A mashup of Map Projection Distortions and examples using the d3 projections plugin
A comparison of map projections by four different types of distortion. Lower is better. Data transcribed from the Natural Earth Projection by @mbostock
Read more about map projections on Wikipedia
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| <!DOCTYPE html> | |
| <meta charset="utf-8"> | |
| <title>Map Projections</title> | |
| <style> | |
| body { | |
| margin-top:30px; | |
| margin-left: 20px; | |
| } | |
| svg { | |
| font: 10px sans-serif; | |
| } | |
| .background path { | |
| fill: none; | |
| stroke: none; | |
| stroke-width: 24px; | |
| pointer-events: stroke; | |
| } | |
| .foreground path { | |
| fill: none; | |
| stroke: steelblue; | |
| stroke-width: 1px; | |
| } | |
| .axis .title { | |
| font-size: 11px; | |
| font-weight: bold; | |
| text-transform: uppercase; | |
| } | |
| .axis line, | |
| .axis path { | |
| fill: none; | |
| stroke: #000; | |
| shape-rendering: crispEdges; | |
| } | |
| .label { | |
| -webkit-transition: fill 125ms linear; | |
| } | |
| .active .label:not(.inactive) { | |
| font-weight: bold; | |
| } | |
| .label.inactive { | |
| fill: #888; | |
| } | |
| .foreground path.inactive { | |
| stroke: #888; | |
| stroke-opacity: .3; | |
| stroke-width: 1px; | |
| } | |
| path.background { | |
| fill: #A5BFDD; | |
| } | |
| path.foreground { | |
| fill: none; | |
| stroke: #333; | |
| stroke-width: 0.51px; | |
| } | |
| path.graticule { | |
| fill: none; | |
| stroke: #fff; | |
| stroke-width: .5px; | |
| } | |
| .line:nth-child(2n) { | |
| stroke-dasharray: 2,2; | |
| } | |
| .land { | |
| fill: #fff; | |
| stroke: #766951; | |
| } | |
| .boundary { | |
| fill: none; | |
| stroke: #a5967e; | |
| } | |
| #projections { margin: 20px 20px 0;} | |
| a { font-family: Helvetica; display: inline-block; margin: 5px; font-size: 15px; color: #88b;} | |
| </style> | |
| <body> | |
| <script src="d3.v2.min.js"></script> | |
| <script src="jquery.min.js"></script> | |
| <div id="projections"></div> | |
| <script src="projection.js"></script> | |
| <script> | |
| /* Projections */ | |
| var projections = { | |
| "Aitoff": d3.geo.aitoff().scale(135), | |
| "Bonne": d3.geo.bonne().scale(135), | |
| "Eckert I": d3.geo.eckert1().scale(140), | |
| "Eckert II": d3.geo.eckert2().scale(140), | |
| "Eckert III": d3.geo.eckert3().scale(144), | |
| "Eckert IV": d3.geo.eckert4().scale(144), | |
| "Eckert V": d3.geo.eckert5().scale(140), | |
| "Eckert VI": d3.geo.eckert6().scale(140), | |
| "Equidistant Cylindrical (Plate Carrée)": d3.geo.equirectangular().scale(660), | |
| "Hammer": d3.geo.hammer().scale(140), | |
| "Kavraisky VII": d3.geo.kavrayskiy7().scale(135), | |
| "Mercator": d3.geo.mercator().scale(380), | |
| "Mollweide": d3.geo.mollweide().scale(100), | |
| "Nell–Hammer": d3.geo.nellHammer().scale(124), | |
| "Robinson": d3.geo.robinson().scale(135), | |
| "Sinusoidal": d3.geo.sinusoidal().scale(130), | |
| "van der Grinten (I)": d3.geo.vanDerGrinten().scale(84), | |
| "Wagner VI": d3.geo.wagner6().scale(135), | |
| "Winkel Tripel": d3.geo.winkel3().scale(135) | |
| }; | |
| $.each(projections, function(name) { | |
| var a = $('<a href="#">'+name+'</a>'); | |
| a.click(function(e) { | |
| e.preventDefault(); | |
| changeproj($(e.target).html()); | |
| }); | |
| $('#projections').append(a); | |
| }) | |
| /* Map */ | |
| var map_width = 860, | |
| map_height = 500; | |
| var projection = d3.geo.aitoff() | |
| .translate([map_width / 2 - .5, map_height / 2 - .5]).scale(135); | |
| var path = d3.geo.path() | |
| .projection(projection); | |
| var graticule = d3.geo.graticule(); | |
| var map_svg = d3.select("body").append("svg") | |
| .attr("width", map_width) | |
| .attr("height", map_height); | |
| map_svg.append("path") | |
| .datum(graticule.outline) | |
| .attr("class", "background") | |
| .attr("d", path) | |
| map_svg.selectAll(".graticule") | |
| .data(graticule.lines) | |
| .enter().append("path") | |
| .attr("class", "graticule") | |
| .attr("d", path); | |
| map_svg.append("path") | |
| .datum(graticule.outline) | |
| .attr("class", "foreground") | |
| .attr("d", path); | |
| d3.json("readme-boundaries.json", function(collection) { | |
| map_svg.insert("g", ".graticule") | |
| .attr("class", "boundary") | |
| .selectAll("path") | |
| .data(collection.geometries) | |
| .enter().append("path") | |
| .attr("d", path); | |
| }); | |
| d3.json("readme-land.json", function(collection) { | |
| map_svg.insert("g", ".graticule,.boundary") | |
| .attr("class", "land") | |
| .selectAll("path") | |
| .data(collection.geometries) | |
| .enter().append("path") | |
| .attr("d", path); | |
| }); | |
| /* Parallel Coordinates */ | |
| function changeproj(name) { | |
| if (!(name in projections)) return; | |
| // update map | |
| projection = projections[name] | |
| .translate([map_width / 2 - .5, map_height / 2 - .5]); | |
| path = d3.geo.path() | |
| .projection(projection); | |
| map_svg.selectAll("path") | |
| .transition() | |
| .duration(1200) | |
| .attr("d", path); | |
| } | |
| function draw(d) { | |
| return line(dimensions.map(function(dimension) { | |
| return [x(dimension.name), dimension.scale(d[dimension.name])]; | |
| })); | |
| } | |
| </script> | |
| </body> | |
| </html> |
| /*! jQuery v1.6.4 http://jquery.com/ | http://jquery.org/license */ | |
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| (function() { | |
| var ε = 1e-6, | |
| π = Math.PI, | |
| sqrtπ = Math.sqrt(π); | |
| var robinsonConstants = [ | |
| [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] | |
| ]; | |
| function identity(d) { | |
| return d; | |
| } | |
| function sinci(x) { | |
| return x ? x / Math.sin(x) : 1; | |
| } | |
| function sgn(x) { | |
| return x > 0 ? 1 : x < 0 ? -1 : 0; | |
| } | |
| function aitoff(λ, φ) { | |
| var cosφ = Math.cos(φ), | |
| sinciα = sinci(Math.acos(cosφ * Math.cos(λ /= 2))); | |
| return [ | |
| 2 * cosφ * Math.sin(λ) * sinciα, | |
| Math.sin(φ) * sinciα | |
| ]; | |
| } | |
| function winkel3(λ, φ) { | |
| var coordinates = aitoff(λ, φ); | |
| return [ | |
| (coordinates[0] + λ * 2 / π) / 2, | |
| (coordinates[1] + φ) / 2 | |
| ]; | |
| } | |
| function kavrayskiy7(λ, φ) { | |
| return [ | |
| 3 * λ / (2 * π) * Math.sqrt(π * π / 3 - φ * φ), | |
| φ | |
| ]; | |
| } | |
| function kavrayskiy7Inverse(x, y) { | |
| return [ | |
| 2 / 3 * π * x / Math.sqrt(π * π / 3 - y * y), | |
| y | |
| ]; | |
| } | |
| function wagner6(λ, φ) { | |
| return [ | |
| λ * Math.sqrt(1 - 3 * φ * φ / (π * π)), | |
| φ | |
| ]; | |
| } | |
| function robinson(λ, φ) { | |
| var i = Math.min(18, Math.abs(φ) * 36 / π), | |
| i0 = Math.floor(i), | |
| di = i - i0, | |
| k0 = robinsonConstants[i0], | |
| k1 = robinsonConstants[Math.ceil(i)], | |
| ax = k0[0], | |
| ay = k0[1], | |
| dx = k1[0] - ax, | |
| dy = k1[1] - ay; | |
| return [ | |
| λ * (ax + dx * di), | |
| (φ > 0 ? π : -π) / 2 * (ay + dy * di) | |
| ]; | |
| } | |
| function cylindricalEqualArea(φ0) { | |
| var cosφ0 = Math.cos(φ0); | |
| return function(λ, φ) { | |
| return [ | |
| λ * cosφ0, | |
| Math.sin(φ) / cosφ0 | |
| ]; | |
| }; | |
| } | |
| function cylindricalEqualAreaInverse(φ0) { | |
| var cosφ0 = Math.cos(φ0); | |
| return function(x, y) { | |
| return [ | |
| x / cosφ0, | |
| Math.asin(y * cosφ0) | |
| ]; | |
| }; | |
| } | |
| function sinusoidal(λ, φ) { | |
| return [ | |
| λ * Math.cos(φ), | |
| φ | |
| ]; | |
| } | |
| function sinusoidalInverse(x, y) { | |
| return [ | |
| x / Math.cos(y), | |
| y | |
| ]; | |
| } | |
| function hammer(λ, φ) { | |
| var cosφ = Math.cos(φ), | |
| k = Math.sqrt(2 / (1 + cosφ * Math.cos(λ /= 2))); | |
| return [ | |
| Math.sin(λ) * cosφ * k * 2, | |
| Math.sin(φ) * k | |
| ]; | |
| } | |
| function hammerInverse(x, y) { | |
| var z2 = 1 - x * x / 16 - y * y / 4, | |
| z = Math.sqrt(z2); | |
| return [ | |
| 2 * Math.atan2(z * x, 4 * z2 - 2), | |
| Math.asin(z * y) | |
| ]; | |
| } | |
| function eckert1(λ, φ) { | |
| var α = Math.sqrt(8 / (3 * π)); | |
| return [ | |
| α * λ * (1 - Math.abs(φ) / π), | |
| α * φ | |
| ]; | |
| } | |
| function eckert1Inverse(x, y) { | |
| var α = Math.sqrt(8 / (3 * π)), | |
| φ = y / α; | |
| return [ | |
| x / (α * (1 - Math.abs(φ) / π)), | |
| φ | |
| ]; | |
| } | |
| function eckert2(λ, φ) { | |
| var α = Math.sqrt(4 - 3 * Math.sin(Math.abs(φ))); | |
| return [ | |
| 2 / Math.sqrt(6 * π) * λ * α, | |
| sgn(φ) * Math.sqrt(2 * π / 3) * (2 - α) | |
| ]; | |
| } | |
| function eckert2Inverse(x, y) { | |
| var α = 2 - Math.abs(y) / Math.sqrt(2 * π / 3); | |
| return [ | |
| x * Math.sqrt(6 * π) / (2 * α), | |
| sgn(y) * Math.asin((4 - α * α) / 3) | |
| ]; | |
| } | |
| function eckert3(λ, φ) { | |
| var k = Math.sqrt(π * (4 + π)); | |
| return [ | |
| 2 / k * λ * (1 + Math.sqrt(1 - 4 * φ * φ / (π * π))), | |
| 4 / k * φ | |
| ]; | |
| } | |
| function eckert3Inverse(x, y) { | |
| var k = Math.sqrt(π * (4 + π)) / 2; | |
| return [ | |
| x * k / (1 + Math.sqrt(Math.max(0, 1 - y * y * (4 + π) / (4 * π)))), | |
| y * k / 2 | |
| ]; | |
| } | |
| function eckert4(λ, φ) { | |
| var k = (2 + π / 2) * Math.sin(φ); | |
| φ /= 2; | |
| for (var i = 0, δ = Infinity; i < 10 && Math.abs(δ) > ε; i++) { | |
| var cosφ = Math.cos(φ); | |
| φ -= δ = (φ + Math.sin(φ) * (cosφ + 2) - k) / (2 * cosφ * (1 + cosφ)); | |
| } | |
| return [ | |
| 2 / Math.sqrt(π * (4 + π)) * λ * (1 + Math.cos(φ)), | |
| 2 * Math.sqrt(π / (4 + π)) * Math.sin(φ) | |
| ]; | |
| } | |
| function eckert4Inverse(x, y) { | |
| var j = 2 * Math.sqrt(π / (4 + π)), | |
| k = Math.asin(y / cy); | |
| return [ | |
| x / (2 / Math.sqrt(π * (4 + π)) * (1 + (c = Math.cos(k)))), | |
| Math.asin((k + y / j * (c + 2)) / (2 + π / 2)) | |
| ]; | |
| } | |
| function eckert5(λ, φ) { | |
| return [ | |
| λ * (1 + Math.cos(φ)) / Math.sqrt(2 + π), | |
| 2 * φ / Math.sqrt(2 + π) | |
| ]; | |
| } | |
| function eckert5Inverse(x, y) { | |
| var k = Math.sqrt(2 + π), | |
| φ = y * k / 2; | |
| return [ | |
| k * x / (1 + Math.cos(φ)), | |
| φ | |
| ]; | |
| } | |
| function eckert6(λ, φ) { | |
| var k = (1 + π / 2) * Math.sin(φ); | |
| for (var i = 0, δ = Infinity; i < 10 && Math.abs(δ) > ε; i++) { | |
| φ -= δ = (φ + Math.sin(φ) - k) / (1 + Math.cos(φ)); | |
| } | |
| k = Math.sqrt(2 + π); | |
| return [ | |
| λ * (1 + Math.cos(φ)) / k, | |
| 2 * φ / k | |
| ]; | |
| } | |
| function eckert6Inverse(x, y) { | |
| var j = 1 + Math.PI / 2, | |
| k = Math.sqrt(j / 2); | |
| return [ | |
| x * 2 * k / (1 + Math.cos(y *= k)), | |
| Math.asin((y + Math.sin(y)) / j) | |
| ]; | |
| } | |
| function mollweide(λ, φ) { | |
| if (Math.abs(φ) !== π / 2) { | |
| var k = π / 2 * Math.sin(φ); | |
| for (var i = 0, δ = Infinity; i < 10 && Math.abs(δ) > ε; i++) { | |
| φ -= δ = (φ + Math.sin(2 * φ) / 2 - k) / (1 + Math.cos(2 * φ)); | |
| } | |
| } | |
| return [ | |
| 2 * Math.SQRT2 / π * λ * Math.cos(φ), | |
| Math.SQRT2 * Math.sin(φ) | |
| ]; | |
| } | |
| function mollweideInverse(x, y) { | |
| var θ = Math.asin(y / Math.SQRT2); | |
| return [ | |
| π * x / (2 * Math.SQRT2 * Math.cos(θ)), | |
| Math.asin((2 * θ + Math.sin(2 * θ)) / π) | |
| ]; | |
| } | |
| function homolosine(λ, φ) { | |
| if (Math.abs(φ) > 40.733 * π / 180) { | |
| var coordinates = mollweide(λ, φ); | |
| coordinates[1] -= φ >= 0 ? .0528 : -.0528; | |
| return coordinates; | |
| } else return sinusoidal(λ, φ); | |
| } | |
| function homolosineInverse(x, y) { | |
| if (Math.abs(y) > 40.733 * π / 180) { | |
| coordinates = mollweideInverse(x, y); | |
| coordinates[1] += y >= 0 ? .0528 : -.0528; | |
| return coordinates; | |
| } else return sinusoidalInverse(x, y); | |
| } | |
| function august(λ, φ) { | |
| var tanφ = Math.tan(φ / 2), | |
| k = 1 - tanφ * tanφ, | |
| c = 1 + k * Math.cos(λ /= 2), | |
| x = Math.sin(λ) * k / c, | |
| y = tanφ / c, | |
| x2 = x * x, | |
| y2 = y * y; | |
| return [ | |
| 4 / 3 * x * (3 + x2 - 3 * y2), | |
| 4 / 3 * y * (3 + 3 * x2 - y2) | |
| ]; | |
| } | |
| function eisenlohr(λ, φ) { | |
| var f = 3 + Math.sqrt(8), | |
| s1 = Math.sin(λ /= 2), | |
| c1 = Math.cos(λ), | |
| k = Math.sqrt(Math.cos(φ) / 2), | |
| cosφ2 = Math.cos(φ /= 2), | |
| t = Math.sin(φ) / (cosφ2 + 2 * c1 * k), | |
| c = Math.sqrt(2 / (1 + t * t)), | |
| v = Math.sqrt((cosφ2 + (c1 + s1) * k) | |
| / (cosφ2 + (c1 - s1) * k)); | |
| return [ | |
| f * (c * (v - 1 / v) - 2 * Math.log(v)), | |
| f * (c * t * (v + 1 / v) - 2 * Math.atan(t)) | |
| ]; | |
| } | |
| function bonne(φ0) { | |
| var cotφ0 = 1 / Math.tan(φ0); | |
| return function(λ, φ) { | |
| var ρ = cotφ0 + φ0 - φ, | |
| E = λ * Math.cos(φ) / ρ; | |
| return [ | |
| ρ * Math.sin(E), | |
| cotφ0 - ρ * Math.cos(E) | |
| ]; | |
| }; | |
| } | |
| function bonneInverse(φ0) { | |
| var cotφ0 = 1 / Math.tan(φ0); | |
| return function(x, y) { | |
| var ρ = Math.sqrt(x * x + (y = cotφ0 - y) * y), | |
| φ = cotφ0 + φ0 - ρ; | |
| return [ | |
| ρ / Math.cos(φ) * Math.atan2(x, y), | |
| φ | |
| ]; | |
| }; | |
| } | |
| function collignon(λ, φ) { | |
| var α = Math.sqrt(Math.max(0, 1 - Math.sin(φ))); | |
| return [ | |
| (2 / sqrtπ) * λ * α, | |
| sqrtπ * (1 - α) | |
| ]; | |
| } | |
| function collignonInverse(x, y) { | |
| var λ = (λ = y / sqrtπ - 1) * λ; | |
| return [ | |
| λ > 0 ? x * Math.sqrt(π / λ) / 2 : 0, | |
| Math.asin(Math.max(-1, Math.min(1, 1 - λ))) | |
| ]; | |
| } | |
| function larrivee(λ, φ) { | |
| return [ | |
| λ * (1 + Math.sqrt(Math.cos(φ))) / 2, | |
| φ / (Math.cos(φ / 2) * Math.cos(λ / 6)) | |
| ]; | |
| } | |
| function vanDerGrinten(λ, φ) { | |
| if (Math.abs(φ) < ε) return [λ, 0]; | |
| var sinθ = Math.abs(2 * φ / π), | |
| θ = Math.asin(sinθ); | |
| if (Math.abs(λ) < ε || Math.abs(Math.abs(φ) - π / 2) < ε) return [0, sgn(φ) * π * Math.tan(θ / 2)]; | |
| var cosθ = Math.cos(θ), | |
| A = Math.abs(π / λ - λ / π) / 2, | |
| A2 = A * A, | |
| G = cosθ / (sinθ + cosθ - 1), | |
| P = G * (2 / sinθ - 1), | |
| P2 = P * P, | |
| P2_A2 = P2 + A2, | |
| G_P2 = G - P2, | |
| Q = A2 + G; | |
| return [ | |
| sgn(λ) * π * (A * G_P2 + Math.sqrt(A2 * G_P2 * G_P2 - P2_A2 * (G * G - P2))) / P2_A2, | |
| sgn(φ) * π * (P * Q - A * Math.sqrt((A2 + 1) * P2_A2 - Q * Q)) / P2_A2 | |
| ]; | |
| } | |
| function vanDerGrintenInverse(x, y) { | |
| if (Math.abs(y) < ε) return [x, 0]; | |
| if (Math.abs(x) < ε) return [0, π / 2 * Math.sin(2 * Math.atan(y / π))]; | |
| var x2 = (x /= π) * x, | |
| y2 = (y /= π) * y, | |
| x2_y2 = x2 + y2, | |
| z = x2_y2 * x2_y2, | |
| c1 = -Math.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 * Math.sqrt(-a1 / 3), | |
| θ1 = Math.acos(3 * d / (a1 * m1)) / 3; | |
| return [ | |
| π * (x2_y2 - 1 + Math.sqrt(1 + 2 * (x2 - y2) + z)) / (2 * x), | |
| sgn(y) * π * (-m1 * Math.cos(θ1 + π / 3) - c2 / (3 * c3)) | |
| ]; | |
| } | |
| function nellHammer(λ, φ) { | |
| return [ | |
| λ * (1 + Math.cos(φ)) / 2, | |
| 2 * (φ - Math.tan(φ / 2)) | |
| ]; | |
| } | |
| function nellHammerInverse(x, y) { | |
| var p = y / 2; | |
| for (var i = 0, δ = Infinity; i < 10 && Math.abs(δ) > ε; i++) { | |
| var c = Math.cos(y / 2); | |
| y -= δ = (y - Math.tan(y / 2) - p) / (1 - .5 / (c * c)); | |
| } | |
| return [ | |
| 2 * x / (1 + Math.cos(y)), | |
| y | |
| ]; | |
| } | |
| function polyconic(λ, φ) { | |
| if (Math.abs(φ) < ε) return [λ, 0]; | |
| var tanφ = Math.tan(φ), | |
| k = λ * Math.sin(φ); | |
| return [ | |
| Math.sin(k) / tanφ, | |
| φ + (1 - Math.cos(k)) / tanφ | |
| ]; | |
| } | |
| function polyconicInverse(x, y) { | |
| if (Math.abs(y) < ε) return [x, 0]; | |
| var k = x * x + y * y, | |
| φ = y; | |
| for (var i = 0, δ = Infinity; i < 10 && Math.abs(δ) > ε; i++) { | |
| var tanφ = Math.tan(φ); | |
| φ -= δ = (y * (φ * tanφ + 1) - φ - .5 * (φ * φ + k) * tanφ) / ((φ - y) / tanφ - 1); | |
| } | |
| return [ | |
| Math.asin(x * Math.tan(φ)) / Math.sin(φ), | |
| φ | |
| ]; | |
| } | |
| function miller(λ, φ) { | |
| return [ | |
| λ, | |
| 1.25 * Math.log(Math.tan(π / 4 + .4 * φ)) | |
| ]; | |
| } | |
| function millerInverse(x, y) { | |
| return [ | |
| x, | |
| 2.5 * Math.atan(Math.exp(.8 * y)) - .625 * π | |
| ]; | |
| } | |
| function conicConformal(φ0, φ1) { | |
| var cosφ0 = Math.cos(φ0), | |
| n = Math.log(cosφ0 / Math.cos(φ1)) / Math.log(t(φ1) / t(φ0)), | |
| F = cosφ0 * Math.pow(t(φ0), n) / n; | |
| function t(φ) { return Math.tan(π / 4 + φ / 2); } | |
| return function(λ, φ) { | |
| var ρ = Math.abs(Math.abs(φ) - π / 2) < ε ? 0 : F / Math.pow(t(φ), n); | |
| return [ | |
| ρ * Math.sin(n * λ), | |
| F - ρ * Math.cos(n * λ) | |
| ]; | |
| }; | |
| } | |
| function conicConformalInverse(φ0, φ1) { | |
| var cosφ0 = Math.cos(φ0), | |
| n = Math.log(cosφ0 / Math.cos(φ1)) / Math.log(t(φ1) / t(φ0)), | |
| F = cosφ0 * Math.pow(t(φ0), n) / n; | |
| function t(φ) { return Math.tan(π / 4 + φ / 2); } | |
| return function(x, y) { | |
| var ρ0_y = F - y, | |
| ρ = sgn(n) * Math.sqrt(x * x + ρ0_y * ρ0_y); | |
| return [ | |
| Math.atan2(x, ρ0_y) / n, | |
| 2 * Math.atan(Math.pow(F / ρ, 1 / n)) - π / 2 | |
| ]; | |
| }; | |
| } | |
| function albers(φ0, φ1) { | |
| var sinφ0 = Math.sin(φ0), | |
| n = (sinφ0 + Math.sin(φ1)) / 2, | |
| C = 1 + sinφ0 * (2 * n - sinφ0), | |
| ρ0 = Math.sqrt(C) / n; | |
| return function(λ, φ) { | |
| var ρ = Math.sqrt(C - 2 * n * Math.sin(φ)) / n; | |
| return [ | |
| ρ * Math.sin(n * λ), | |
| ρ0 - ρ * Math.cos(n * λ) | |
| ]; | |
| }; | |
| } | |
| function albersInverse(φ0, φ1) { | |
| var sinφ0 = Math.sin(φ0), | |
| n = (sinφ0 + Math.sin(φ1)) / 2, | |
| C = 1 + sinφ0 * (2 * n - sinφ0), | |
| ρ0 = Math.sqrt(C) / n; | |
| return function(x, y) { | |
| var ρ0_y = ρ0 - y; | |
| return [ | |
| Math.atan2(x, ρ0_y) / n, | |
| Math.asin((C - (x * x + ρ0_y * ρ0_y) * n * n) / (2 * n)) | |
| ]; | |
| }; | |
| } | |
| function conicEquidistant(φ0, φ1) { | |
| var cosφ0 = Math.cos(φ0), | |
| n = (cosφ0 - Math.cos(φ1)) / (φ1 - φ0), | |
| G = cosφ0 / n + φ0; | |
| return function(λ, φ) { | |
| var ρ = G - φ; | |
| return [ | |
| ρ * Math.sin(n * λ), | |
| G - ρ * Math.cos(n * λ) | |
| ]; | |
| }; | |
| } | |
| function conicEquidistantInverse(φ0, φ1) { | |
| var cosφ0 = Math.cos(φ0), | |
| n = (cosφ0 - Math.cos(φ1)) / (φ1 - φ0), | |
| G = cosφ0 / n + φ0; | |
| return function(x, y) { | |
| var ρ0_y = G - y; | |
| return [ | |
| Math.atan2(x, ρ0_y) / n, | |
| G - sgn(n) * Math.sqrt(x * x + ρ0_y * ρ0_y) | |
| ]; | |
| }; | |
| } | |
| function projection(forward, inverse) { | |
| var scale = 150, | |
| translate = [480, 250]; | |
| function p(coordinates) { | |
| coordinates = forward(coordinates[0] * π / 180, coordinates[1] * π / 180); | |
| return [coordinates[0] * scale + translate[0], translate[1] - coordinates[1] * scale]; | |
| } | |
| if (arguments.length > 1) { | |
| p.invert = function(coordinates) { | |
| coordinates = inverse((coordinates[0] - translate[0]) / scale, (translate[1] - coordinates[1]) / scale); | |
| return [coordinates[0] * 180 / π, coordinates[1] * 180 / π]; | |
| }; | |
| } | |
| p.scale = function(_) { | |
| if (!arguments.length) return scale; | |
| scale = +_; | |
| return p; | |
| }; | |
| p.translate = function(_) { | |
| if (!arguments.length) return translate; | |
| translate = [+_[0], +_[1]]; | |
| return p; | |
| }; | |
| return p; | |
| } | |
| function singleParallelProjection(forwardAt, inverseAt) { | |
| var φ0 = 0, | |
| forward = forwardAt(φ0), | |
| inverse = inverseAt ? inverseAt(φ0) : null, | |
| p = inverseAt | |
| ? projection(function(λ, φ) { return forward(λ, φ); }, function(x, y) { return inverse(x, y); }) | |
| : projection(function(λ, φ) { return forward(λ, φ); }); | |
| p.parallel = function(_) { | |
| if (!arguments.length) return φ0 / π * 180; | |
| forward = forwardAt(φ0 = _ * π / 180); | |
| if (inverseAt) inverse = inverseAt(φ0); | |
| return p; | |
| }; | |
| return p; | |
| } | |
| function doubleParallelProjection(forwardAt, inverseAt) { | |
| var φ0 = 0, | |
| φ1 = π / 3, | |
| forward = forwardAt(φ0, φ1), | |
| inverse = inverseAt ? inverseAt(φ0, φ1) : null, | |
| p = inverseAt | |
| ? projection(function(λ, φ) { return forward(λ, φ); }, function(x, y) { return inverse(x, y); }) | |
| : projection(function(λ, φ) { return forward(λ, φ); }); | |
| p.parallels = function(_) { | |
| if (!arguments.length) return [φ0 / π * 180, φ1 / π * 180]; | |
| forward = forwardAt(φ0 = _[0] * π / 180, φ1 = _[1] * π / 180); | |
| if (inverseAt) inverse = inverseAt(φ0, φ1); | |
| return p; | |
| }; | |
| return p; | |
| } | |
| d3.geo.graticule = function() { | |
| var extent = [[-180, -90], [180, 90]], | |
| step = [22.5, 22.5], | |
| precision = [2, 2]; | |
| function graticule() { | |
| return { | |
| type: "GeometryCollection", | |
| geometries: graticule.lines() | |
| }; | |
| } | |
| graticule.lines = function() { | |
| var xSteps = d3.range(extent[0][0], extent[1][0] + precision[0] / 2, precision[0]), | |
| ySteps = d3.range(extent[0][1], extent[1][1] + precision[1] / 2, precision[1]), | |
| xLines = d3.range(extent[0][0], extent[1][0] + step[0] / 2, step[0]).map(function(x) { return ySteps.map(function(y) { return [x, y]; }); }), | |
| yLines = d3.range(extent[0][1], extent[1][1] + step[1] / 2, step[1]).map(function(y) { return xSteps.map(function(x) { return [x, y]; }); }); | |
| return xLines.concat(yLines).map(function(coordinates) { | |
| return { | |
| type: "LineString", | |
| coordinates: coordinates | |
| }; | |
| }); | |
| } | |
| graticule.outline = function() { | |
| var ySteps = d3.range(extent[0][1], extent[1][1] + precision[1] / 2, precision[1]), | |
| xSteps = d3.range(extent[0][0], extent[1][0] + precision[0] / 2, precision[0]), | |
| xLine0 = ySteps.map(function(y) { return [extent[0][0], y]; }), | |
| yLine0 = xSteps.map(function(x) { return [x, extent[1][1]]; }), | |
| xLine1 = ySteps.map(function(y) { return [extent[1][0], y]; }).reverse(), | |
| yLine1 = xSteps.map(function(x) { return [x, extent[0][1]]; }).reverse(); | |
| yLine1.push(xLine0[0]); // closing coordinate | |
| return { | |
| type: "Polygon", | |
| coordinates: [xLine0.concat(yLine0, xLine1, yLine1)] | |
| }; | |
| }; | |
| graticule.extent = function(_) { | |
| if (!arguments.length) return extent; | |
| extent = _; | |
| return graticule; | |
| }; | |
| graticule.step = function(_) { | |
| if (!arguments.length) return step; | |
| step = _; | |
| return graticule; | |
| }; | |
| graticule.precision = function(_) { | |
| if (!arguments.length) return precision; | |
| precision = _; | |
| return graticule; | |
| }; | |
| return graticule; | |
| }; | |
| d3.geo.projection = projection; | |
| d3.geo.aitoff = function() { return projection(aitoff); }; | |
| d3.geo.albersEqualArea = function() { return doubleParallelProjection(albers, albersInverse); }; | |
| d3.geo.august = function() { return projection(august); }; | |
| d3.geo.bonne = function() { return singleParallelProjection(bonne, bonneInverse).parallel(45); }; | |
| d3.geo.collignon = function() { return projection(collignon, collignonInverse); }; | |
| d3.geo.conicConformal = function() { return doubleParallelProjection(conicConformal, conicConformalInverse); }; | |
| d3.geo.conicEquidistant = function() { return doubleParallelProjection(conicEquidistant, conicEquidistantInverse); }; | |
| d3.geo.cylindricalEqualArea = function() { return singleParallelProjection(cylindricalEqualArea, cylindricalEqualAreaInverse); }; | |
| d3.geo.eckert1 = function() { return projection(eckert1, eckert1Inverse); }; | |
| d3.geo.eckert2 = function() { return projection(eckert2, eckert2Inverse); }; | |
| d3.geo.eckert3 = function() { return projection(eckert3, eckert3Inverse); }; | |
| d3.geo.eckert4 = function() { return projection(eckert4, eckert4Inverse); }; | |
| d3.geo.eckert5 = function() { return projection(eckert5, eckert5Inverse); }; | |
| d3.geo.eckert6 = function() { return projection(eckert6, eckert6Inverse); }; | |
| d3.geo.eisenlohr = function() { return projection(eisenlohr); }; | |
| d3.geo.hammer = function() { return projection(hammer, hammerInverse); }; | |
| d3.geo.homolosine = function() { return projection(homolosine, homolosineInverse); }; | |
| d3.geo.kavrayskiy7 = function() { return projection(kavrayskiy7, kavrayskiy7Inverse); }; | |
| d3.geo.larrivee = function() { return projection(larrivee); }; | |
| d3.geo.miller = function() { return projection(miller, millerInverse); }; | |
| d3.geo.mollweide = function() { return projection(mollweide, mollweideInverse); }; | |
| d3.geo.nellHammer = function() { return projection(nellHammer, nellHammerInverse); }; | |
| d3.geo.polyconic = function() { return projection(polyconic, polyconicInverse); }; | |
| d3.geo.robinson = function() { return projection(robinson); }; | |
| d3.geo.sinusoidal = function() { return projection(sinusoidal, sinusoidalInverse); }; | |
| d3.geo.vanDerGrinten = function() { return projection(vanDerGrinten, vanDerGrintenInverse); }; | |
| d3.geo.wagner6 = function() { return projection(wagner6); }; | |
| d3.geo.winkel3 = function() { return projection(winkel3); }; | |
| })(); |
| Acc. 40º 150% | Scale | Areal | Angular | name | |
|---|---|---|---|---|---|
| 87.7 | 0.29 | 0.37 | 18.25 | Eckert III | |
| 87.5 | 0.25 | 0.19 | 20.54 | Natural Earth | |
| 87.4 | 0.27 | 0.17 | 24.2 | Winkel II | |
| 86.5 | 0.23 | 0.28 | 19.15 | Kavraisky VII | |
| 85 | 0.26 | 0.18 | 23.28 | Winkel Tripel | |
| 84.3 | 0.27 | 0.19 | 21.27 | Robinson | |
| 83.2 | 0.25 | 0.43 | 16.14 | Fahey | |
| 81.9 | 0.36 | 0 | 28.73 | Eckert IV | |
| 81.8 | 0.26 | 0.24 | 22.31 | Hölzel | |
| 80.4 | 0.26 | 0.34 | 20.41 | Wagner VI | |
| 80 | 0.3 | 0.29 | 23.47 | Eckert V | |
| 78.4 | 0.32 | 0.07 | 26.38 | McBryde–Thomas Flat-Pole Sine (No. 2) | |
| 78.1 | 0.29 | 0.23 | 25.8 | Winkel I | |
| 77.9 | 0.28 | 0.3 | 22.68 | Wagner III | |
| 76.5 | 0.32 | 0.12 | 26.88 | Wagner II | |
| 76.2 | 0.31 | 0.25 | NaN | Denoyer Semi-elliptical | |
| 75.2 | 0.3 | 0.31 | 24.31 | Putnins P5' | |
| 74.3 | 0.29 | 0.57 | 16.84 | Equidistant Cylindrical (Plate Carrée) | |
| 74.1 | 0.38 | 0 | 30.56 | Kavraisky V | |
| 74 | 0.37 | 0 | 30.71 | Wagner VII | |
| 72.4 | 0.39 | 0 | 31.54 | Putnins P4' | |
| 71.9 | 0.57 | 0 | 30.9 | Cylindrical Equal-Area | |
| 70.6 | 0.39 | 0 | 32.28 | Mollweide | |
| 70.5 | 0.29 | 0.51 | 20.36 | Ginzburg VIII (TsNIIGAiK 1944) | |
| 70.2 | 0.43 | 0 | 30.9 | Nell–Hammer | |
| 69.1 | 0.39 | 0.1 | 30.79 | Putnins P1 | |
| 68.1 | 0.36 | 0.23 | 30.17 | Aitoff | |
| 68.1 | 0.36 | 0.29 | 30.3 | Eckert I | |
| 67 | 0.44 | 0 | 33.33 | Foucaut Sinusoidal | |
| 63.7 | 0.44 | 0 | 35.2 | Boggs Eumorphic | |
| 63 | 0.45 | 0 | 35.5 | Eckert–Greifendorff | |
| 62.9 | 0.39 | 1.3 | 7.63 | Miller Cylindrical I | |
| 62.4 | 0.47 | 0 | 36 | Quartic Authalic | |
| 61.7 | 0.35 | 1.05 | 10.06 | Larrivée | |
| 60.3 | 0.48 | 0 | 36.99 | Craster Parabolic (Putnins P4) | |
| 58.9 | 0.46 | 0 | 36.39 | Goode Homolosine | |
| 57.4 | 0.41 | 1.46 | 7.75 | van der Grinten (I) | |
| 57.4 | 0.57 | 4.79 | 0 | Mercator | |
| 57.1 | 0.51 | 0 | 39.01 | Sinusoidal | |
| 49 | 0.3 | 0.73 | 10.62 | Gall (Gall Stereographic) | |
| 42.2 | 0.74 | 0 | 52.39 | Foucaut |