index.js

import {geoBounds as bounds, geoCentroid as centroid, geoInterpolate as interpolate, geoProjection as projection} from "d3-geo";
import {abs, degrees, epsilon, radians} from "../math.js";
import {default as matrix, multiply, inverse} from "./matrix.js";

// 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).
export default function(root, face) {

  recurse(root, {transform: null});

  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(shared[0], edges[i][1]) && pointEqual(shared[1], edges[i][0])) edges[i] = node;
        if (pointEqual(shared[0], edges[i][0]) && pointEqual(shared[1], edges[i][1])) edges[i] = node;
      }
      edges = node.edges;
      for (i = 0, n = edges.length; i < n; ++i) {
        if (pointEqual(shared[0], edges[i][0]) && pointEqual(shared[1], edges[i][1])) edges[i] = parent;
        if (pointEqual(shared[0], edges[i][1]) && pointEqual(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 = projection(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.angle(-30);
}

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 = bounds({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]
      : centroid(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 = interpolate(edge[0], c)(epsilon))[0], point[1]);
        inside = true;
      }
      stream.point((point = interpolate(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(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);
}