d3/d3.geom.js

d3.geom = {};
/**
 * Computes a contour for a given input grid function using the
 * <a href="http://en.wikipedia.org/wiki/Marching_squares">
 * marching squares</a> algorithm. Returns the contour polygon as an
 * array of points [[x1, y1], [x2, y2], ...]
 *
 * @param grid a two input (x,y) function that returns either 0 or 1
 * @param start [x1, y1] an optional starting point on the grid
 */
d3["geom"]["contour"] = function(grid, start) {
  var s = start || d3_geom_contour_start(grid),
      c = [], x = s[0], y = s[1],
      i, dx=0, dy=0, pdx=NaN, pdy=NaN;

  do {
    i = grid(x-1,y-1) + 2*grid(x,y-1) + 4*grid(x-1,y) + 8*grid(x,y);
    if (i == 6) {
      dx = pdy==-1 ? -1 : 1;
      dy = 0;
    } else if (i == 9) {
      dx = 0;
      dy = pdx==1 ? -1 : 1;
    } else {
      dx = d3_geom_contour_dx[i];
      dy = d3_geom_contour_dy[i];
    }
	if (dx != pdx && dy != pdy) {
      c.push([x, y]);
      pdx = dx; pdy = dy;
    }
    x += dx;
    y += dy;
  } while (s[0] != x || s[1] != y);

  return c;
}

var d3_geom_contour_dx = [1, 0, 1, 1,-1, 0,-1, 1,0, 0,0,0,-1, 0,-1,NaN];
var d3_geom_contour_dy = [0,-1, 0, 0, 0,-1, 0, 0,1,-1,1,1, 0,-1, 0,NaN];

function d3_geom_contour_start(grid) {
  // search for a starting point; begin at origin
  // and proceed along outward-expanding diagonals 
  var x = 0, y = 0;
  while (true) {
    if (grid(x,y)) {
      return [x,y];
    }
    if (x == 0) {
      x = y + 1;
      y = 0;
    } else {
      x = x - 1;
      y = y + 1;
    }
  }
}/**
 * Computes the 2D convex hull of a set of points using Graham's scanning
 * algorithm. The algorithm has been implemented as described in Cormen,
 * Leiserson, and Rivest's Introduction to Algorithms. The running time of
 * this algorithm is O(n log n), where n is the number of input points.
 *
 * @param vertices [[x1, y1], [x2, y2], …]
 * @returns polygon [[x1, y1], [x2, y2], …],
 */
d3.geom.hull = function(vertices) {
  if (vertices.length < 3) return [];

  var len = vertices.length,
      plen = len - 1,
      points = [],
      stack = [],
      i, j, h = 0, x1, y1, x2, y2, u, v, a, sp;

  // find the starting ref point: leftmost point with the minimum y coord
  for (i=1; i<len; ++i) {
    if (vertices[i][1] < vertices[h][1]) {
      h = i;
    } else if (vertices[i][1] == vertices[h][1]) {
      h = (vertices[i][0] < vertices[h][0] ? i : h);
    }
  }

  // calculate polar angles from ref point and sort
  for (i=0; i<len; ++i) {
    if (i == h) continue;
    y1 = vertices[i][1] - vertices[h][1];
    x1 = vertices[i][0] - vertices[h][0];
    points.push({angle: Math.atan2(y1, x1), index: i});
  }
  points.sort(function(a, b) { return a.angle - b.angle; });

  // toss out duplicate angles
  a = points[0].angle;
  v = points[0].index;
  u = 0;
  for (i=1; i<plen; ++i) {
    j = points[i].index;
    if (a == points[i].angle) {
      // keep angle for point most distant from the reference
      x1 = vertices[v][0] - vertices[h][0];
      y1 = vertices[v][1] - vertices[h][1];
      x2 = vertices[j][0] - vertices[h][0];
      y2 = vertices[j][1] - vertices[h][1];
      if ((x1*x1 + y1*y1) >= (x2*x2 + y2*y2)) {
        points[i].index = -1;
      } else {
        points[u].index = -1;
        a = points[i].angle;
        u = i;
        v = j;
      }
    } else {
      a = points[i].angle;
      u = i;
      v = j;
    }
  }

  // initialize the stack
  stack.push(h);
  for (i=0, j=0; i<2; ++j) {
    if (points[j].index != -1) {
      stack.push(points[j].index);
      i++;
    }
  }
  sp = stack.length;

  // do graham's scan
  for (; j<plen; ++j) {
    if (points[j].index == -1) continue; // skip tossed out points
    while (!d3_geom_hullCCW(stack[sp-2], stack[sp-1], points[j].index, vertices)) {
      --sp;
    }
    stack[sp++] = points[j].index;
  }

  // construct the hull
  var poly = [];
  for (i=0; i<sp; ++i) {
    poly.push(vertices[stack[i]]);
  }
  return poly;
}

// are three points in counter-clockwise order?
function d3_geom_hullCCW(i1, i2, i3, v) {
  var t, a, b, c, d, e, f;
  t = v[i1]; a = t[0]; b = t[1];
  t = v[i2]; c = t[0]; d = t[1];
  t = v[i3]; e = t[0]; f = t[1];
  return ((f-b)*(c-a) - (d-b)*(e-a)) > 0;
}// Note: requires coordinates to be counterclockwise and convex!
d3.geom.polygon = function(coordinates) {

  coordinates.area = function() {
    var i = 0,
        n = coordinates.length,
        a = coordinates[n - 1][0] * coordinates[0][1],
        b = coordinates[n - 1][1] * coordinates[0][0];
    while (++i < n) {
      a += coordinates[i - 1][0] * coordinates[i][1];
      b += coordinates[i - 1][1] * coordinates[i][0];
    }
    return (b - a) * .5;
  };

  // The Sutherland-Hodgman clipping algorithm.
  coordinates.clip = function(subject) {
    var input,
        i = -1,
        n = coordinates.length,
        j,
        m,
        a = coordinates[n - 1],
        b,
        c,
        d;
    while (++i < n) {
      input = subject.slice();
      subject.length = 0;
      b = coordinates[i];
      c = input[(m = input.length) - 1];
      j = -1;
      while (++j < m) {
        d = input[j];
        if (d3_geom_polygonInside(d, a, b)) {
          if (!d3_geom_polygonInside(c, a, b)) {
            subject.push(d3_geom_polygonIntersect(c, d, a, b));
          }
          subject.push(d);
        } else if (d3_geom_polygonInside(c, a, b)) {
          subject.push(d3_geom_polygonIntersect(c, d, a, b));
        }
        c = d;
      }
      a = b;
    }
    return subject;
  };

  return coordinates;
};

function d3_geom_polygonInside(p, a, b) {
  return (b[0] - a[0]) * (p[1] - a[1]) < (b[1] - a[1]) * (p[0] - a[0]);
}

// Intersect two infinite lines cd and ab.
function d3_geom_polygonIntersect(c, d, a, b) {
  var x1 = c[0], x2 = d[0], x3 = a[0], x4 = b[0],
      y1 = c[1], y2 = d[1], y3 = a[1], y4 = b[1],
      x13 = x1 - x3,
      x21 = x2 - x1,
      x43 = x4 - x3,
      y13 = y1 - y3,
      y21 = y2 - y1,
      y43 = y4 - y3,
      ua = (x43 * y13 - y43 * x13) / (y43 * x21 - x43 * y21);
  return [x1 + ua * x21, y1 + ua * y21];
}
// Adapted from Nicolas Garcia Belmonte's JIT implementation:
// http://blog.thejit.org/2010/02/12/voronoi-tessellation/
// http://blog.thejit.org/assets/voronoijs/voronoi.js
// See lib/jit/LICENSE for details.

/**
 * @param vertices [[x1, y1], [x2, y2], …]
 * @returns polygons [[[x1, y1], [x2, y2], …], …]
 */
d3.geom.voronoi = function(vertices) {
  var polygons = vertices.map(function() { return []; });

  // Note: we expect the caller to clip the polygons, if needed.
  d3_voronoi_tessellate(vertices, function(e) {
    var s1,
        s2,
        x1,
        x2,
        y1,
        y2;
    if (e.a == 1 && e.b >= 0) {
      s1 = e.ep["r"];
      s2 = e.ep["l"];
    } else {
      s1 = e.ep["l"];
      s2 = e.ep["r"];
    }
    if (e.a == 1) {
      y1 = s1 ? s1.y : -1e6;
      x1 = e.c - e.b * y1;
      y2 = s2 ? s2.y : 1e6;
      x2 = e.c - e.b * y2;
    } else {
      x1 = s1 ? s1.x : -1e6;
      y1 = e.c - e.a * x1;
      x2 = s2 ? s2.x : 1e6;
      y2 = e.c - e.a * x2;
    }
    var v1 = [x1, y1],
        v2 = [x2, y2];
    polygons[e.region["l"].index].push(v1, v2);
    polygons[e.region["r"].index].push(v1, v2);
  });

  // Reconnect the polygon segments into counterclockwise loops.
  return polygons.map(function(polygon, i) {
    var cx = vertices[i][0],
        cy = vertices[i][1];
    polygon.forEach(function(v) {
      v.angle = Math.atan2(v[0] - cx, v[1] - cy);
    });
    return polygon.sort(function(a, b) {
      return a.angle - b.angle;
    }).filter(function(d, i) {
      return !i || (d.angle - polygon[i - 1].angle > 1e-10);
    });
  });
};

var d3_voronoi_opposite = {"l": "r", "r": "l"};

function d3_voronoi_tessellate(vertices, callback) {

  var Sites = {
    list: vertices
      .map(function(v, i) {
        return {
          index: i,
          x: v[0],
          y: v[1]
        };
      })
      .sort(function(a, b) {
        return a.y < b.y ? -1
          : a.y > b.y ? 1
          : a.x < b.x ? -1
          : a.x > b.x ? 1
          : 0;
      }),
    bottomSite: null
  };

  var EdgeList = {
    list: [],
    leftEnd: null,
    rightEnd: null,

    init: function() {
      EdgeList.leftEnd = EdgeList.createHalfEdge(null, "l");
      EdgeList.rightEnd = EdgeList.createHalfEdge(null, "l");
      EdgeList.leftEnd["r"] = EdgeList.rightEnd;
      EdgeList.rightEnd["l"] = EdgeList.leftEnd;
      EdgeList.list.unshift(EdgeList.leftEnd, EdgeList.rightEnd);
    },

    createHalfEdge: function(edge, side) {
      return {
        edge: edge,
        side: side,
        vertex: null,
        "l": null,
        "r": null
      };
    },

    insert: function(lb, he) {
      he["l"] = lb;
      he["r"] = lb["r"];
      lb["r"]["l"] = he;
      lb["r"] = he;
    },

    leftBound: function(p) {
      var he = EdgeList.leftEnd;
      do {
        he = he["r"];
      } while (he != EdgeList.rightEnd && Geom.rightOf(he, p));
      he = he["l"];
      return he;
    },

    del: function(he) {
      he["l"]["r"] = he["r"];
      he["r"]["l"] = he["l"];
      he.edge = null;
    },

    right: function(he) {
      return he["r"];
    },

    left: function(he) {
      return he["l"];
    },

    leftRegion: function(he) {
      return he.edge == null
          ? Sites.bottomSite
          : he.edge.region[he.side];
    },

    rightRegion: function(he) {
      return he.edge == null
          ? Sites.bottomSite
          : he.edge.region[d3_voronoi_opposite[he.side]];
    }
  };

  var Geom = {

    bisect: function(s1, s2) {
      var newEdge = {
        region: {"l": s1, "r": s2},
        ep: {"l": null, "r": null}
      };

      var dx = s2.x - s1.x,
          dy = s2.y - s1.y,
          adx = dx > 0 ? dx : -dx,
          ady = dy > 0 ? dy : -dy;

      newEdge.c = s1.x * dx + s1.y * dy
          + (dx * dx + dy * dy) * .5;

      if (adx > ady) {
        newEdge.a = 1;
        newEdge.b = dy / dx;
        newEdge.c /= dx;
      } else {
        newEdge.b = 1;
        newEdge.a = dx / dy;
        newEdge.c /= dy;
      }

      return newEdge;
    },

    intersect: function(el1, el2) {
      var e1 = el1.edge,
          e2 = el2.edge;
      if (!e1 || !e2 || (e1.region["r"] == e2.region["r"])) {
        return null;
      }
      var d = (e1.a * e2.b) - (e1.b * e2.a);
      if (Math.abs(d) < 1e-10) {
        return null;
      }
      var xint = (e1.c * e2.b - e2.c * e1.b) / d,
          yint = (e2.c * e1.a - e1.c * e2.a) / d,
          e1r = e1.region["r"],
          e2r = e2.region["r"],
          el,
          e;
      if ((e1r.y < e2r.y) ||
         (e1r.y == e2r.y && e1r.x < e2r.x)) {
        el = el1;
        e = e1;
      } else {
        el = el2;
        e = e2;
      }
      var rightOfSite = (xint >= e.region["r"].x);
      if ((rightOfSite && (el.side == "l")) ||
        (!rightOfSite && (el.side == "r"))) {
        return null;
      }
      return {
        x: xint,
        y: yint
      };
    },

    rightOf: function(he, p) {
      var e = he.edge,
          topsite = e.region["r"],
          rightOfSite = (p.x > topsite.x);

      if (rightOfSite && (he.side == "l")) {
        return 1;
      }
      if (!rightOfSite && (he.side == "r")) {
        return 0;
      }
      if (e.a == 1) {
        var dyp = p.y - topsite.y,
            dxp = p.x - topsite.x,
            fast = 0,
            above = 0;

        if ((!rightOfSite && (e.b < 0)) ||
          (rightOfSite && (e.b >= 0))) {
          above = fast = (dyp >= e.b * dxp);
        } else {
          above = ((p.x + p.y * e.b) > e.c);
          if (e.b < 0) {
            above = !above;
          }
          if (!above) {
            fast = 1;
          }
        }
        if (!fast) {
          var dxs = topsite.x - e.region["l"].x;
          above = (e.b * (dxp * dxp - dyp * dyp)) <
            (dxs * dyp * (1 + 2 * dxp / dxs + e.b * e.b));

          if (e.b < 0) {
            above = !above;
          }
        }
      } else /* e.b == 1 */ {
        var yl = e.c - e.a * p.x,
            t1 = p.y - yl,
            t2 = p.x - topsite.x,
            t3 = yl - topsite.y;

        above = (t1 * t1) > (t2 * t2 + t3 * t3);
      }
      return he.side == "l" ? above : !above;
    },

    endPoint: function(edge, side, site) {
      edge.ep[side] = site;
      if (!edge.ep[d3_voronoi_opposite[side]]) return;
      callback(edge);
    },

    distance: function(s, t) {
      var dx = s.x - t.x,
          dy = s.y - t.y;
      return Math.sqrt(dx * dx + dy * dy);
    }
  };

  var EventQueue = {
    list: [],

    insert: function(he, site, offset) {
      he.vertex = site;
      he.ystar = site.y + offset;
      for (var i=0, list=EventQueue.list, l=list.length; i<l; i++) {
        var next = list[i];
        if (he.ystar > next.ystar ||
          (he.ystar == next.ystar &&
          site.x > next.vertex.x)) {
          continue;
        } else {
          break;
        }
      }
      list.splice(i, 0, he);
    },

    del: function(he) {
      for (var i=0, ls=EventQueue.list, l=ls.length; i<l && (ls[i] != he); ++i) {}
      ls.splice(i, 1);
    },

    empty: function() { return EventQueue.list.length == 0; },

    nextEvent: function(he) {
      for (var i=0, ls=EventQueue.list, l=ls.length; i<l; ++i) {
        if (ls[i] == he) return ls[i+1];
      }
      return null;
    },

    min: function() {
      var elem = EventQueue.list[0];
      return {
        x: elem.vertex.x,
        y: elem.ystar
      };
    },

    extractMin: function() {
      return EventQueue.list.shift();
    }
  };

  EdgeList.init();
  Sites.bottomSite = Sites.list.shift();

  var newSite = Sites.list.shift(), newIntStar;
  var lbnd, rbnd, llbnd, rrbnd, bisector;
  var bot, top, temp, p, v;
  var e, pm;

  while (true) {
    if (!EventQueue.empty()) {
      newIntStar = EventQueue.min();
    }
    if (newSite && (EventQueue.empty()
      || newSite.y < newIntStar.y
      || (newSite.y == newIntStar.y
      && newSite.x < newIntStar.x))) { //new site is smallest
      lbnd = EdgeList.leftBound(newSite);
      rbnd = EdgeList.right(lbnd);
      bot = EdgeList.rightRegion(lbnd);
      e = Geom.bisect(bot, newSite);
      bisector = EdgeList.createHalfEdge(e, "l");
      EdgeList.insert(lbnd, bisector);
      p = Geom.intersect(lbnd, bisector);
      if (p) {
        EventQueue.del(lbnd);
        EventQueue.insert(lbnd, p, Geom.distance(p, newSite));
      }
      lbnd = bisector;
      bisector = EdgeList.createHalfEdge(e, "r");
      EdgeList.insert(lbnd, bisector);
      p = Geom.intersect(bisector, rbnd);
      if (p) {
        EventQueue.insert(bisector, p, Geom.distance(p, newSite));
      }
      newSite = Sites.list.shift();
    } else if (!EventQueue.empty()) { //intersection is smallest
      lbnd = EventQueue.extractMin();
      llbnd = EdgeList.left(lbnd);
      rbnd = EdgeList.right(lbnd);
      rrbnd = EdgeList.right(rbnd);
      bot = EdgeList.leftRegion(lbnd);
      top = EdgeList.rightRegion(rbnd);
      v = lbnd.vertex;
      Geom.endPoint(lbnd.edge, lbnd.side, v);
      Geom.endPoint(rbnd.edge, rbnd.side, v);
      EdgeList.del(lbnd);
      EventQueue.del(rbnd);
      EdgeList.del(rbnd);
      pm = "l";
      if (bot.y > top.y) {
        temp = bot;
        bot = top;
        top = temp;
        pm = "r";
      }
      e = Geom.bisect(bot, top);
      bisector = EdgeList.createHalfEdge(e, pm);
      EdgeList.insert(llbnd, bisector);
      Geom.endPoint(e, d3_voronoi_opposite[pm], v);
      p = Geom.intersect(llbnd, bisector);
      if (p) {
        EventQueue.del(llbnd);
        EventQueue.insert(llbnd, p, Geom.distance(p, bot));
      }
      p = Geom.intersect(bisector, rrbnd);
      if (p) {
        EventQueue.insert(bisector, p, Geom.distance(p, bot));
      }
    } else {
      break;
    }
  }//end while

  for (lbnd = EdgeList.right(EdgeList.leftEnd);
      lbnd != EdgeList.rightEnd;
      lbnd = EdgeList.right(lbnd)) {
    callback(lbnd.edge);
  }
}
/**
* @param vertices [[x1, y1], [x2, y2], …]
* @returns triangles [[[x1, y1], [x2, y2], [x3, y3]], …]
 */
d3.geom.delaunay = function(vertices) {
  var edges = vertices.map(function() { return []; }),
      triangles = [];

  // Use the Voronoi tessellation to determine Delaunay edges.
  d3_voronoi_tessellate(vertices, function(e) {
    edges[e.region["l"].index].push(vertices[e.region["r"].index]);
  });

  // Reconnect the edges into counterclockwise triangles.
  edges.forEach(function(edge, i) {
    var v = vertices[i],
        cx = v[0],
        cy = v[1];
    edge.forEach(function(v) {
      v.angle = Math.atan2(v[0] - cx, v[1] - cy);
    });
    edge.sort(function(a, b) {
      return a.angle - b.angle;
    });
    for (var j = 0, m = edge.length - 1; j < m; j++) {
      triangles.push([v, edge[j], edge[j + 1]]);
    }
  });

  return triangles;
};