geodesic.js

(function() {
  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 faces = [
    [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(face) {
    return face.map(function(i) {
      return vertices[i];
    });
  });

  d3.geodesic = {
    multipolygon: function(n) {
      return {
        type: "MultiPolygon",
        coordinates: subdivideFaces(~~n).map(function(face) {
          face = face.map(project);
          face.push(face[0]);
          face = [face];
          return face;
        })
      };
    },
    polygons: function(n) {
      return d3.geodesic.multipolygon(~~n).coordinates.map(function(face) {
        return {type: "Polygon", coordinates: face};
      });
    },
    multilinestring: function(n) {
      return {
        type: "MultiLineString",
        coordinates: subdivideEdges(~~n).map(function(edge) {
          return edge.map(project);
        })
      };
    }
  };

  function subdivideFaces(n) {
    return d3.merge(faces.map(function(face) {
      var i01 = interpolate(face[0], face[1]),
          i02 = interpolate(face[0], face[2]),
          faces = [];

      faces.push([
        face[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) {
          faces.push([
            i1(j / i),
            i2(j / (i + 1)),
            i2((j + 1) / (i + 1))
          ]);
        }
        for (var j = 0; j < i; ++j) {
          faces.push([
            i1(j / i),
            i2((j + 1) / (i + 1)),
            i1((j + 1) / i)
          ]);
        }
      }

      return faces;
    }));
  }

  function subdivideEdges(n) {
    var edges = {};

    subdivideFaces(n).forEach(function(face) {
      add(face[0], face[1]);
      add(face[1], face[2]);
      add(face[2], face[0]);
    });

    function add(p0, p1) {
      var t;
      if (p0[0] < p1[0] || (p0[0] == p1[0] && (p0[1] < p1[1] || (p0[1] == p1[1] && p0[2] < p1[2])))) t = p0, p0 = p1, p1 = t;
      edges[p0.map(round) + " " + p1.map(round)] = [p0, p1];
    }

    function round(d) {
      return d3.round(d, 4);
    }

    return d3.values(edges);
  }

  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
    ];
  }
})();