path: root/src/Geometry/Geometry.js

'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 };