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Tobler Projection
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| license: mit |
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| <!DOCTYPE html> | |
| <head> | |
| <meta charset="utf-8"> | |
| <script src="https://d3js.org/d3.v4.min.js"></script> | |
| <script src="https://cdnjs.cloudflare.com/ajax/libs/topojson/2.2.0/topojson.js"> | |
| </script> | |
| <script>module={}</script> | |
| <script src="https://unpkg.com/integrate-adaptive-simpson/index.js"></script> | |
| <style> | |
| body { margin:0;position:fixed;top:0;right:0;bottom:0;left:0; } | |
| </style> | |
| </head> | |
| <body> | |
| <script> | |
| var abs = Math.abs, | |
| pi = Math.pi, | |
| sign = Math.sign, | |
| sin = Math.sin, | |
| pow = Math.pow | |
| epsilon = 0.00001 | |
| function toblerY(phi, alpha, gamma, k) { | |
| var y=0.01, i = 30, delta; | |
| do { | |
| y -= delta = (sin(phi) - alpha * y + ((alpha - 1) / gamma) * integrate((y) => elipticFunc(y, gamma, k),0, y,1e-4)) / (((alpha - 1) / gamma) * elipticFunc(y, gamma, k) - alpha); | |
| if (y >= gamma) { y = gamma; break }; | |
| if (y <= 0) { y = 0; break } ; | |
| } | |
| while (abs(delta) > epsilon && --i > 0); | |
| return y; | |
| } | |
| function toblerRaw(alpha, gamma, k) { | |
| function forward(lambda, phi) { | |
| return [(alpha + ((1- alpha) / gamma) * elipticFunc(y = toblerY(abs(phi), alpha, gamma, k), gamma, k)) * lambda * 0.8679, sign(phi) * y / 0.8679] | |
| } | |
| return forward; | |
| } | |
| var tobler = function() { | |
| return d3.geoProjection(toblerRaw(0, 1.183136, 2.5)) | |
| } | |
| function elipticFunc(y, gamma, k) { | |
| if (y >= gamma) { return 0 }; | |
| if (y <= 0) { return gamma }; | |
| return pow((pow(gamma, k) - pow(y, k)) , 1.0 / k); | |
| } | |
| function toblerIntegrate(f, a, b) { | |
| var n = 54, | |
| h = (b - a) / n, | |
| s = f(a) + f(b); | |
| for (var i = 1; i < n; i+=2) s += 2 * f(a + i * h); | |
| for (var i = 1; i < n - 1; i+=2) s += 4 * f(a + i * h); | |
| return s * h / 3; | |
| } | |
| var width = 960, | |
| height = 500; | |
| var projection = tobler() | |
| .translate([width / 2, height / 2]) | |
| var canvas = d3.select("body").append("canvas") | |
| .attr("width", width) | |
| .attr("height", height); | |
| var context = canvas.node().getContext("2d"); | |
| var path = d3.geoPath() | |
| .projection(projection.precision(0.1)) | |
| .context(context); | |
| d3.json("https://gist.githubusercontent.com/abenrob/787723ca91772591b47e/raw/8a7f176072d508218e120773943b595c998991be/world-50m.json", | |
| function(error, world) { | |
| if (error) throw error; | |
| var land = topojson.feature(world, world.objects.land), | |
| graticule = d3.geoGraticule(), | |
| outline = {type: "Sphere"}; | |
| context.fillStyle = "#fff"; | |
| context.fillRect(0, 0, width, height); | |
| context.save(); | |
| context.beginPath(); | |
| path(graticule()); | |
| context.strokeStyle = "rgba(119,119,119,0.5)"; | |
| context.stroke(); | |
| context.beginPath(); | |
| path(land); | |
| context.fillStyle = "#000"; | |
| context.fill(); | |
| context.restore(); | |
| context.beginPath(); | |
| path(outline); | |
| context.strokeStyle = "#000"; | |
| context.stroke(); | |
| }); | |
| d3.select(self.frameElement).style("height", height + "px"); | |
| </script> | |
| </body> |
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