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Simple Ellipsoid Gravity
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| (function() { | |
| // From http://bl.ocks.org/mbostock/3057239 | |
| var φ = 1.618033988749895, | |
| ρ = 180 / Math.PI; | |
| var vertices = [ | |
| [1,φ,0], [-1,φ,0], [1,-φ,0], [-1,-φ,0], | |
| [0,1,φ], [0,-1,φ], [0,1,-φ], [0,-1,-φ], | |
| [φ,0,1], [-φ,0,1], [φ,0,-1], [-φ,0,-1] | |
| ]; | |
| var triangles = [ | |
| [0,1,4], [1,9,4], [4,9,5], [5,9,3], [2,3,7], | |
| [3,2,5], [7,10,2], [0,8,10], [0,4,8], [8,2,10], | |
| [8,4,5], [8,5,2], [1,0,6], [11,1,6], [3,9,11], | |
| [6,10,7], [3,11,7], [11,6,7], [6,0,10], [9,1,11] | |
| ].map(function(triangle) { | |
| return triangle.map(function(i) { | |
| return vertices[i]; | |
| }); | |
| }); | |
| d3.geodesic = { | |
| multipolygon: function(n) { | |
| return { | |
| type: "MultiPolygon", | |
| coordinates: geodesic(~~n).map(function(triangle) { | |
| triangle = triangle.map(project); | |
| triangle.push(triangle[0]); | |
| return [triangle]; | |
| }) | |
| }; | |
| }, | |
| polygons: function(n) { | |
| return geodesic(~~n).map(function(triangle) { | |
| triangle = triangle.map(project); | |
| triangle.push(triangle[0]); | |
| return {type: "Polygon", coordinates: [triangle]}; | |
| }); | |
| } | |
| }; | |
| function geodesic(n) { | |
| return d3.merge(triangles.map(function(triangle) { | |
| var i01 = interpolate(triangle[0], triangle[1]), | |
| i02 = interpolate(triangle[0], triangle[2]), | |
| triangles = []; | |
| triangles.push([ | |
| triangle[0], | |
| i01(1 / n), | |
| i02(1 / n) | |
| ]); | |
| for (var i = 1; i < n; ++i) { | |
| var i1 = interpolate(i01(i / n), i02(i / n)), | |
| i2 = interpolate(i01((i + 1) / n), i02((i + 1) / n)); | |
| for (var j = 0; j <= i; ++j) { | |
| triangles.push([ | |
| i1(j / i), | |
| i2(j / (i + 1)), | |
| i2((j + 1) / (i + 1)) | |
| ]); | |
| } | |
| for (var j = 0; j < i; ++j) { | |
| triangles.push([ | |
| i1(j / i), | |
| i1((j + 1) / i), | |
| i2((j + 1) / (i + 1)) | |
| ]); | |
| } | |
| } | |
| return triangles; | |
| })); | |
| } | |
| function interpolate(p0, p1) { | |
| var x0 = p0[0], | |
| y0 = p0[1], | |
| z0 = p0[2], | |
| x1 = p1[0] - x0, | |
| y1 = p1[1] - y0, | |
| z1 = p1[2] - z0; | |
| return function(t) { | |
| return [ | |
| x0 + t * x1, | |
| y0 + t * y1, | |
| z0 + t * z1 | |
| ]; | |
| }; | |
| } | |
| function project(p) { | |
| var x = p[0], | |
| y = p[1], | |
| z = p[2]; | |
| return [ | |
| Math.atan2(y, x) * ρ, | |
| Math.acos(z / Math.sqrt(x * x + y * y + z * z)) * ρ - 90 | |
| ]; | |
| } | |
| })(); |
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| <!DOCTYPE html> | |
| <meta charset="utf-8"> | |
| <style> | |
| path { | |
| stroke: #000; | |
| stroke-width: .5px; | |
| } | |
| circle { | |
| fill: none; | |
| stroke: #000; | |
| stroke-width: 2px; | |
| } | |
| </style> | |
| <body> | |
| <script src="http://d3js.org/d3.v2.min.js?2.9.6"></script> | |
| <script src="geodesic.js"></script> | |
| <script> | |
| var width = 960, | |
| height = 500; | |
| var origin = [0, 0], | |
| velocity = [.010, .005], | |
| t0 = Date.now(); | |
| var projection = d3.geo.azimuthal() | |
| .mode("orthographic") | |
| .origin(origin) | |
| .scale(240); | |
| var path = d3.geo.path() | |
| .projection(projection); | |
| var arc = d3.geo.greatArc() | |
| .source(origin) | |
| .target(function(d) { return d; }); | |
| var svg = d3.select("body").append("svg") | |
| .attr("width", width) | |
| .attr("height", height); | |
| svg.selectAll("path") | |
| .data(d3.geodesic.polygons(8)) | |
| .enter().append("path") | |
| .style("fill", function(d) { return d3.hsl(d.coordinates[0][0][0], .7, .5); }); | |
| svg.append("circle") | |
| .attr("transform", "translate(" + projection(origin) + ")") | |
| .attr("r", 240); | |
| d3.timer(function() { | |
| var t = Date.now() - t0, | |
| o = [origin[0] + t * velocity[0], origin[1] + t * velocity[1]]; | |
| projection.origin(o); | |
| arc.source(o); | |
| svg.selectAll("path").attr("d", function(d) { return visible(d) ? path(d) : null; }); | |
| }); | |
| function visible(d) { | |
| return d.coordinates[0].some(function(p) { | |
| return arc.distance(p) < Math.PI / 2; | |
| }); | |
| } | |
| </script> |
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