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Copy pathd3.geom.js
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835 lines (753 loc) · 21.6 KB
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(function(){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.
*
* @param grid a two-input function(x, y) that returns true for values
* inside the contour and false for values outside the contour.
* @param start an optional starting point [x, y] on the grid.
* @returns polygon [[x1, y1], [x2, y2], …]
*/
d3.geom.contour = function(grid, start) {
var s = start || d3_geom_contourStart(grid), // starting point
c = [], // contour polygon
x = s[0], // current x position
y = s[1], // current y position
dx = 0, // next x direction
dy = 0, // next y direction
pdx = NaN, // previous x direction
pdy = NaN, // previous y direction
i = 0;
do {
// determine marching squares index
i = 0;
if (grid(x-1, y-1)) i += 1;
if (grid(x, y-1)) i += 2;
if (grid(x-1, y )) i += 4;
if (grid(x, y )) i += 8;
// determine next direction
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_contourDx[i];
dy = d3_geom_contourDy[i];
}
// update contour polygon
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;
};
// lookup tables for marching directions
var d3_geom_contourDx = [1, 0, 1, 1,-1, 0,-1, 1,0, 0,0,0,-1, 0,-1,NaN],
d3_geom_contourDy = [0,-1, 0, 0, 0,-1, 0, 0,1,-1,1,1, 0,-1, 0,NaN];
function d3_geom_contourStart(grid) {
var x = 0,
y = 0;
// search for a starting point; begin at origin
// and proceed along outward-expanding diagonals
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;
};
coordinates.centroid = function(k) {
var i = -1,
n = coordinates.length - 1,
x = 0,
y = 0,
a,
b,
c;
if (!arguments.length) k = -1 / (6 * coordinates.area());
while (++i < n) {
a = coordinates[i];
b = coordinates[i + 1];
c = a[0] * b[1] - b[0] * a[1];
x += (a[0] + b[0]) * c;
y += (a[1] + b[1]) * c;
}
return [x * k, y * k];
};
// 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.
// 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 vertices 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 vertices [[x1, y1], [x2, y2], …]
* @returns polygons [[[x1, y1], [x2, y2], …], …]
*/
d3.geom.voronoi = function(vertices) {
var polygons = vertices.map(function() { return []; });
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;
};
// Constructs a new quadtree for the specified array of points. A quadtree is a
// two-dimensional recursive spatial subdivision. This implementation uses
// square partitions, dividing each square into four equally-sized squares. Each
// point exists in a unique node; if multiple points are in the same position,
// some points may be stored on internal nodes rather than leaf nodes. Quadtrees
// can be used to accelerate various spatial operations, such as the Barnes-Hut
// approximation for computing n-body forces, or collision detection.
d3.geom.quadtree = function(points, x1, y1, x2, y2) {
var p,
i = -1,
n = points.length;
// Type conversion for deprecated API.
if (n && isNaN(points[0].x)) points = points.map(d3_geom_quadtreePoint);
// Allow bounds to be specified explicitly.
if (arguments.length < 5) {
if (arguments.length === 3) {
y2 = x2 = y1;
y1 = x1;
} else {
x1 = y1 = Infinity;
x2 = y2 = -Infinity;
// Compute bounds.
while (++i < n) {
p = points[i];
if (p.x < x1) x1 = p.x;
if (p.y < y1) y1 = p.y;
if (p.x > x2) x2 = p.x;
if (p.y > y2) y2 = p.y;
}
// Squarify the bounds.
var dx = x2 - x1,
dy = y2 - y1;
if (dx > dy) y2 = y1 + dx;
else x2 = x1 + dy;
}
}
// Recursively inserts the specified point p at the node n or one of its
// descendants. The bounds are defined by [x1, x2] and [y1, y2].
function insert(n, p, x1, y1, x2, y2) {
if (isNaN(p.x) || isNaN(p.y)) return; // ignore invalid points
if (n.leaf) {
var v = n.point;
if (v) {
// If the point at this leaf node is at the same position as the new
// point we are adding, we leave the point associated with the
// internal node while adding the new point to a child node. This
// avoids infinite recursion.
if ((Math.abs(v.x - p.x) + Math.abs(v.y - p.y)) < .01) {
insertChild(n, p, x1, y1, x2, y2);
} else {
n.point = null;
insertChild(n, v, x1, y1, x2, y2);
insertChild(n, p, x1, y1, x2, y2);
}
} else {
n.point = p;
}
} else {
insertChild(n, p, x1, y1, x2, y2);
}
}
// Recursively inserts the specified point p into a descendant of node n. The
// bounds are defined by [x1, x2] and [y1, y2].
function insertChild(n, p, x1, y1, x2, y2) {
// Compute the split point, and the quadrant in which to insert p.
var sx = (x1 + x2) * .5,
sy = (y1 + y2) * .5,
right = p.x >= sx,
bottom = p.y >= sy,
i = (bottom << 1) + right;
// Recursively insert into the child node.
n.leaf = false;
n = n.nodes[i] || (n.nodes[i] = d3_geom_quadtreeNode());
// Update the bounds as we recurse.
if (right) x1 = sx; else x2 = sx;
if (bottom) y1 = sy; else y2 = sy;
insert(n, p, x1, y1, x2, y2);
}
// Create the root node.
var root = d3_geom_quadtreeNode();
root.add = function(p) {
insert(root, p, x1, y1, x2, y2);
};
root.visit = function(f) {
d3_geom_quadtreeVisit(f, root, x1, y1, x2, y2);
};
// Insert all points.
points.forEach(root.add);
return root;
};
function d3_geom_quadtreeNode() {
return {
leaf: true,
nodes: [],
point: null
};
}
function d3_geom_quadtreeVisit(f, node, x1, y1, x2, y2) {
if (!f(node, x1, y1, x2, y2)) {
var sx = (x1 + x2) * .5,
sy = (y1 + y2) * .5,
children = node.nodes;
if (children[0]) d3_geom_quadtreeVisit(f, children[0], x1, y1, sx, sy);
if (children[1]) d3_geom_quadtreeVisit(f, children[1], sx, y1, x2, sy);
if (children[2]) d3_geom_quadtreeVisit(f, children[2], x1, sy, sx, y2);
if (children[3]) d3_geom_quadtreeVisit(f, children[3], sx, sy, x2, y2);
}
}
function d3_geom_quadtreePoint(p) {
return {
x: p[0],
y: p[1]
};
}
})();