
// rbush.js

/*
 (c) 2013, Vladimir Agafonkin
 RBush, a JavaScript library for high-performance 2D spatial indexing of points and rectangles.
 https://github.com/mourner/rbush
*/

(function () { 

    function rbush(maxEntries, format) {
    
        // jshint newcap: false, validthis: true
        if (!(this instanceof rbush)) return new rbush(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();
    }
    
    rbush.prototype = {
    
        all: function () {
            return this._all(this.data, []);
        },
    
        search: function (bbox) {
    
            var node = this.data,
                result = [],
                toBBox = this.toBBox;
    
            if (!intersects(bbox, node.bbox)) 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.bbox;
    
                    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;
        },
    
        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 stratch 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;
        },
    
        clear: function () {
            this.data = {
                children: [],
                height: 1,
                bbox: empty(),
                leaf: true
            };
            return this;
        },
    
        remove: function (item) {
            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 = node.children.indexOf(item);
    
                    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, 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;
        },
    
        toBBox: function (item) { return item; },
    
        compareMinX: function (a, b) { return a[0] - b[0]; },
        compareMinY: function (a, b) { return a[1] - b[1]; },
    
        toJSON: function () { return this.data; },
    
        fromJSON: function (data) {
            this.data = data;
            return this;
        },
    
        _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 = {
                    children: items.slice(left, right + 1),
                    height: 1,
                    bbox: null,
                    leaf: true
                };
                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));
            }
    
            // TODO eliminate recursion?
    
            node = {
                children: [],
                height: height,
                bbox: null
            };
    
            // 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.bbox);
                    enlargement = enlargedArea(bbox, child.bbox) - 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;
            }
    
            return node;
        },
    
        _insert: function (item, level, isNode) {
    
            var toBBox = this.toBBox,
                bbox = isNode ? item.bbox : 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, 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 newNode = {
                children: node.children.splice(this._chooseSplitIndex(node, m, M)),
                height: node.height
            };
    
            if (node.leaf) newNode.leaf = true;
    
            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 = {
                children: [node, newNode],
                height: node.height + 1
            };
            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 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
        _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.bbox);
                margin += bboxMargin(leftBBox);
            }
    
            for (i = M - m - 1; i >= m; i--) {
                child = node.children[i];
                extend(rightBBox, node.leaf ? toBBox(child) : child.bbox);
                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, 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 (minX, minY, maxX, maxY 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
    
            // jshint evil: true
    
            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 [a' + format.join(', a') + '];');
        }
    };
    
    
    // calculate node's bbox from bboxes of its children
    function calcBBox(node, toBBox) {
        node.bbox = distBBox(node, 0, node.children.length, toBBox);
    }
    
    // min bounding rectangle of node children from k to p-1
    function distBBox(node, k, p, toBBox) {
        var bbox = empty();
    
        for (var i = k, child; i < p; i++) {
            child = node.children[i];
            extend(bbox, node.leaf ? toBBox(child) : child.bbox);
        }
    
        return bbox;
    }
    
    function empty() { return [Infinity, Infinity, -Infinity, -Infinity]; }
    
    function extend(a, b) {
        a[0] = Math.min(a[0], b[0]);
        a[1] = Math.min(a[1], b[1]);
        a[2] = Math.max(a[2], b[2]);
        a[3] = Math.max(a[3], b[3]);
        return a;
    }
    
    function compareNodeMinX(a, b) { return a.bbox[0] - b.bbox[0]; }
    function compareNodeMinY(a, b) { return a.bbox[1] - b.bbox[1]; }
    
    function bboxArea(a)   { return (a[2] - a[0]) * (a[3] - a[1]); }
    function bboxMargin(a) { return (a[2] - a[0]) + (a[3] - a[1]); }
    
    function enlargedArea(a, b) {
        return (Math.max(b[2], a[2]) - Math.min(b[0], a[0])) *
               (Math.max(b[3], a[3]) - Math.min(b[1], a[1]));
    }
    
    function intersectionArea(a, b) {
        var minX = Math.max(a[0], b[0]),
            minY = Math.max(a[1], b[1]),
            maxX = Math.min(a[2], b[2]),
            maxY = Math.min(a[3], b[3]);
    
        return Math.max(0, maxX - minX) *
               Math.max(0, maxY - minY);
    }
    
    function contains(a, b) {
        return a[0] <= b[0] &&
               a[1] <= b[1] &&
               b[2] <= a[2] &&
               b[3] <= a[3];
    }
    
    function intersects(a, b) {
        return b[0] <= a[2] &&
               b[1] <= a[3] &&
               b[2] >= a[0] &&
               b[3] >= a[1];
    }
    
    // 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;
            select(arr, left, right, mid, compare);
    
            stack.push(left, mid, mid, right);
        }
    }
    
    // sort array between left and right (inclusive) so that the smallest k elements come first (unordered)
    function select(arr, left, right, k, compare) {
        var n, i, z, s, sd, newLeft, newRight, t, j;
    
        while (right > left) {
            if (right - left > 600) {
                n = right - left + 1;
                i = k - left + 1;
                z = Math.log(n);
                s = 0.5 * Math.exp(2 * z / 3);
                sd = 0.5 * Math.sqrt(z * s * (n - s) / n) * (i - n / 2 < 0 ? -1 : 1);
                newLeft = Math.max(left, Math.floor(k - i * s / n + sd));
                newRight = Math.min(right, Math.floor(k + (n - i) * s / n + sd));
                select(arr, newLeft, newRight, k, compare);
            }
    
            t = arr[k];
            i = left;
            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;
    }
    
    // export as AMD/CommonJS module or global variable
    if (typeof window.define === 'function' && window.define.amd) window.define('rbush', function() { return rbush; });
    else if (typeof module !== 'undefined') module.exports = rbush;
    else if (typeof window.self !== 'undefined') window.self.rbush = rbush;
    else window.rbush = rbush;

    window.self.rbush = rbush;
    
    })();