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Diffstat (limited to 'media/d3.geom.js')
-rw-r--r-- | media/d3.geom.js | 835 |
1 files changed, 0 insertions, 835 deletions
diff --git a/media/d3.geom.js b/media/d3.geom.js deleted file mode 100644 index d860c2bf..00000000 --- a/media/d3.geom.js +++ /dev/null @@ -1,835 +0,0 @@ -(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] - }; -} -})(); |