length && j > 0; ++i) { | |
| s = segments[i]; | |
| if (intersectPointOnLine(point, s)) { | |
| t = 1e-4; | |
| lambda = (lambda + 3 * pi + (Math.random() < .5 ? t : -t)) % (2 * pi) - pi; | |
| phi = Math.min(pi / 2 - 1e-4, Math.max(1e-4 - pi / 2, phi + (Math.random() < .5 ? t : -t))); | |
| point = cartesian([lambda, phi]); | |
| i = -1, --j; | |
| } | |
| } | |
| if (v00 = v = visible(lambda00 = lambda, phi00 = phi)) stream.lineStart(), stream.point(lambda, phi); | |
| } | |
| point0 = point, v0 = v; | |
| }, | |
| lineEnd: function() { | |
| if (v0) stream.lineEnd(); | |
| }, | |
| // Rejoin first and last segments if there were intersections and the first | |
| // and last points were visible. | |
| clean: function() { | |
| return clean | ((v00 && v0) << 1); | |
| } | |
| }; | |
| } | |
| function interpolate(from, to, direction, stream) { | |
| if (from == null) { | |
| var n = polygon.length; | |
| polygon.forEach(function(ring, i) { | |
| ring.forEach(function(point) { stream.point(point[0], point[1]); }); | |
| if (i < n - 1) stream.lineEnd(), stream.lineStart(); | |
| }); | |
| } else if (from.index !== to.index && from.index != null && to.index != null) { | |
| for (var i = from.index; i !== to.index; i = (i + direction + segments.length) % segments.length) { | |
| var segment = segments[i], | |
| point = spherical(direction > 0 ? segment.to : segment.from); | |
| stream.point(point[0], point[1]); | |
| } | |
| } | |
| } | |
| return clip(visible, clipLine, interpolate, polygon[0][0], clipPolygonSort); | |
| } | |
| function clipPolygonSort(a, b) { | |
| a = a.x, b = b.x; | |
| return a.index - b.index || a.t - b.t; | |
| } | |
| // Geodesic coordinates for two 3D points. | |
| function clipPolygonDistance(a, b) { | |
| var axb = cartesianCross(a, b); | |
| return atan2(sqrt(cartesianDot(axb, axb)), cartesianDot(a, b)); | |
| } | |
| function transform(methods) { | |
| return { | |
| stream: transformer(methods) | |
| }; | |
| } | |
| function transformer(methods) { | |
| return function(stream) { | |
| var s = new TransformStream; | |
| for (var key in methods) s[key] = methods[key]; | |
| s.stream = stream; | |
| return s; | |
| }; | |
| } | |
| function TransformStream() {} | |
| TransformStream.prototype = { | |
| constructor: TransformStream, | |
| point: function(x, y) { this.stream.point(x, y); }, | |
| sphere: function() { this.stream.sphere(); }, | |
| lineStart: function() { this.stream.lineStart(); }, | |
| lineEnd: function() { this.stream.lineEnd(); }, | |
| polygonStart: function() { this.stream.polygonStart(); }, | |
| polygonEnd: function() { this.stream.polygonEnd(); } | |
| }; | |
| function fitExtent(projection, extent, object) { | |
| var w = extent[1][0] - extent[0][0], | |
| h = extent[1][1] - extent[0][1], | |
| clip = projection.clipExtent && projection.clipExtent(); | |
| projection | |
| .scale(150) | |
| .translate([0, 0]); | |
| if (clip != null) projection.clipExtent(null); | |
| geoStream(object, projection.stream(boundsStream$1)); | |
| var b = boundsStream$1.result(), | |
| k = Math.min(w / (b[1][0] - b[0][0]), h / (b[1][1] - b[0][1])), | |
| x = +extent[0][0] + (w - k * (b[1][0] + b[0][0])) / 2, | |
| y = +extent[0][1] + (h - k * (b[1][1] + b[0][1])) / 2; | |
| if (clip != null) projection.clipExtent(clip); | |
| return projection | |
| .scale(k * 150) | |
| .translate([x, y]); | |
| } | |
| function fitSize(projection, size, object) { | |
| return fitExtent(projection, [[0, 0], size], object); | |
| } | |
| var maxDepth = 16; | |
| var cosMinDistance = cos(30 * radians); | |
| // cos(minimum angular distance) | |
| function resample(project, delta2) { | |
| return +delta2 ? resample$1(project, delta2) : resampleNone(project); | |
| } | |
| function resampleNone(project) { | |
| return transformer({ | |
| point: function(x, y) { | |
| x = project(x, y); | |
| this.stream.point(x[0], x[1]); | |
| } | |
| }); | |
| } | |
| function resample$1(project, delta2) { | |
| function resampleLineTo(x0, y0, lambda0, a0, b0, c0, x1, y1, lambda1, a1, b1, c1, depth, stream) { | |
| var dx = x1 - x0, | |
| dy = y1 - y0, | |
| d2 = dx * dx + dy * dy; | |
| if (d2 > 4 * delta2 && depth--) { | |
| var a = a0 + a1, | |
| b = b0 + b1, | |
| c = c0 + c1, | |
| m = sqrt(a * a + b * b + c * c), | |
| phi2 = asin(c /= m), | |
| lambda2 = abs(abs(c) - 1) < epsilon || abs(lambda0 - lambda1) < epsilon ? (lambda0 + lambda1) / 2 : atan2(b, a), | |
| p = project(lambda2, phi2), | |
| x2 = p[0], | |
| y2 = p[1], | |
| dx2 = x2 - x0, | |
| dy2 = y2 - y0, | |
| dz = dy * dx2 - dx * dy2; | |
| if (dz * dz / d2 > delta2 // perpendicular projected distance | |
| || abs((dx * dx2 + dy * dy2) / d2 - 0.5) > 0.3 // midpoint close to an end | |
| || a0 * a1 + b0 * b1 + c0 * c1 < cosMinDistance) { // angular distance | |
| resampleLineTo(x0, y0, lambda0, a0, b0, c0, x2, y2, lambda2, a /= m, b /= m, c, depth, stream); | |
| stream.point(x2, y2); | |
| resampleLineTo(x2, y2, lambda2, a, b, c, x1, y1, lambda1, a1, b1, c1, depth, stream); | |
| } | |
| } | |
| } | |
| return function(stream) { | |
| var lambda00, x00, y00, a00, b00, c00, // first point | |
| lambda0, x0, y0, a0, b0, c0; // previous point | |
| var resampleStream = { | |
| point: point, | |
| lineStart: lineStart, | |
| lineEnd: lineEnd, | |
| polygonStart: function() { stream.polygonStart(); resampleStream.lineStart = ringStart; }, | |
| polygonEnd: function() { stream.polygonEnd(); resampleStream.lineStart = lineStart; } | |
| }; | |
| function point(x, y) { | |
| x = project(x, y); | |
| stream.point(x[0], x[1]); | |
| } | |
| function lineStart() { | |
| x0 = NaN; | |
| resampleStream.point = linePoint; | |
| stream.lineStart(); | |
| } | |
| function linePoint(lambda, phi) { | |
| var c = cartesian([lambda, phi]), p = project(lambda, phi); | |
| resampleLineTo(x0, y0, lambda0, a0, b0, c0, x0 = p[0], y0 = p[1], lambda0 = lambda, a0 = c[0], b0 = c[1], c0 = c[2], maxDepth, stream); | |
| stream.point(x0, y0); | |
| } | |
| function lineEnd() { | |
| resampleStream.point = point; | |
| stream.lineEnd(); | |
| } | |
| function ringStart() { | |
| lineStart(); | |
| resampleStream.point = ringPoint; | |
| resampleStream.lineEnd = ringEnd; | |
| } | |
| function ringPoint(lambda, phi) { | |
| linePoint(lambda00 = lambda, phi), x00 = x0, y00 = y0, a00 = a0, b00 = b0, c00 = c0; | |
| resampleStream.point = linePoint; | |
| } | |
| function ringEnd() { | |
| resampleLineTo(x0, y0, lambda0, a0, b0, c0, x00, y00, lambda00, a00, b00, c00, maxDepth, stream); | |
| resampleStream.lineEnd = lineEnd; | |
| lineEnd(); | |
| } | |
| return resampleStream; | |
| }; | |
| } | |
| var transformRadians = transformer({ | |
| point: function(x, y) { | |
| this.stream.point(x * radians, y * radians); | |
| } | |
| }); | |
| function projection(project) { | |
| return projectionMutator(function() { return project; })(); | |
| } | |
| function projectionMutator(projectAt) { | |
| var project, | |
| k = 150, // scale | |
| x = 480, y = 250, // translate | |
| dx, dy, lambda = 0, phi = 0, // center | |
| deltaLambda = 0, deltaPhi = 0, deltaGamma = 0, rotate, projectRotate, // rotate | |
| preclip = clipAntimeridian(), // default clip | |
| theta = null, // clip angle | |
| polygon = null, // clip polygon | |
| x0 = null, y0, x1, y1, postclip = identity, // clip extent | |
| delta2 = 0.5, projectResample = resample(projectTransform, delta2), // precision | |
| cache, | |
| cacheStream; | |
| function projection(point) { | |
| point = projectRotate(point[0] * radians, point[1] * radians); | |
| return [point[0] * k + dx, dy - point[1] * k]; | |
| } | |
| function invert(point) { | |
| point = projectRotate.invert((point[0] - dx) / k, (dy - point[1]) / k); | |
| return point && [point[0] * degrees, point[1] * degrees]; | |
| } | |
| function projectTransform(x, y) { | |
| return x = project(x, y), [x[0] * k + dx, dy - x[1] * k]; | |
| } | |
| projection.stream = function(stream) { | |
| return cache && cacheStream === stream ? cache : cache = transformRadians(preclip(rotate, projectResample(postclip(cacheStream = stream)))); | |
| }; | |
| // spherical clipping (preclip) | |
| // if argument is false-ish, falls back to clipNone | |
| projection.clipAntimeridian = function(_) { | |
| if (!arguments.length) return polygon === null && theta === null; | |
| return preclip = _ ? clipAntimeridian() : clipNone(), polygon = theta = null, reset(); | |
| }; | |
| // if argument is false-ish, falls back to Antimeridian | |
| projection.clipAngle = function(_) { | |
| if (!arguments.length) return theta ? theta * degrees : null; | |
| theta = +_ * radians; | |
| if (!theta) return theta = null, preclip = clipAntimeridian(), reset(); | |
| return preclip = clipCircle(theta, 6 * radians), reset(); | |
| }; | |
| // if argument is false-ish, falls back to clipNone | |
| projection.clipPolygon = function(_) { | |
| return arguments.length ? (preclip = _ ? clipPolygon(polygon = _) : (polygon = theta = null, clipNone()), reset()) : polygon; | |
| }; | |
| // planar clipping (postclip) | |
| projection.clipExtent = function(_) { | |
| return arguments.length ? (postclip = _ == null ? (x0 = y0 = x1 = y1 = null, identity) : clipExtent(x0 = +_[0][0], y0 = +_[0][1], x1 = +_[1][0], y1 = +_[1][1]), reset()) : x0 == null ? null : [[x0, y0], [x1, y1]]; | |
| }; | |
| projection.scale = function(_) { | |
| return arguments.length ? (k = +_, recenter()) : k; | |
| }; | |
| projection.translate = function(_) { | |
| return arguments.length ? (x = +_[0], y = +_[1], recenter()) : [x, y]; | |
| }; | |
| projection.center = function(_) { | |
| return arguments.length ? (lambda = _[0] % 360 * radians, phi = _[1] % 360 * radians, recenter()) : [lambda * degrees, phi * degrees]; | |
| }; | |
| projection.rotate = function(_) { | |
| return arguments.length ? (deltaLambda = _[0] % 360 * radians, deltaPhi = _[1] % 360 * radians, deltaGamma = _.length > 2 ? _[2] % 360 * radians : 0, recenter()) : [deltaLambda * degrees, deltaPhi * degrees, deltaGamma * degrees]; | |
| }; | |
| projection.precision = function(_) { | |
| return arguments.length ? (projectResample = resample(projectTransform, delta2 = _ * _), reset()) : sqrt(delta2); | |
| }; | |
| projection.fitExtent = function(extent, object) { | |
| return fitExtent(projection, extent, object); | |
| }; | |
| projection.fitSize = function(size, object) { | |
| return fitSize(projection, size, object); | |
| }; | |
| function recenter() { | |
| projectRotate = compose(rotate = rotateRadians(deltaLambda, deltaPhi, deltaGamma), project); | |
| var center = project(lambda, phi); | |
| dx = x - center[0] * k; | |
| dy = y + center[1] * k; | |
| return reset(); | |
| } | |
| function reset() { | |
| cache = cacheStream = null; | |
| return projection; | |
| } | |
| return function() { | |
| project = projectAt.apply(this, arguments); | |
| projection.invert = project.invert && invert; | |
| return recenter(); | |
| }; | |
| } | |
| function conicProjection(projectAt) { | |
| var phi0 = 0, | |
| phi1 = pi / 3, | |
| m = projectionMutator(projectAt), | |
| p = m(phi0, phi1); | |
| p.parallels = function(_) { | |
| return arguments.length ? m(phi0 = _[0] * radians, phi1 = _[1] * radians) : [phi0 * degrees, phi1 * degrees]; | |
| }; | |
| return p; | |
| } | |
| function cylindricalEqualAreaRaw(phi0) { | |
| var cosPhi0 = cos(phi0); | |
| function forward(lambda, phi) { | |
| return [lambda * cosPhi0, sin(phi) / cosPhi0]; | |
| } | |
| forward.invert = function(x, y) { | |
| return [x / cosPhi0, asin(y * cosPhi0)]; | |
| }; | |
| return forward; | |
| } | |
| function conicEqualAreaRaw(y0, y1) { | |
| var sy0 = sin(y0), n = (sy0 + sin(y1)) / 2; | |
| // Are the parallels symmetrical around the Equator? | |
| if (abs(n) < epsilon) return cylindricalEqualAreaRaw(y0); | |
| var c = 1 + sy0 * (2 * n - sy0), r0 = sqrt(c) / n; | |
| function project(x, y) { | |
| var r = sqrt(c - 2 * n * sin(y)) / n; | |
| return [r * sin(x *= n), r0 - r * cos(x)]; | |
| } | |
| project.invert = function(x, y) { | |
| var r0y = r0 - y; | |
| return [atan2(x, abs(r0y)) / n * sign(r0y), asin((c - (x * x + r0y * r0y) * n * n) / (2 * n))]; | |
| }; | |
| return project; | |
| } | |
| function conicEqualArea() { | |
| return conicProjection(conicEqualAreaRaw) | |
| .scale(155.424) | |
| .center([0, 33.6442]); | |
| } | |
| function albers() { | |
| return conicEqualArea() | |
| .parallels([29.5, 45.5]) | |
| .scale(1070) | |
| .translate([480, 250]) | |
| .rotate([96, 0]) | |
| .center([-0.6, 38.7]); | |
| } | |
| // The projections must have mutually exclusive clip regions on the sphere, | |
| // as this will avoid emitting interleaving lines and polygons. | |
| function multiplex(streams) { | |
| var n = streams.length; | |
| return { | |
| point: function(x, y) { var i = -1; while (++i < n) streams[i].point(x, y); }, | |
| sphere: function() { var i = -1; while (++i < n) streams[i].sphere(); }, | |
| lineStart: function() { var i = -1; while (++i < n) streams[i].lineStart(); }, | |
| lineEnd: function() { var i = -1; while (++i < n) streams[i].lineEnd(); }, | |
| polygonStart: function() { var i = -1; while (++i < n) streams[i].polygonStart(); }, | |
| polygonEnd: function() { var i = -1; while (++i < n) streams[i].polygonEnd(); } | |
| }; | |
| } | |
| // A composite projection for the United States, configured by default for | |
| // 960×500. The projection also works quite well at 960×600 if you change the | |
| // scale to 1285 and adjust the translate accordingly. The set of standard | |
| // parallels for each region comes from USGS, which is published here: | |
| // http://egsc.usgs.gov/isb/pubs/MapProjections/projections.html#albers | |
| function albersUsa() { | |
| var cache, | |
| cacheStream, | |
| lower48 = albers(), lower48Point, | |
| alaska = conicEqualArea().rotate([154, 0]).center([-2, 58.5]).parallels([55, 65]), alaskaPoint, // EPSG:3338 | |
| hawaii = conicEqualArea().rotate([157, 0]).center([-3, 19.9]).parallels([8, 18]), hawaiiPoint, // ESRI:102007 | |
| point, pointStream = {point: function(x, y) { point = [x, y]; }}; | |
| function albersUsa(coordinates) { | |
| var x = coordinates[0], y = coordinates[1]; | |
| return point = null, | |
| (lower48Point.point(x, y), point) | |
| || (alaskaPoint.point(x, y), point) | |
| || (hawaiiPoint.point(x, y), point); | |
| } | |
| albersUsa.invert = function(coordinates) { | |
| var k = lower48.scale(), | |
| t = lower48.translate(), | |
| x = (coordinates[0] - t[0]) / k, | |
| y = (coordinates[1] - t[1]) / k; | |
| return (y >= 0.120 && y < 0.234 && x >= -0.425 && x < -0.214 ? alaska | |
| : y >= 0.166 && y < 0.234 && x >= -0.214 && x < -0.115 ? hawaii | |
| : lower48).invert(coordinates); | |
| }; | |
| albersUsa.stream = function(stream) { | |
| return cache && cacheStream === stream ? cache : cache = multiplex([lower48.stream(cacheStream = stream), alaska.stream(stream), hawaii.stream(stream)]); | |
| }; | |
| albersUsa.precision = function(_) { | |
| if (!arguments.length) return lower48.precision(); | |
| lower48.precision(_), alaska.precision(_), hawaii.precision(_); | |
| return reset(); | |
| }; | |
| albersUsa.scale = function(_) { | |
| if (!arguments.length) return lower48.scale(); | |
| lower48.scale(_), alaska.scale(_ * 0.35), hawaii.scale(_); | |
| return albersUsa.translate(lower48.translate()); | |
| }; | |
| albersUsa.translate = function(_) { | |
| if (!arguments.length) return lower48.translate(); | |
| var k = lower48.scale(), x = +_[0], y = +_[1]; | |
| lower48Point = lower48 | |
| .translate(_) | |
| .clipExtent([[x - 0.455 * k, y - 0.238 * k], [x + 0.455 * k, y + 0.238 * k]]) | |
| .stream(pointStream); | |
| alaskaPoint = alaska | |
| .translate([x - 0.307 * k, y + 0.201 * k]) | |
| .clipExtent([[x - 0.425 * k + epsilon, y + 0.120 * k + epsilon], [x - 0.214 * k - epsilon, y + 0.234 * k - epsilon]]) | |
| .stream(pointStream); | |
| hawaiiPoint = hawaii | |
| .translate([x - 0.205 * k, y + 0.212 * k]) | |
| .clipExtent([[x - 0.214 * k + epsilon, y + 0.166 * k + epsilon], [x - 0.115 * k - epsilon, y + 0.234 * k - epsilon]]) | |
| .stream(pointStream); | |
| return reset(); | |
| }; | |
| albersUsa.fitExtent = function(extent, object) { | |
| return fitExtent(albersUsa, extent, object); | |
| }; | |
| albersUsa.fitSize = function(size, object) { | |
| return fitSize(albersUsa, size, object); | |
| }; | |
| function reset() { | |
| cache = cacheStream = null; | |
| return albersUsa; | |
| } | |
| return albersUsa.scale(1070); | |
| } | |
| function azimuthalRaw(scale) { | |
| return function(x, y) { | |
| var cx = cos(x), | |
| cy = cos(y), | |
| k = scale(cx * cy); | |
| return [ | |
| k * cy * sin(x), | |
| k * sin(y) | |
| ]; | |
| } | |
| } | |
| function azimuthalInvert(angle) { | |
| return function(x, y) { | |
| var z = sqrt(x * x + y * y), | |
| c = angle(z), | |
| sc = sin(c), | |
| cc = cos(c); | |
| return [ | |
| atan2(x * sc, z * cc), | |
| asin(z && y * sc / z) | |
| ]; | |
| } | |
| } | |
| var azimuthalEqualAreaRaw = azimuthalRaw(function(cxcy) { | |
| return sqrt(2 / (1 + cxcy)); | |
| }); | |
| azimuthalEqualAreaRaw.invert = azimuthalInvert(function(z) { | |
| return 2 * asin(z / 2); | |
| }); | |
| function azimuthalEqualArea() { | |
| return projection(azimuthalEqualAreaRaw) | |
| .scale(124.75) | |
| .clipAngle(180 - 1e-3); | |
| } | |
| var azimuthalEquidistantRaw = azimuthalRaw(function(c) { | |
| return (c = acos(c)) && c / sin(c); | |
| }); | |
| azimuthalEquidistantRaw.invert = azimuthalInvert(function(z) { | |
| return z; | |
| }); | |
| function azimuthalEquidistant() { | |
| return projection(azimuthalEquidistantRaw) | |
| .scale(79.4188) | |
| .clipAngle(180 - 1e-3); | |
| } | |
| function mercatorRaw(lambda, phi) { | |
| return [lambda, log(tan((halfPi + phi) / 2))]; | |
| } | |
| mercatorRaw.invert = function(x, y) { | |
| return [x, 2 * atan(exp(y)) - halfPi]; | |
| }; | |
| function mercator() { | |
| return mercatorProjection(mercatorRaw) | |
| .scale(961 / tau); | |
| } | |
| function mercatorProjection(project) { | |
| var m = projection(project), | |
| center = m.center, | |
| scale = m.scale, | |
| translate = m.translate, | |
| clipExtent = m.clipExtent, | |
| x0 = null, y0, x1, y1; // clip extent | |
| m.scale = function(_) { | |
| return arguments.length ? (scale(_), reclip()) : scale(); | |
| }; | |
| m.translate = function(_) { | |
| return arguments.length ? (translate(_), reclip()) : translate(); | |
| }; | |
| m.center = function(_) { | |
| return arguments.length ? (center(_), reclip()) : center(); | |
| }; | |
| m.clipExtent = function(_) { | |
| return arguments.length ? ((_ == null ? x0 = y0 = x1 = y1 = null : (x0 = +_[0][0], y0 = +_[0][1], x1 = +_[1][0], y1 = +_[1][1])), reclip()) : x0 == null ? null : [[x0, y0], [x1, y1]]; | |
| }; | |
| function reclip() { | |
| var k = pi * scale(), | |
| t = m(rotation(m.rotate()).invert([0, 0])); | |
| return clipExtent(x0 == null | |
| ? [[t[0] - k, t[1] - k], [t[0] + k, t[1] + k]] : project === mercatorRaw | |
| ? [[Math.max(t[0] - k, x0), y0], [Math.min(t[0] + k, x1), y1]] | |
| : [[x0, Math.max(t[1] - k, y0)], [x1, Math.min(t[1] + k, y1)]]); | |
| } | |
| return reclip(); | |
| } | |
| function tany(y) { | |
| return tan((halfPi + y) / 2); | |
| } | |
| function conicConformalRaw(y0, y1) { | |
| var cy0 = cos(y0), | |
| n = y0 === y1 ? sin(y0) : log(cy0 / cos(y1)) / log(tany(y1) / tany(y0)), | |
| f = cy0 * pow(tany(y0), n) / n; | |
| if (!n) return mercatorRaw; | |
| function project(x, y) { | |
| if (f > 0) { if (y < -halfPi + epsilon) y = -halfPi + epsilon; } | |
| else { if (y > halfPi - epsilon) y = halfPi - epsilon; } | |
| var r = f / pow(tany(y), n); | |
| return [r * sin(n * x), f - r * cos(n * x)]; | |
| } | |
| project.invert = function(x, y) { | |
| var fy = f - y, r = sign(n) * sqrt(x * x + fy * fy); | |
| return [atan2(x, abs(fy)) / n * sign(fy), 2 * atan(pow(f / r, 1 / n)) - halfPi]; | |
| }; | |
| return project; | |
| } | |
| function conicConformal() { | |
| return conicProjection(conicConformalRaw) | |
| .scale(109.5) | |
| .parallels([30, 30]); | |
| } | |
| function equirectangularRaw(lambda, phi) { | |
| return [lambda, phi]; | |
| } | |
| equirectangularRaw.invert = equirectangularRaw; | |
| function equirectangular() { | |
| return projection(equirectangularRaw) | |
| .scale(152.63); | |
| } | |
| function conicEquidistantRaw(y0, y1) { | |
| var cy0 = cos(y0), | |
| n = y0 === y1 ? sin(y0) : (cy0 - cos(y1)) / (y1 - y0), | |
| g = cy0 / n + y0; | |
| if (abs(n) < epsilon) return equirectangularRaw; | |
| function project(x, y) { | |
| var gy = g - y, nx = n * x; | |
| return [gy * sin(nx), g - gy * cos(nx)]; | |
| } | |
| project.invert = function(x, y) { | |
| var gy = g - y; | |
| return [atan2(x, abs(gy)) / n * sign(gy), g - sign(n) * sqrt(x * x + gy * gy)]; | |
| }; | |
| return project; | |
| } | |
| function conicEquidistant() { | |
| return conicProjection(conicEquidistantRaw) | |
| .scale(131.154) | |
| .center([0, 13.9389]); | |
| } | |
| function gnomonicRaw(x, y) { | |
| var cy = cos(y), k = cos(x) * cy; | |
| return [cy * sin(x) / k, sin(y) / k]; | |
| } | |
| gnomonicRaw.invert = azimuthalInvert(atan); | |
| function gnomonic() { | |
| return projection(gnomonicRaw) | |
| .scale(144.049) | |
| .clipAngle(60); | |
| } | |
| function scaleTranslate(kx, ky, tx, ty) { | |
| return kx === 1 && ky === 1 && tx === 0 && ty === 0 ? identity : transformer({ | |
| point: function(x, y) { | |
| this.stream.point(x * kx + tx, y * ky + ty); | |
| } | |
| }); | |
| } | |
| function identity$1() { | |
| var k = 1, tx = 0, ty = 0, sx = 1, sy = 1, transform = identity, // scale, translate and reflect | |
| x0 = null, y0, x1, y1, clip = identity, // clip extent | |
| cache, | |
| cacheStream, | |
| projection; | |
| function reset() { | |
| cache = cacheStream = null; | |
| return projection; | |
| } | |
| return projection = { | |
| stream: function(stream) { | |
| return cache && cacheStream === stream ? cache : cache = transform(clip(cacheStream = stream)); | |
| }, | |
| clipExtent: function(_) { | |
| return arguments.length ? (clip = _ == null ? (x0 = y0 = x1 = y1 = null, identity) : clipExtent(x0 = +_[0][0], y0 = +_[0][1], x1 = +_[1][0], y1 = +_[1][1]), reset()) : x0 == null ? null : [[x0, y0], [x1, y1]]; | |
| }, | |
| scale: function(_) { | |
| return arguments.length ? (transform = scaleTranslate((k = +_) * sx, k * sy, tx, ty), reset()) : k; | |
| }, | |
| translate: function(_) { | |
| return arguments.length ? (transform = scaleTranslate(k * sx, k * sy, tx = +_[0], ty = +_[1]), reset()) : [tx, ty]; | |
| }, | |
| reflectX: function(_) { | |
| return arguments.length ? (transform = scaleTranslate(k * (sx = _ ? -1 : 1), k * sy, tx, ty), reset()) : sx < 0; | |
| }, | |
| reflectY: function(_) { | |
| return arguments.length ? (transform = scaleTranslate(k * sx, k * (sy = _ ? -1 : 1), tx, ty), reset()) : sy < 0; | |
| }, | |
| fitExtent: function(extent, object) { | |
| return fitExtent(projection, extent, object); | |
| }, | |
| fitSize: function(size, object) { | |
| return fitSize(projection, size, object); | |
| } | |
| }; | |
| } | |
| function orthographicRaw(x, y) { | |
| return [cos(y) * sin(x), sin(y)]; | |
| } | |
| orthographicRaw.invert = azimuthalInvert(asin); | |
| function orthographic() { | |
| return projection(orthographicRaw) | |
| .scale(249.5) | |
| .clipAngle(90 + epsilon); | |
| } | |
| function stereographicRaw(x, y) { | |
| var cy = cos(y), k = 1 + cos(x) * cy; | |
| return [cy * sin(x) / k, sin(y) / k]; | |
| } | |
| stereographicRaw.invert = azimuthalInvert(function(z) { | |
| return 2 * atan(z); | |
| }); | |
| function stereographic() { | |
| return projection(stereographicRaw) | |
| .scale(250) | |
| .clipAngle(142); | |
| } | |
| function transverseMercatorRaw(lambda, phi) { | |
| return [log(tan((halfPi + phi) / 2)), -lambda]; | |
| } | |
| transverseMercatorRaw.invert = function(x, y) { | |
| return [-y, 2 * atan(exp(x)) - halfPi]; | |
| }; | |
| function transverseMercator() { | |
| var m = mercatorProjection(transverseMercatorRaw), | |
| center = m.center, | |
| rotate = m.rotate; | |
| m.center = function(_) { | |
| return arguments.length ? center([-_[1], _[0]]) : (_ = center(), [_[1], -_[0]]); | |
| }; | |
| m.rotate = function(_) { | |
| return arguments.length ? rotate([_[0], _[1], _.length > 2 ? _[2] + 90 : 90]) : (_ = rotate(), [_[0], _[1], _[2] - 90]); | |
| }; | |
| return rotate([0, 0, 90]) | |
| .scale(159.155); | |
| } | |
| exports.geoArea = area; | |
| exports.geoBounds = bounds; | |
| exports.geoCentroid = centroid; | |
| exports.geoCircle = circle; | |
| exports.geoClipExtent = extent; | |
| exports.geoContains = contains; | |
| exports.geoDistance = distance; | |
| exports.geoGraticule = graticule; | |
| exports.geoGraticule10 = graticule10; | |
| exports.geoInterpolate = interpolate; | |
| exports.geoLength = length; | |
| exports.geoPath = index; | |
| exports.geoAlbers = albers; | |
| exports.geoAlbersUsa = albersUsa; | |
| exports.geoAzimuthalEqualArea = azimuthalEqualArea; | |
| exports.geoAzimuthalEqualAreaRaw = azimuthalEqualAreaRaw; | |
| exports.geoAzimuthalEquidistant = azimuthalEquidistant; | |
| exports.geoAzimuthalEquidistantRaw = azimuthalEquidistantRaw; | |
| exports.geoConicConformal = conicConformal; | |
| exports.geoConicConformalRaw = conicConformalRaw; | |
| exports.geoConicEqualArea = conicEqualArea; | |
| exports.geoConicEqualAreaRaw = conicEqualAreaRaw; | |
| exports.geoConicEquidistant = conicEquidistant; | |
| exports.geoConicEquidistantRaw = conicEquidistantRaw; | |
| exports.geoEquirectangular = equirectangular; | |
| exports.geoEquirectangularRaw = equirectangularRaw; | |
| exports.geoGnomonic = gnomonic; | |
| exports.geoGnomonicRaw = gnomonicRaw; | |
| exports.geoIdentity = identity$1; | |
| exports.geoProjection = projection; | |
| exports.geoProjectionMutator = projectionMutator; | |
| exports.geoMercator = mercator; | |
| exports.geoMercatorRaw = mercatorRaw; | |
| exports.geoOrthographic = orthographic; | |
| exports.geoOrthographicRaw = orthographicRaw; | |
| exports.geoStereographic = stereographic; | |
| exports.geoStereographicRaw = stereographicRaw; | |
| exports.geoTransverseMercator = transverseMercator; | |
| exports.geoTransverseMercatorRaw = transverseMercatorRaw; | |
| exports.geoRotation = rotation; | |
| exports.geoStream = geoStream; | |
| exports.geoTransform = transform; | |
| Object.defineProperty(exports, '__esModule', { value: true }); | |
| })); |
| <!DOCTYPE html> | |
| <html> | |
| <head> | |
| <meta charset="utf-8"> | |
| <style> | |
| .poly { | |
| fill: #999; | |
| fill-opacity: 0.4; | |
| stroke: black; | |
| stroke-width: .5px; | |
| } | |
| .graticule { | |
| fill: none; | |
| stroke: #777; | |
| stroke-width: 0.3px; | |
| stroke-opacity: 0.5; | |
| } | |
| .sphere { | |
| fill: none; | |
| stroke: black; | |
| stroke-width: 2px; | |
| } | |
| .face { | |
| fill: lightblue; | |
| } | |
| </style> | |
| <title>Furuti 1</title> | |
| </head> | |
| <body> | |
| <script src="https://d3js.org/d3.v4.min.js"></script> | |
| <script src="https://unpkg.com/d3-geo"></script> | |
| <script src="https://unpkg.com/d3-geo-polygon"></script> | |
| <script src="https://recifs.neocities.org/d3-geo-projection-clip-polyhedral.js"></script> | |
| <script src="versor.js"></script> | |
| <script> | |
| var width = 960, height = 500; | |
| var scaleProj = Math.min(width/2, height)/Math.PI; | |
| // imports | |
| var atan = Math.atan, sqrt1_2 = Math.sqrt(1/2), pi = Math.PI, degrees = 180 / Math.PI; | |
| var d3Geo = d3, polyhedral = d3.geoPolyhedral; | |
| var phi1 = atan(sqrt1_2) * degrees; | |
| var cube = [ | |
| [0, phi1], [90, phi1], [180, phi1], [-90, phi1], | |
| [0, -phi1], [90, -phi1], [180, -phi1], [-90, -phi1] | |
| ]; | |
| var cube$1 = [ | |
| [0, 3, 2, 1], // N | |
| [0, 1, 5, 4], | |
| [1, 2, 6, 5], | |
| [2, 3, 7, 6], | |
| [3, 0, 4, 7], | |
| [4, 5, 6, 7] // S | |
| ].map(function(face) { | |
| return face.map(function(i) { | |
| return cube[i]; | |
| }); | |
| }); | |
| var f1 = function(faceProjection) { | |
| // it is possible to pass a specific projection on each face | |
| // by default is is a gnomonic projection centered on the face's centroid | |
| // scale 1 by convention | |
| faceProjection = faceProjection || function(face) { | |
| var c = d3Geo.geoCentroid({type: "MultiPoint", coordinates: face}); | |
| return d3Geo.geoGnomonic().scale(1).translate([0, 0]).rotate([-c[0], -c[1]]); | |
| }; | |
| // the faces from the cube each yield | |
| // - face: its four vertices | |
| // - contains: does this face contain a point? | |
| // - project: local projection on this face | |
| var faces = cube$1.map(function(face) { | |
| var polygon = face.slice(); | |
| polygon.push(polygon[0]); | |
| return { | |
| face: face, | |
| contains: function(lambda, phi) { | |
| return d3Geo.geoContains({ type: "Polygon", coordinates: [ polygon ] }, | |
| [lambda * degrees, phi * degrees]); | |
| }, | |
| project: faceProjection(face) | |
| }; | |
| }); | |
| // Build a tree of the faces, starting with face 0 (North Pole) | |
| // which has no parent (-1); the next four faces around the equator | |
| // are attached to the north face (0); the face containing the South Pole | |
| // is attached to South America (4) | |
| [-1, 4, 5, 2, 0, 1].forEach(function(d, i) { | |
| var node = faces[d]; | |
| node && (node.children || (node.children = [])).push(faces[i]); | |
| }); | |
| // Polyhedral projection | |
| var proj = polyhedral(faces[0], function(lambda, phi) { | |
| for (var i = 0; i < faces.length; i++) { | |
| if (faces[i].contains(lambda, phi)) return faces[i]; | |
| } | |
| }, | |
| pi/2, // rotation of the root face in the projected (pixel) space | |
| true // use clipPolygon | |
| ) | |
| //.clipAngle(1) // no antimeridian clipping on the Sphere | |
| .fitExtent([[20,20],[width-20, height-20]], {type:"Sphere"}) | |
| proj.faces = faces; | |
| return proj; | |
| }; | |
| d3.geoPolyhedralFuruti1 = f1; | |
| var projection = d3.geoPolyhedralFuruti1() | |
| .rotate([30,0]) | |
| var path = d3.geoPath().projection(projection); | |
| var graticule = d3.geoGraticule(); | |
| var svg = d3.select("body").append("svg") | |
| .attr("width", width) | |
| .attr("height", height); | |
| svg.call(d3.drag().on("start", dragstarted).on("drag", dragged)); | |
| var movable = svg.append("g"); | |
| var countries = movable.append("g") | |
| .attr("class", "poly"); | |
| d3.json('countries.geo.json', function(err, world) { | |
| countries | |
| .selectAll('path') | |
| .data(world.features) | |
| .enter() | |
| .append('path') | |
| .attr("d", path); | |
| }); | |
| movable.selectAll(".graticule") | |
| .data(graticule.lines) | |
| .enter().append("path") | |
| .attr("class", "graticule") | |
| .attr("d", path); | |
| var rot = projection.rotate(); | |
| projection.rotate([]); | |
| svg.append("path") | |
| .datum({type: "MultiPoint", coordinates: projection.faces.map(function(face) { | |
| return d3.geoCentroid({type: "MultiPoint", coordinates: face.face}); | |
| })}) | |
| .attr("class", "face") | |
| .attr("d", path); | |
| projection.rotate(rot); | |
| movable.append('path') | |
| .datum({type: "Point", coordinates: [0,90]}) | |
| .attr('d', path); | |
| movable.append('path') | |
| .datum({type: "Point", coordinates: [0,-90]}) | |
| .attr('d', path); | |
| svg.append('path') | |
| .datum({type: "Sphere"}) | |
| .attr("class", "sphere") | |
| .attr('d', path); | |
| var render = function() { | |
| movable.selectAll('path').attr('d', path); | |
| }, | |
| v0, // Mouse position in Cartesian coordinates at start of drag gesture. | |
| r0, // Projection rotation as Euler angles at start. | |
| q0; // Projection rotation as versor at start. | |
| function dragstarted() { | |
| v0 = versor.cartesian(projection.invert(d3.mouse(this))); | |
| r0 = projection.rotate(); | |
| q0 = versor(r0); | |
| } | |
| function dragged() { | |
| var inv = projection.rotate(r0).invert(d3.mouse(this)); | |
| if (!inv || isNaN(inv[0])) return; | |
| var v1 = versor.cartesian(inv), | |
| q1 = versor.multiply(q0, versor.delta(v0, v1)), | |
| r1 = versor.rotation(q1); | |
| projection.rotate(r1); | |
| render(); | |
| } | |
| // projection.rotate([29, -11, 12]) && render() | |
| </script> | |
| </body> | |
| </html> |
| // Version 0.0.0. Copyright 2017 Mike Bostock. | |
| (function(global, factory) { | |
| typeof exports === 'object' && typeof module !== 'undefined' ? module.exports = factory() : | |
| typeof define === 'function' && define.amd ? define(factory) : | |
| (global.versor = factory()); | |
| }(this, (function() {'use strict'; | |
| var acos = Math.acos, | |
| asin = Math.asin, | |
| atan2 = Math.atan2, | |
| cos = Math.cos, | |
| max = Math.max, | |
| min = Math.min, | |
| PI = Math.PI, | |
| sin = Math.sin, | |
| sqrt = Math.sqrt, | |
| radians = PI / 180, | |
| degrees = 180 / PI; | |
| // Returns the unit quaternion for the given Euler rotation angles [λ, φ, γ]. | |
| function versor(e) { | |
| var l = e[0] / 2 * radians, sl = sin(l), cl = cos(l), // λ / 2 | |
| p = e[1] / 2 * radians, sp = sin(p), cp = cos(p), // φ / 2 | |
| g = e[2] / 2 * radians, sg = sin(g), cg = cos(g); // γ / 2 | |
| return [ | |
| cl * cp * cg + sl * sp * sg, | |
| sl * cp * cg - cl * sp * sg, | |
| cl * sp * cg + sl * cp * sg, | |
| cl * cp * sg - sl * sp * cg | |
| ]; | |
| } | |
| // Returns Cartesian coordinates [x, y, z] given spherical coordinates [λ, φ]. | |
| versor.cartesian = function(e) { | |
| var l = e[0] * radians, p = e[1] * radians, cp = cos(p); | |
| return [cp * cos(l), cp * sin(l), sin(p)]; | |
| }; | |
| // Returns the Euler rotation angles [λ, φ, γ] for the given quaternion. | |
| versor.rotation = function(q) { | |
| return [ | |
| atan2(2 * (q[0] * q[1] + q[2] * q[3]), 1 - 2 * (q[1] * q[1] + q[2] * q[2])) * degrees, | |
| asin(max(-1, min(1, 2 * (q[0] * q[2] - q[3] * q[1])))) * degrees, | |
| atan2(2 * (q[0] * q[3] + q[1] * q[2]), 1 - 2 * (q[2] * q[2] + q[3] * q[3])) * degrees | |
| ]; | |
| }; | |
| // Returns the quaternion to rotate between two cartesian points on the sphere. | |
| versor.delta = function(v0, v1) { | |
| var w = cross(v0, v1), l = sqrt(dot(w, w)); | |
| if (!l) return [1, 0, 0, 0]; | |
| var t = acos(max(-1, min(1, dot(v0, v1)))) / 2, s = sin(t); // t = θ / 2 | |
| return [cos(t), w[2] / l * s, -w[1] / l * s, w[0] / l * s]; | |
| }; | |
| // Returns the quaternion that represents q0 * q1. | |
| versor.multiply = function(q0, q1) { | |
| return [ | |
| q0[0] * q1[0] - q0[1] * q1[1] - q0[2] * q1[2] - q0[3] * q1[3], | |
| q0[1] * q1[0] + q0[0] * q1[1] + q0[2] * q1[3] - q0[3] * q1[2], | |
| q0[0] * q1[2] - q0[1] * q1[3] + q0[2] * q1[0] + q0[3] * q1[1], | |
| q0[0] * q1[3] + q0[1] * q1[2] - q0[2] * q1[1] + q0[3] * q1[0] | |
| ]; | |
| }; | |
| function cross(v0, v1) { | |
| return [ | |
| v0[1] * v1[2] - v0[2] * v1[1], | |
| v0[2] * v1[0] - v0[0] * v1[2], | |
| v0[0] * v1[1] - v0[1] * v1[0] | |
| ]; | |
| } | |
| function dot(v0, v1) { | |
| return v0[0] * v1[0] + v0[1] * v1[1] + v0[2] * v1[2]; | |
| } | |
| return versor; | |
| }))); |
