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|
L'équateur de Marseille s'appuie sur la Canebière et la prolonge dans les deux directions, jusqu'à faire le tour du monde.
Cette approche a été conçue et développée par Jean-Luc Arnaud dans « Marseille et la Canebière - Echelles du monde », 2017. <halshs-01484193>
Visualisation interactive par Philippe Rivière -- visionscarto.net
Forked from mbostock's block: Versor Dragging II
| // https://d3js.org/d3-geo-projection/ Version 2.1.0. 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 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 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 = guyouComplexAtan(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])]; | |
| } | |
| function guyouComplexAtan(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 guyouComplexDivide(a, b) { | |
| var denominator = b[0] * b[0] + b[1] * b[1]; | |
| return [ | |
| (a[0] * b[0] + a[1] * b[1]) / denominator, | |
| (a[1] * b[0] - a[0] * b[1]) / denominator | |
| ]; | |
| } | |
| 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 = guyouComplexDivide(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 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 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(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(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 = interpolateSphere(lobes); | |
| lobes = 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] | |
| ]; | |
| }); | |
| }); | |
| var 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]]; | |
| }); | |
| }); | |
| 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; | |
| }; | |
| 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); | |
| }; | |
| 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); | |
| }; | |
| 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; | |
| proj.stream = function(stream) { | |
| var rotate = proj.rotate(), | |
| rotateStream = stream_(stream), | |
| sphereStream = (proj.rotate([0, 0]), stream_(stream)); | |
| proj.rotate(rotate); | |
| rotateStream.sphere = function() { | |
| sphereStream.polygonStart(); | |
| sphereStream.lineStart(); | |
| outline(sphereStream, root); | |
| sphereStream.lineEnd(); | |
| sphereStream.polygonEnd(); | |
| }; | |
| return rotateStream; | |
| }; | |
| return proj; | |
| }; | |
| function outline(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)(epsilon))[0], point[1]); | |
| inside = true; | |
| } | |
| stream.point((point = d3Geo.geoInterpolate(edge[1], c)(epsilon))[0], point[1]); | |
| } else { | |
| inside = false; | |
| if (edge !== parent) outline(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]); | |
| }; | |
| // TODO generate on-the-fly to avoid external modification. | |
| var tetrahedron = [ | |
| [0, 90], [-180, -30], [-60, -30], [60, -30] | |
| ]; | |
| var tetrahedron$1 = [ | |
| [0, 2, 1], | |
| [0, 3, 2], | |
| [0, 1, 3], | |
| [1, 2, 3] | |
| ].map(function(face) { | |
| return face.map(function(i) { | |
| return tetrahedron[i]; | |
| }); | |
| }); | |
| var tetrahedricGnomonic = 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 = tetrahedron$1.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) { | |
| if (phi < -pi / 6 ) { | |
| var q = d3Geo.geoGnomonicRaw(lambda,phi); | |
| /// ……… | |
| } | |
| return faces[phi < -pi / 6 ? 3 | |
| : lambda < -pi / 3 ? 0 | |
| : lambda < pi / 3 ? 1 | |
| : 2]; | |
| }) | |
| .scale(301.858) | |
| .center([0, 30]); | |
| }; | |
| 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]); | |
| }; | |
| 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.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.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.geoPolyhedralTetrahedricGnomonic = tetrahedricGnomonic; | |
| exports.geoPolyhedralCollignon = collignon$1; | |
| 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 }); | |
| }))); |
| topo-sans-antarctica: | |
| ndjson-cat ~/Sites/maps/some-geo-data/ne_110m_admin_0_countries/countries.geojson | ndjson-split 'd.features' | ndjson-filter 'd.properties.iso_a3 !== "ATA"' | ndjson-reduce 'p.features.push(d), p' '{type: "FeatureCollection", features: []}' | geo2topo > ~/Sites/d3/269920a4dd223bc48620f284e886cc6c/110m-sans-antarctica.json |
| // https://d3js.org Version 4.8.0. Copyright 2017 Mike Bostock. | |
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(Sorry about that, but we can’t show files that are this big right now.)
(Sorry about that, but we can’t show files that are this big right now.)
(Sorry about that, but we can’t show files that are this big right now.)
