1 files changed, 233 insertions, 0 deletions
diff --git a/src/Geometry/Geometry.js b/src/Geometry/Geometry.js
new file mode 100644
index 0000000..43f277f
--- /dev/null
+++ b/src/Geometry/Geometry.js
@@ -0,0 +1,233 @@
+'use strict';
+
+function dist(a, b) {
+	return Math.sqrt((a.x - b.x)**2 + (a.y - b.y)**2);
+}
+
+/* AABB - axis-aligned bounding box */
+class AABB {
+	/* create a new AABB */
+	constructor(x, y, width, height) {
+		this.x = x; this.y = y;
+		this.width = width; this.height = height;
+	}
+
+	/* check if a point is inside the box
+	 *
+	 * a "point" is any object with an x- and y-coordinate.
+	 * any other data in the object is ignored.
+	 *
+	 * returns true if the point is inside, and false otherwise.
+	 */
+	contains(point) {
+		if (point.x >= this.x && point.y >= this.y
+		    && point.x < this.x + this.width
+			&& point.y < this.y + this.height)
+			return true;
+		return false;
+	}
+
+	/* check if two AABBs overlap */
+	intersects(aabb) {
+		const overlap = (ax, arange, bx, brange) => {
+			const range = ax < bx ? arange : brange;
+			if (Math.abs(bx - ax) < range)
+				return true;
+			return false;
+		};
+
+		if (overlap(this.x, this.width, aabb.x, aabb.width) &&
+		    overlap(this.y, this.height, aabb.y, aabb.height))
+			return true;
+		return false;
+	}
+}
+
+
+/* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ *
+ * QUADTREE
+ *
+ * ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+ */
+
+/* lil enum class for QTNode types */
+class QTNodeType {
+	constructor(name) { this.name = name; }
+	toString() { return `QTNode.${this.name}`; }
+}
+
+
+/* nodes in a quadtree
+ *
+ * they can be either "Empty" (no point),
+ * "Leaf" (they contain a point and no sub-nodes),
+ * or "Branch" (they contain no point and have sub-nodes).
+ * There are no QTNodes with children and point data.
+ */
+class QTNode {
+	static Empty = new QTNodeType('Empty');
+	static Leaf = new QTNodeType('Leaf');
+	static Branch = new QTNodeType('Branch');
+
+	constructor(x, y, width, height) {
+		this.aabb = new AABB(x, y, width, height);
+		/* all QTNodes start empty */
+		this.type = QTNode.Empty;
+	}
+
+	/* insert a point into the tree, starting with this node
+	 *
+	 * as above, points are just objects with 'x' and 'y' values.
+	 * other data in the point is not examined and is incorporated into the
+	 * tree.
+	 *
+	 * this function returns false if the point was not contained in the bounding box,
+	 * and true otherwise. inserting a point may cause the node's type to change
+	 * (e.g. a Leaf node would become a Branch node and its point data would be
+	 * moved lower in the tree).
+	 */
+	insert(point) {
+		if (this.aabb.contains(point)) {
+			if (this.type == QTNode.Empty) {
+				/* empty nodes are easy -- just switch to Leaf and add the point */
+				this.type = QTNode.Leaf;
+				this.point = point;
+				return true;
+			}
+			else if (this.type == QTNode.Leaf) {
+				/* Leaf must become a Branch */
+				this.type = QTNode.Branch;
+				this.subdivide();
+
+				/* move current point into a child */
+				let result = this.insert(this.point);
+				if (!result) return false;
+				this.point = undefined;
+
+				/* add new point */
+				return this.insert(point);
+			}
+			else {
+				/* This is a Branch, and we should insert into a child node */
+				/* just try them all until we find one where the point can go */
+				if (this.subnode[0].insert(point)) return true;
+				if (this.subnode[1].insert(point)) return true;
+				if (this.subnode[2].insert(point)) return true;
+				if (this.subnode[3].insert(point)) return true;
+				return false; // something strange has happened!!
+			}
+		}
+		/* point not in this node, return false */
+		return false;
+	}
+
+	/* subdivide the node into four child nodes
+	 *
+	 * under normal circumstances, the user should not call this function --
+	 * it's just meant to be used during insertion.
+	 */
+	subdivide() {
+		/* some useful constants */
+		const x = this.aabb.x; const y = this.aabb.y;
+		const w = this.aabb.width/2; const h = this.aabb.height/2;
+
+		/* generate sub-nodes */
+		this.subnode = [
+			new QTNode(x, y, w, h),
+			new QTNode(x+w, y, w, h),
+			new QTNode(x, y+h, w, h),
+			new QTNode(x+w, y+h, w, h),
+		];
+	}
+
+	/* query the tree for all points contained within a region recursively
+	 *
+	 * returns an array containing any points in the tree beneath this node
+	 * that are inside the supplied AABB.
+	 */
+	getPointsInRegion(aabb) {
+		if (this.type == QTNode.Empty) return [];
+		if (!this.aabb.intersects(aabb)) return [];
+		if (this.type == QTNode.Leaf) return [this.point];
+		
+		/* Branch - recusively query children */
+		return [
+			...this.subnode[0].getPointsInRegion(aabb),
+			...this.subnode[1].getPointsInRegion(aabb),
+			...this.subnode[2].getPointsInRegion(aabb),
+			...this.subnode[3].getPointsInRegion(aabb),
+		];
+	}
+}
+
+
+/* full-blown quadtree! */
+class QuadTree {
+	/* create a new quadtree */
+	constructor(width, height) {
+		this.root = new QTNode(0, 0, width, height);
+	}
+
+	/* insert a point into the tree */
+	insert(point) {
+		return this.root.insert(point);
+	}
+
+	/* get the closest tree point to the given point */
+	closest(point) {
+		/* the algorithm goes like this:
+		 *   1. find the smallest node containing the point
+		 *   2. the closest point is within a box at most 4x the
+		 *      size of that lowest node, so query all points within
+		 *      such a region.
+		 *   3. brute-force within the list of points.
+		 */
+
+		/* recursively find the node containing a point */
+		const getLeaf = (point, node) => {
+			/* is point in bounding box? */
+			if (!node.aabb.contains(point)) return null;
+			/* is this a Leaf or Empty node? */
+			if (node.type == QTNode.Empty ||
+			    node.type == QTNode.Leaf) return node;
+			
+			/* this is a branch node, so recurse */
+			for (let subnode of node.subnode) {
+				const leaf = getLeaf(point, subnode);
+				if (leaf !== null) return leaf;
+			}
+
+			/* should never get here */
+			return null;
+		}
+
+		/* find the node, starting at the tree root */
+		const leaf = getLeaf(point, this.root);
+		if (leaf === null) return leaf;
+
+		/* construct the 4x AABB, centered on the query point */
+		const dim = 2*Math.max(leaf.aabb.width, leaf.aabb.height);
+		const region = new AABB(point.x - dim, point.y - dim, 2*dim, 2*dim);
+
+		/* get all points */
+		const points = this.root.getPointsInRegion(region);
+
+		/* brute force search within the small list */
+		let closest = null;
+		let min_dist = 100 * this.root.aabb.width * this.root.aabb.height;
+		const dist = (a, b) => (a.x - b.x)**2 + (a.y - b.y)**2;
+		for (let pt of points) {
+			const d = dist(point, pt);
+			if (d < min_dist) {
+				closest = pt;
+				min_dist = d;
+			}
+		}
+
+		/* done! */
+		return closest;
+	}
+}
+
+export { dist, AABB, QTNode, QuadTree };