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545 lines (481 loc) · 13.9 KB
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import "../arrays/range";
import "../core/functor";
import "../math/trigonometry";
import "../svg/line";
import "delaunay";
import "geom";
import "polygon";
// 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.
// Notes:
//
// This implementation does not clip the returned polygons, so if you want to
// clip them to a particular shape you will need to do that either in SVG or by
// post-processing with d3.geom.polygon's clip method.
//
// If any points are coincident or have NaN positions, the behavior of this
// method is undefined. Most likely invalid polygons will be returned. You
// should filter invalid points, and consolidate coincident points, before
// computing the tessellation.
/**
* @param points [[x1, y1], [x2, y2], …]
* @returns polygons [[[x1, y1], [x2, y2], …], …]
*/
d3.geom.voronoi = function(points) {
var x = d3_svg_lineX,
y = d3_svg_lineY,
clipPolygon = null;
// For backwards-compatibility.
if (arguments.length) return voronoi(points);
function voronoi(data) {
var points,
polygons = data.map(function() { return []; }),
fx = d3_functor(x),
fy = d3_functor(y),
d,
i,
n = data.length,
Z = 1e6;
if (fx === d3_svg_lineX && fy === d3_svg_lineY) points = data;
else for (points = new Array(n), i = 0; i < n; ++i) {
points[i] = [+fx.call(this, d = data[i], i), +fy.call(this, d, i)];
}
d3_geom_voronoiTessellate(points, 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 : -Z;
x1 = e.c - e.b * y1;
y2 = s2 ? s2.y : Z;
x2 = e.c - e.b * y2;
} else {
x1 = s1 ? s1.x : -Z;
y1 = e.c - e.a * x1;
x2 = s2 ? s2.x : Z;
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);
});
// Connect edges into counterclockwise polygons without coincident points.
polygons = polygons.map(function(polygon, i) {
var cx = points[i][0],
cy = points[i][1],
angle = polygon.map(function(v) { return Math.atan2(v[0] - cx, v[1] - cy); }),
order = d3.range(polygon.length).sort(function(a, b) { return angle[a] - angle[b]; });
return order
.filter(function(d, i) { return !i || (angle[d] - angle[order[i - 1]] > ε); })
.map(function(d) { return polygon[d]; });
});
// Fix degenerate polygons.
polygons.forEach(function(polygon, i) {
var n = polygon.length;
if (!n) return polygon.push([-Z, -Z], [-Z, Z], [Z, Z], [Z, -Z]);
if (n > 2) return;
var p0 = points[i],
p1 = polygon[0],
p2 = polygon[1],
x0 = p0[0], y0 = p0[1],
x1 = p1[0], y1 = p1[1],
x2 = p2[0], y2 = p2[1],
dx = Math.abs(x2 - x1), dy = y2 - y1;
if (Math.abs(dy) < ε) { // 0°
var y = y0 < y1 ? -Z : Z;
polygon.push([-Z, y], [Z, y]);
} else if (dx < ε) { // ±90°
var x = x0 < x1 ? -Z : Z;
polygon.push([x, -Z], [x, Z]);
} else {
var y = (x2 - x1) * (y1 - y0) < (x1 - x0) * (y2 - y1) ? Z : -Z,
z = Math.abs(dy) - dx;
if (Math.abs(z) < ε) { // ±45°
<
8000
div>
polygon.push([dy < 0 ? y : -y, y]);
} else {
if (z > 0) y *= -1;
polygon.push([-Z, y], [Z, y]);
}
}
});
if (clipPolygon) for (i = 0; i < n; ++i) clipPolygon.clip(polygons[i]);
for (i = 0; i < n; ++i) polygons[i].point = data[i];
return polygons;
}
voronoi.x = function(_) {
return arguments.length ? (x = _, voronoi) : x;
};
voronoi.y = function(_) {
return arguments.length ? (y = _, voronoi) : y;
};
voronoi.clipExtent = function(_) {
if (!arguments.length) return clipPolygon && [clipPolygon[0], clipPolygon[2]];
if (_ == null) clipPolygon = null;
else {
var x1 = +_[0][0], y1 = +_[0][1], x2 = +_[1][0], y2 = +_[1][1];
clipPolygon = d3.geom.polygon([[x1, y1], [x1, y2], [x2, y2], [x2, y1]]);
}
return voronoi;
};
// @deprecated; use clipExtent instead
voronoi.size = function(_) {
if (!arguments.length) return clipPolygon && clipPolygon[2];
return voronoi.clipExtent(_ && [[0, 0], _]);
};
voronoi.links = function(data) {
var points,
graph = data.map(function() { return []; }),
links = [],
fx = d3_functor(x),
fy = d3_functor(y),
d,
i,
n = data.length;
if (fx === d3_svg_lineX && fy === d3_svg_lineY) points = data;
else for (points = new Array(n), i = 0; i < n; ++i) {
points[i] = [+fx.call(this, d = data[i], i), +fy.call(this, d, i)];
}
d3_geom_voronoiTessellate(points, function(e) {
var l = e.region.l.index,
r = e.region.r.index;
if (graph[l][r]) return;
graph[l][r] = graph[r][l] = true;
links.push({source: data[l], target: data[r]});
});
return links;
};
voronoi.triangles = function(data) {
if (x === d3_svg_lineX && y === d3_svg_lineY) return d3.geom.delaunay(data);
var points = new Array(n),
fx = d3_functor(x),
fy = d3_functor(y),
d,
i = -1,
n = data.length;
while (++i < n) {
(points[i] = [+fx.call(this, d = data[i], i), +fy.call(this, d, i)]).data = d;
}
return d3.geom.delaunay(points).map(function(triangle) {
return triangle.map(function(point) {
return point.data;
});
});
};
return voronoi;
};
var d3_geom_voronoiOpposite = {l: "r", r: "l"};
function d3_geom_voronoiTessellate(points, callback) {
var Sites = {
list: points
.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_geom_voronoiOpposite[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;
CBD1
}
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_geom_voronoiOpposite[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_geom_voronoiOpposite[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);
}
}