You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
567 lines
16 KiB
JavaScript
567 lines
16 KiB
JavaScript
function quickselect(arr, k, left, right, compare) {
|
|
quickselectStep(arr, k, left || 0, right || (arr.length - 1), compare || defaultCompare);
|
|
}
|
|
|
|
function quickselectStep(arr, k, left, right, compare) {
|
|
|
|
while (right > left) {
|
|
if (right - left > 600) {
|
|
var n = right - left + 1;
|
|
var m = k - left + 1;
|
|
var z = Math.log(n);
|
|
var s = 0.5 * Math.exp(2 * z / 3);
|
|
var sd = 0.5 * Math.sqrt(z * s * (n - s) / n) * (m - n / 2 < 0 ? -1 : 1);
|
|
var newLeft = Math.max(left, Math.floor(k - m * s / n + sd));
|
|
var newRight = Math.min(right, Math.floor(k + (n - m) * s / n + sd));
|
|
quickselectStep(arr, k, newLeft, newRight, compare);
|
|
}
|
|
|
|
var t = arr[k];
|
|
var i = left;
|
|
var j = right;
|
|
|
|
swap(arr, left, k);
|
|
if (compare(arr[right], t) > 0) { swap(arr, left, right); }
|
|
|
|
while (i < j) {
|
|
swap(arr, i, j);
|
|
i++;
|
|
j--;
|
|
while (compare(arr[i], t) < 0) { i++; }
|
|
while (compare(arr[j], t) > 0) { j--; }
|
|
}
|
|
|
|
if (compare(arr[left], t) === 0) { swap(arr, left, j); }
|
|
else {
|
|
j++;
|
|
swap(arr, j, right);
|
|
}
|
|
|
|
if (j <= k) { left = j + 1; }
|
|
if (k <= j) { right = j - 1; }
|
|
}
|
|
}
|
|
|
|
function swap(arr, i, j) {
|
|
var tmp = arr[i];
|
|
arr[i] = arr[j];
|
|
arr[j] = tmp;
|
|
}
|
|
|
|
function defaultCompare(a, b) {
|
|
return a < b ? -1 : a > b ? 1 : 0;
|
|
}
|
|
|
|
function RBush(maxEntries) {
|
|
if ( maxEntries === void 0 ) maxEntries = 9;
|
|
|
|
// max entries in a node is 9 by default; min node fill is 40% for best performance
|
|
this._maxEntries = Math.max(4, maxEntries);
|
|
this._minEntries = Math.max(2, Math.ceil(this._maxEntries * 0.4));
|
|
this.clear();
|
|
};
|
|
|
|
RBush.prototype.all = function all () {
|
|
return this._all(this.data, []);
|
|
};
|
|
|
|
RBush.prototype.search = function search (bbox) {
|
|
var node = this.data;
|
|
var result = [];
|
|
|
|
if (!intersects(bbox, node)) { return result; }
|
|
|
|
var toBBox = this.toBBox;
|
|
var nodesToSearch = [];
|
|
|
|
while (node) {
|
|
for (var i = 0; i < node.children.length; i++) {
|
|
var child = node.children[i];
|
|
var 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;
|
|
};
|
|
|
|
RBush.prototype.collides = function collides (bbox) {
|
|
var node = this.data;
|
|
|
|
if (!intersects(bbox, node)) { return false; }
|
|
|
|
var nodesToSearch = [];
|
|
while (node) {
|
|
for (var i = 0; i < node.children.length; i++) {
|
|
var child = node.children[i];
|
|
var childBBox = node.leaf ? this.toBBox(child) : child;
|
|
|
|
if (intersects(bbox, childBBox)) {
|
|
if (node.leaf || contains(bbox, childBBox)) { return true; }
|
|
nodesToSearch.push(child);
|
|
}
|
|
}
|
|
node = nodesToSearch.pop();
|
|
}
|
|
|
|
return false;
|
|
};
|
|
|
|
RBush.prototype.load = function load (data) {
|
|
if (!(data && data.length)) { return this; }
|
|
|
|
if (data.length < this._minEntries) {
|
|
for (var i = 0; i < data.length; 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;
|
|
};
|
|
|
|
RBush.prototype.insert = function insert (item) {
|
|
if (item) { this._insert(item, this.data.height - 1); }
|
|
return this;
|
|
};
|
|
|
|
RBush.prototype.clear = function clear () {
|
|
this.data = createNode([]);
|
|
return this;
|
|
};
|
|
|
|
RBush.prototype.remove = function remove (item, equalsFn) {
|
|
if (!item) { return this; }
|
|
|
|
var node = this.data;
|
|
var bbox = this.toBBox(item);
|
|
var path = [];
|
|
var indexes = [];
|
|
var i, parent, 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
|
|
var 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;
|
|
};
|
|
|
|
RBush.prototype.toBBox = function toBBox (item) { return item; };
|
|
|
|
RBush.prototype.compareMinX = function compareMinX (a, b) { return a.minX - b.minX; };
|
|
RBush.prototype.compareMinY = function compareMinY (a, b) { return a.minY - b.minY; };
|
|
|
|
RBush.prototype.toJSON = function toJSON () { return this.data; };
|
|
|
|
RBush.prototype.fromJSON = function fromJSON (data) {
|
|
this.data = data;
|
|
return this;
|
|
};
|
|
|
|
RBush.prototype._all = function _all (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;
|
|
};
|
|
|
|
RBush.prototype._build = function _build (items, left, right, height) {
|
|
|
|
var N = right - left + 1;
|
|
var M = this._maxEntries;
|
|
var 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);
|
|
var N1 = N2 * Math.ceil(Math.sqrt(M));
|
|
|
|
multiSelect(items, left, right, N1, this.compareMinX);
|
|
|
|
for (var i = left; i <= right; i += N1) {
|
|
|
|
var right2 = Math.min(i + N1 - 1, right);
|
|
|
|
multiSelect(items, i, right2, N2, this.compareMinY);
|
|
|
|
for (var j = i; j <= right2; j += N2) {
|
|
|
|
var 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;
|
|
};
|
|
|
|
RBush.prototype._chooseSubtree = function _chooseSubtree (bbox, node, level, path) {
|
|
while (true) {
|
|
path.push(node);
|
|
|
|
if (node.leaf || path.length - 1 === level) { break; }
|
|
|
|
var minArea = Infinity;
|
|
var minEnlargement = Infinity;
|
|
var targetNode = (void 0);
|
|
|
|
for (var i = 0; i < node.children.length; i++) {
|
|
var child = node.children[i];
|
|
var area = bboxArea(child);
|
|
var 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;
|
|
};
|
|
|
|
RBush.prototype._insert = function _insert (item, level, isNode) {
|
|
var bbox = isNode ? item : this.toBBox(item);
|
|
var 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
|
|
RBush.prototype._split = function _split (insertPath, level) {
|
|
var node = insertPath[level];
|
|
var M = node.children.length;
|
|
var 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); }
|
|
};
|
|
|
|
RBush.prototype._splitRoot = function _splitRoot (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);
|
|
};
|
|
|
|
RBush.prototype._chooseSplitIndex = function _chooseSplitIndex (node, m, M) {
|
|
var index;
|
|
var minOverlap = Infinity;
|
|
var minArea = Infinity;
|
|
|
|
for (var i = m; i <= M - m; i++) {
|
|
var bbox1 = distBBox(node, 0, i, this.toBBox);
|
|
var bbox2 = distBBox(node, i, M, this.toBBox);
|
|
|
|
var overlap = intersectionArea(bbox1, bbox2);
|
|
var 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 || M - m;
|
|
};
|
|
|
|
// sorts node children by the best axis for split
|
|
RBush.prototype._chooseSplitAxis = function _chooseSplitAxis (node, m, M) {
|
|
var compareMinX = node.leaf ? this.compareMinX : compareNodeMinX;
|
|
var compareMinY = node.leaf ? this.compareMinY : compareNodeMinY;
|
|
var xMargin = this._allDistMargin(node, m, M, compareMinX);
|
|
var yMargin = this._allDistMargin(node, m, M, compareMinY);
|
|
|
|
// if total distributions margin value is minimal for x, sort by minX,
|
|
// otherwise it's already sorted by minY
|
|
if (xMargin < yMargin) { node.children.sort(compareMinX); }
|
|
};
|
|
|
|
// total margin of all possible split distributions where each node is at least m full
|
|
RBush.prototype._allDistMargin = function _allDistMargin (node, m, M, compare) {
|
|
node.children.sort(compare);
|
|
|
|
var toBBox = this.toBBox;
|
|
var leftBBox = distBBox(node, 0, m, toBBox);
|
|
var rightBBox = distBBox(node, M - m, M, toBBox);
|
|
var margin = bboxMargin(leftBBox) + bboxMargin(rightBBox);
|
|
|
|
for (var i = m; i < M - m; i++) {
|
|
var child = node.children[i];
|
|
extend(leftBBox, node.leaf ? toBBox(child) : child);
|
|
margin += bboxMargin(leftBBox);
|
|
}
|
|
|
|
for (var i$1 = M - m - 1; i$1 >= m; i$1--) {
|
|
var child$1 = node.children[i$1];
|
|
extend(rightBBox, node.leaf ? toBBox(child$1) : child$1);
|
|
margin += bboxMargin(rightBBox);
|
|
}
|
|
|
|
return margin;
|
|
};
|
|
|
|
RBush.prototype._adjustParentBBoxes = function _adjustParentBBoxes (bbox, path, level) {
|
|
// adjust bboxes along the given tree path
|
|
for (var i = level; i >= 0; i--) {
|
|
extend(path[i], bbox);
|
|
}
|
|
};
|
|
|
|
RBush.prototype._condense = function _condense (path) {
|
|
// go through the path, removing empty nodes and updating bboxes
|
|
for (var i = path.length - 1, siblings = (void 0); 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); }
|
|
}
|
|
};
|
|
|
|
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.minX = Infinity;
|
|
destNode.minY = Infinity;
|
|
destNode.maxX = -Infinity;
|
|
destNode.maxY = -Infinity;
|
|
|
|
for (var i = k; i < p; i++) {
|
|
var child = node.children[i];
|
|
extend(destNode, node.leaf ? toBBox(child) : child);
|
|
}
|
|
|
|
return destNode;
|
|
}
|
|
|
|
function extend(a, b) {
|
|
a.minX = Math.min(a.minX, b.minX);
|
|
a.minY = Math.min(a.minY, b.minY);
|
|
a.maxX = Math.max(a.maxX, b.maxX);
|
|
a.maxY = Math.max(a.maxY, b.maxY);
|
|
return a;
|
|
}
|
|
|
|
function compareNodeMinX(a, b) { return a.minX - b.minX; }
|
|
function compareNodeMinY(a, b) { return a.minY - b.minY; }
|
|
|
|
function bboxArea(a) { return (a.maxX - a.minX) * (a.maxY - a.minY); }
|
|
function bboxMargin(a) { return (a.maxX - a.minX) + (a.maxY - a.minY); }
|
|
|
|
function enlargedArea(a, b) {
|
|
return (Math.max(b.maxX, a.maxX) - Math.min(b.minX, a.minX)) *
|
|
(Math.max(b.maxY, a.maxY) - Math.min(b.minY, a.minY));
|
|
}
|
|
|
|
function intersectionArea(a, b) {
|
|
var minX = Math.max(a.minX, b.minX);
|
|
var minY = Math.max(a.minY, b.minY);
|
|
var maxX = Math.min(a.maxX, b.maxX);
|
|
var maxY = Math.min(a.maxY, b.maxY);
|
|
|
|
return Math.max(0, maxX - minX) *
|
|
Math.max(0, maxY - minY);
|
|
}
|
|
|
|
function contains(a, b) {
|
|
return a.minX <= b.minX &&
|
|
a.minY <= b.minY &&
|
|
b.maxX <= a.maxX &&
|
|
b.maxY <= a.maxY;
|
|
}
|
|
|
|
function intersects(a, b) {
|
|
return b.minX <= a.maxX &&
|
|
b.minY <= a.maxY &&
|
|
b.maxX >= a.minX &&
|
|
b.maxY >= a.minY;
|
|
}
|
|
|
|
function createNode(children) {
|
|
return {
|
|
children: children,
|
|
height: 1,
|
|
leaf: true,
|
|
minX: Infinity,
|
|
minY: Infinity,
|
|
maxX: -Infinity,
|
|
maxY: -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];
|
|
|
|
while (stack.length) {
|
|
right = stack.pop();
|
|
left = stack.pop();
|
|
|
|
if (right - left <= n) { continue; }
|
|
|
|
var mid = left + Math.ceil((right - left) / n / 2) * n;
|
|
quickselect(arr, mid, left, right, compare);
|
|
|
|
stack.push(left, mid, mid, right);
|
|
}
|
|
}
|
|
|
|
export default RBush;
|