diff --git a/js/x11/win/rtree.js b/js/x11/win/rtree.js new file mode 100644 index 0000000..f9cc5d5 --- /dev/null +++ b/js/x11/win/rtree.js @@ -0,0 +1,615 @@ +'use strict'; + +module.exports = rtree; +module.exports.default = rtree; +var Comp = Require('com/compat'); + +var quickselect = Require('x11/win/quickselect'); + +function rtree(maxEntries, format) { + if (!(this instanceof rtree)) return new rtree(maxEntries, format); + + // max entries in a node is 9 by default; min node fill is 40% for best performance + this._maxEntries = Math.max(4, maxEntries || 9); + this._minEntries = Math.max(2, Math.ceil(this._maxEntries * 0.4)); + + if (format) { + this._initFormat(format); + } + + this.clear(); +} + +rtree.prototype = { + + all: function () { + return this._all(this.data, []); + }, + + clear: function () { + this.data = createNode([]); + return this; + }, + + collides: function (bbox) { + + var node = this.data, + toBBox = this.toBBox; + + if (!intersects(bbox, node)) return false; + + var nodesToSearch = [], + i, len, child, childBBox; + + while (node) { + for (i = 0, len = node.children.length; i < len; i++) { + + child = node.children[i]; + childBBox = node.leaf ? toBBox(child) : child; + + if (intersects(bbox, childBBox)) { + if (node.leaf || contains(bbox, childBBox)) return true; + nodesToSearch.push(child); + } + } + node = nodesToSearch.pop(); + } + + return false; + }, + + load: function (data) { + if (!(data && data.length)) return this; + + if (data.length < this._minEntries) { + for (var i = 0, len = data.length; i < len; i++) { + this.insert(data[i]); + } + return this; + } + + // recursively build the tree with the given data from scratch using OMT algorithm + var node = this._build(data.slice(), 0, data.length - 1, 0); + + if (!this.data.children.length) { + // save as is if tree is empty + this.data = node; + + } else if (this.data.height === node.height) { + // split root if trees have the same height + this._splitRoot(this.data, node); + + } else { + if (this.data.height < node.height) { + // swap trees if inserted one is bigger + var tmpNode = this.data; + this.data = node; + node = tmpNode; + } + + // insert the small tree into the large tree at appropriate level + this._insert(node, this.data.height - node.height - 1, true); + } + + return this; + }, + + insert: function (item) { + if (item) this._insert(item, this.data.height - 1); + return this; + }, + + print: function (node,indent) { + if (!node) node=this.data; + if (!indent) indent=0; + var b=node, + s='', + sp=indent==0?'':Comp.printf.spaces(indent); + s=sp+'['+b.x0+','+b.y0+':'+b.x1+','+b.y1+']'+ + (node.shape?' '+node.shape.id:''); + if (node.children) for(var i in node.children) { + s+='\n'; + s+=this.print(node.children[i],indent+2); + } + return s; + }, + + remove: function (item, equalsFn) { + if (!item) return this; + + var node = this.data, + bbox = this.toBBox(item), + path = [], + indexes = [], + i, parent, index, goingUp; + + // depth-first iterative tree traversal + while (node || path.length) { + + if (!node) { // go up + node = path.pop(); + parent = path[path.length - 1]; + i = indexes.pop(); + goingUp = true; + } + + if (node.leaf) { // check current node + index = findItem(item, node.children, equalsFn); + + if (index !== -1) { + // item found, remove the item and condense tree upwards + node.children.splice(index, 1); + path.push(node); + this._condense(path); + return this; + } + } + + if (!goingUp && !node.leaf && contains(node, bbox)) { // go down + path.push(node); + indexes.push(i); + i = 0; + parent = node; + node = node.children[0]; + + } else if (parent) { // go right + i++; + node = parent.children[i]; + goingUp = false; + + } else node = null; // nothing found + } + + return this; + }, + + search: function (bbox) { + + var node = this.data, + result = [], + toBBox = this.toBBox; + + if (!intersects(bbox, node)) return result; + + var nodesToSearch = [], + i, len, child, childBBox; + + while (node) { + for (i = 0, len = node.children.length; i < len; i++) { + + child = node.children[i]; + childBBox = node.leaf ? toBBox(child) : child; + + if (intersects(bbox, childBBox)) { + if (node.leaf) result.push(child); + else if (contains(bbox, childBBox)) this._all(child, result); + else nodesToSearch.push(child); + } + } + node = nodesToSearch.pop(); + } + + return result; + }, + + + + // HELPERS + + toBBox: function (item) { return item; }, + + compareMinX: compareNodeMinX, + compareMinY: compareNodeMinY, + + toJSON: function () { return this.data; }, + + fromJSON: function (data) { + this.data = data; + return this; + }, + + BBoxGroup: function (nodes) { + var bbox={x0:Number.MAX_VALUE,y0:Number.MAX_VALUE,x1:Number.MIN_VALUE,y1:Number.MIN_VALUE}; + for(var i in nodes) { + var node=nodes[i]; + bbox.x0=Math.min(bbox.x0,node.x0); + bbox.y0=Math.min(bbox.y0,node.y0); + bbox.x1=Math.max(bbox.x1,node.x1); + bbox.y1=Math.max(bbox.y1,node.y1); + } + return bbox; + }, + + equal : function (bbox1,bbox2) { + return bbox1.x0 == bbox2.x0 && bbox1.x1 == bbox2.x1 && + bbox1.y0 == bbox2.y0 && bbox1.y1 == bbox2.y1; + }, + + overlap : function (bbox1,bbox2) { + // If one rectangle is on left side of other, l1.x > r2.x || l2.x > r1.x + if (bbox1.x0 > bbox2.x1 || bbox2.x0 > bbox1.x1) + return false; + // If one rectangle is above other, l1.y < r2.y || l2.y < r1.y + if (bbox1.y0 > bbox2.y1 || bbox2.y0 > bbox1.y1) + return false; + return true; + }, + + within : function (bbox1,bbox2) { + return bbox1.x0 >= bbox2.x0 && bbox1.x1 <= bbox2.x1 && + bbox1.y0 >= bbox2.y0 && bbox1.y1 <= bbox2.y1; + }, + + // INTERNALS + _all: function (node, result) { + var nodesToSearch = []; + while (node) { + if (node.leaf) result.push.apply(result, node.children); + else nodesToSearch.push.apply(nodesToSearch, node.children); + + node = nodesToSearch.pop(); + } + return result; + }, + + _build: function (items, left, right, height) { + + var N = right - left + 1, + M = this._maxEntries, + node; + + if (N <= M) { + // reached leaf level; return leaf + node = createNode(items.slice(left, right + 1)); + calcBBox(node, this.toBBox); + return node; + } + + if (!height) { + // target height of the bulk-loaded tree + height = Math.ceil(Math.log(N) / Math.log(M)); + + // target number of root entries to maximize storage utilization + M = Math.ceil(N / Math.pow(M, height - 1)); + } + + node = createNode([]); + node.leaf = false; + node.height = height; + + // split the items into M mostly square tiles + + var N2 = Math.ceil(N / M), + N1 = N2 * Math.ceil(Math.sqrt(M)), + i, j, right2, right3; + + multiSelect(items, left, right, N1, this.compareMinX); + + for (i = left; i <= right; i += N1) { + + right2 = Math.min(i + N1 - 1, right); + + multiSelect(items, i, right2, N2, this.compareMinY); + + for (j = i; j <= right2; j += N2) { + + right3 = Math.min(j + N2 - 1, right2); + + // pack each entry recursively + node.children.push(this._build(items, j, right3, height - 1)); + } + } + + calcBBox(node, this.toBBox); + + return node; + }, + + _chooseSubtree: function (bbox, node, level, path) { + + var i, len, child, targetNode, area, enlargement, minArea, minEnlargement; + + while (true) { + path.push(node); + + if (node.leaf || path.length - 1 === level) break; + + minArea = minEnlargement = Infinity; + + for (i = 0, len = node.children.length; i < len; i++) { + child = node.children[i]; + area = bboxArea(child); + enlargement = enlargedArea(bbox, child) - area; + + // choose entry with the least area enlargement + if (enlargement < minEnlargement) { + minEnlargement = enlargement; + minArea = area < minArea ? area : minArea; + targetNode = child; + + } else if (enlargement === minEnlargement) { + // otherwise choose one with the smallest area + if (area < minArea) { + minArea = area; + targetNode = child; + } + } + } + + node = targetNode || node.children[0]; + } + + return node; + }, + + _insert: function (item, level, isNode) { + + var toBBox = this.toBBox, + bbox = isNode ? item : toBBox(item), + insertPath = []; + + // find the best node for accommodating the item, saving all nodes along the path too + var node = this._chooseSubtree(bbox, this.data, level, insertPath); + + // put the item into the node + node.children.push(item); + extend(node, bbox); + + // split on node overflow; propagate upwards if necessary + while (level >= 0) { + if (insertPath[level].children.length > this._maxEntries) { + this._split(insertPath, level); + level--; + } else break; + } + + // adjust bboxes along the insertion path + this._adjustParentBBoxes(bbox, insertPath, level); + }, + + // split overflowed node into two + _split: function (insertPath, level) { + + var node = insertPath[level], + M = node.children.length, + m = this._minEntries; + + this._chooseSplitAxis(node, m, M); + + var splitIndex = this._chooseSplitIndex(node, m, M); + + var newNode = createNode(node.children.splice(splitIndex, node.children.length - splitIndex)); + newNode.height = node.height; + newNode.leaf = node.leaf; + + calcBBox(node, this.toBBox); + calcBBox(newNode, this.toBBox); + + if (level) insertPath[level - 1].children.push(newNode); + else this._splitRoot(node, newNode); + }, + + _splitRoot: function (node, newNode) { + // split root node + this.data = createNode([node, newNode]); + this.data.height = node.height + 1; + this.data.leaf = false; + calcBBox(this.data, this.toBBox); + }, + + _chooseSplitIndex: function (node, m, M) { + + var i, bbox1, bbox2, overlap, area, minOverlap, minArea, index; + + minOverlap = minArea = Infinity; + + for (i = m; i <= M - m; i++) { + bbox1 = distBBox(node, 0, i, this.toBBox); + bbox2 = distBBox(node, i, M, this.toBBox); + + overlap = intersectionArea(bbox1, bbox2); + area = bboxArea(bbox1) + bboxArea(bbox2); + + // choose distribution with minimum overlap + if (overlap < minOverlap) { + minOverlap = overlap; + index = i; + + minArea = area < minArea ? area : minArea; + + } else if (overlap === minOverlap) { + // otherwise choose distribution with minimum area + if (area < minArea) { + minArea = area; + index = i; + } + } + } + + return index; + }, + + // sorts node children by the best axis for split + _chooseSplitAxis: function (node, m, M) { + + var compareMinX = node.leaf ? this.compareMinX : compareNodeMinX, + compareMinY = node.leaf ? this.compareMinY : compareNodeMinY, + xMargin = this._allDistMargin(node, m, M, compareMinX), + yMargin = this._allDistMargin(node, m, M, compareMinY); + + // if total distributions margin value is minimal for x, sort by x0, + // otherwise it's already sorted by y0 + if (xMargin < yMargin) node.children.sort(compareMinX); + }, + + // total margin of all possible split distributions where each node is at least m full + _allDistMargin: function (node, m, M, compare) { + + node.children.sort(compare); + + var toBBox = this.toBBox, + leftBBox = distBBox(node, 0, m, toBBox), + rightBBox = distBBox(node, M - m, M, toBBox), + margin = bboxMargin(leftBBox) + bboxMargin(rightBBox), + i, child; + + for (i = m; i < M - m; i++) { + child = node.children[i]; + extend(leftBBox, node.leaf ? toBBox(child) : child); + margin += bboxMargin(leftBBox); + } + + for (i = M - m - 1; i >= m; i--) { + child = node.children[i]; + extend(rightBBox, node.leaf ? toBBox(child) : child); + margin += bboxMargin(rightBBox); + } + + return margin; + }, + + _adjustParentBBoxes: function (bbox, path, level) { + // adjust bboxes along the given tree path + for (var i = level; i >= 0; i--) { + extend(path[i], bbox); + } + }, + + _condense: function (path) { + // go through the path, removing empty nodes and updating bboxes + for (var i = path.length - 1, siblings; i >= 0; i--) { + if (path[i].children.length === 0) { + if (i > 0) { + siblings = path[i - 1].children; + siblings.splice(siblings.indexOf(path[i]), 1); + + } else this.clear(); + + } else calcBBox(path[i], this.toBBox); + } + }, + + _initFormat: function (format) { + // data format (x0, y0, x1, y1 accessors) + + // uses eval-type function compilation instead of just accepting a toBBox function + // because the algorithms are very sensitive to sorting functions performance, + // so they should be dead simple and without inner calls + + var compareArr = ['return a', ' - b', ';']; + + this.compareMinX = new Function('a', 'b', compareArr.join(format[0])); + this.compareMinY = new Function('a', 'b', compareArr.join(format[1])); + + this.toBBox = new Function('a', + 'return {x0: a' + format[0] + + ', y0: a' + format[1] + + ', x1: a' + format[2] + + ', y1: a' + format[3] + '};'); + } +}; + +function findItem(item, items, equalsFn) { + if (!equalsFn) return items.indexOf(item); + + for (var i = 0; i < items.length; i++) { + if (equalsFn(item, items[i])) return i; + } + return -1; +} + +// calculate node's bbox from bboxes of its children +function calcBBox(node, toBBox) { + distBBox(node, 0, node.children.length, toBBox, node); +} + +// min bounding rectangle of node children from k to p-1 +function distBBox(node, k, p, toBBox, destNode) { + if (!destNode) destNode = createNode(null); + destNode.x0 = Infinity; + destNode.y0 = Infinity; + destNode.x1 = -Infinity; + destNode.y1 = -Infinity; + + for (var i = k, child; i < p; i++) { + child = node.children[i]; + extend(destNode, node.leaf ? toBBox(child) : child); + } + + return destNode; +} + +function extend(a, b) { + a.x0 = Math.min(a.x0, b.x0); + a.y0 = Math.min(a.y0, b.y0); + a.x1 = Math.max(a.x1, b.x1); + a.y1 = Math.max(a.y1, b.y1); + return a; +} + +function compareNodeMinX(a, b) { return a.x0 - b.x0; } +function compareNodeMinY(a, b) { return a.y0 - b.y0; } + +function bboxArea(a) { return (a.x1 - a.x0) * (a.y1 - a.y0); } +function bboxMargin(a) { return (a.x1 - a.x0) + (a.y1 - a.y0); } + +function enlargedArea(a, b) { + return (Math.max(b.x1, a.x1) - Math.min(b.x0, a.x0)) * + (Math.max(b.y1, a.y1) - Math.min(b.y0, a.y0)); +} + +function intersectionArea(a, b) { + var x0 = Math.max(a.x0, b.x0), + y0 = Math.max(a.y0, b.y0), + x1 = Math.min(a.x1, b.x1), + y1 = Math.min(a.y1, b.y1); + + return Math.max(0, x1 - x0) * + Math.max(0, y1 - y0); +} + +function contains(a, b) { + return a.x0 <= b.x0 && + a.y0 <= b.y0 && + b.x1 <= a.x1 && + b.y1 <= a.y1; +} + +function intersects(a, b) { + return b.x0 <= a.x1 && + b.y0 <= a.y1 && + b.x1 >= a.x0 && + b.y1 >= a.y0; +} + +function createNode(children) { + return { + children: children, + height: 1, + leaf: true, + x0: Infinity, + y0: Infinity, + x1: -Infinity, + y1: -Infinity + }; +} + +// sort an array so that items come in groups of n unsorted items, with groups sorted between each other; +// combines selection algorithm with binary divide & conquer approach + +function multiSelect(arr, left, right, n, compare) { + var stack = [left, right], + mid; + + while (stack.length) { + right = stack.pop(); + left = stack.pop(); + + if (right - left <= n) continue; + + mid = left + Math.ceil((right - left) / n / 2) * n; + quickselect(arr, mid, left, right, compare); + + stack.push(left, mid, mid, right); + } +}