bundles/org.eclipse.draw2d/src/org/eclipse/draw2d/geometry/Geometry.java

/*******************************************************************************
 * Copyright (c) 2005, 2010 IBM Corporation and others.
 * All rights reserved. This program and the accompanying materials
 * are made available under the terms of the Eclipse Public License v1.0
 * which accompanies this distribution, and is available at
 * http://www.eclipse.org/legal/epl-v10.html
 *
 * Contributors:
 *     IBM Corporation - initial API and implementation
 *     Alexander Shatalin (Borland) - Contribution for Bug 238874
 *******************************************************************************/
package org.eclipse.draw2d.geometry;

/**
 * A Utilities class for geometry operations.
 * 
 * @author Pratik Shah
 * @author Alexander Nyssen
 * @since 3.1
 */
public class Geometry {

	/**
	 * Determines whether the two line segments p1->p2 and p3->p4, given by
	 * p1=(x1, y1), p2=(x2,y2), p3=(x3,y3), p4=(x4,y4) intersect. Two line
	 * segments are regarded to be intersecting in case they share at least one
	 * common point, i.e if one of the two line segments starts or ends on the
	 * other line segment or the line segments are collinear and overlapping,
	 * then they are as well considered to be intersecting.
	 * 
	 * @param x1
	 *            x coordinate of starting point of line segment 1
	 * @param y1
	 *            y coordinate of starting point of line segment 1
	 * @param x2
	 *            x coordinate of ending point of line segment 1
	 * @param y2
	 *            y coordinate of ending point of line segment 1
	 * @param x3
	 *            x coordinate of the starting point of line segment 2
	 * @param y3
	 *            y coordinate of the starting point of line segment 2
	 * @param x4
	 *            x coordinate of the ending point of line segment 2
	 * @param y4
	 *            y coordinate of the ending point of line segment 2
	 * 
	 * @return <code>true</code> if the two line segments formed by the given
	 *         coordinates share at least one common point.
	 * 
	 * @since 3.1
	 */
	public static boolean linesIntersect(int x1, int y1, int x2, int y2,
			int x3, int y3, int x4, int y4) {

		// calculate bounding box of segment p1->p2
		int bb1_x = Math.min(x1, x2);
		int bb1_y = Math.min(y1, y2);
		int bb2_x = Math.max(x1, x2);
		int bb2_y = Math.max(y1, y2);

		// calculate bounding box of segment p3->p4
		int bb3_x = Math.min(x3, x4);
		int bb3_y = Math.min(y3, y4);
		int bb4_x = Math.max(x3, x4);
		int bb4_y = Math.max(y3, y4);

		// check if bounding boxes intersect
		if (!(bb2_x >= bb3_x && bb4_x >= bb1_x && bb2_y >= bb3_y && bb4_y >= bb1_y)) {
			// if bounding boxes do not intersect, line segments cannot
			// intersect either
			return false;
		}

		// If p3->p4 is inside the triangle p1-p2-p3, then check whether the
		// line p1->p2 crosses the line p3->p4.
		long p1p3_x = (long) x1 - x3;
		long p1p3_y = (long) y1 - y3;
		long p2p3_x = (long) x2 - x3;
		long p2p3_y = (long) y2 - y3;
		long p3p4_x = (long) x3 - x4;
		long p3p4_y = (long) y3 - y4;
		if (productSign(crossProduct(p2p3_x, p2p3_y, p3p4_x, p3p4_y),
				crossProduct(p3p4_x, p3p4_y, p1p3_x, p1p3_y)) >= 0) {
			long p2p1_x = (long) x2 - x1;
			long p2p1_y = (long) y2 - y1;
			long p1p4_x = (long) x1 - x4;
			long p1p4_y = (long) y1 - y4;
			return productSign(crossProduct(-p1p3_x, -p1p3_y, p2p1_x, p2p1_y),
					crossProduct(p2p1_x, p2p1_y, p1p4_x, p1p4_y)) <= 0;
		}
		return false;
	}

	private static int productSign(long x, long y) {
		if (x == 0 || y == 0) {
			return 0;
		} else if (x < 0 ^ y < 0) {
			return -1;
		}
		return 1;
	}

	private static long crossProduct(long x1, long y1, long x2, long y2) {
		return x1 * y2 - x2 * y1;
	}

	/**
	 * @see PointList#polylineContainsPoint(int, int, int)
	 * @since 3.5
	 */
	public static boolean polylineContainsPoint(PointList points, int x, int y,
			int tolerance) {
		int coordinates[] = points.toIntArray();
		/*
		 * For each segment of PolyLine calling isSegmentPoint
		 */
		for (int index = 0; index < coordinates.length - 3; index += 2) {
			if (segmentContainsPoint(coordinates[index],
					coordinates[index + 1], coordinates[index + 2],
					coordinates[index + 3], x, y, tolerance)) {
				return true;
			}
		}
		return false;
	}

	/**
	 * @return true if the least distance between point (px,py) and segment
	 *         (x1,y1) - (x2,y2) is less then specified tolerance
	 */
	private static boolean segmentContainsPoint(int x1, int y1, int x2, int y2,
			int px, int py, int tolerance) {
		/*
		 * Point should be located inside Rectangle(x1 -+ tolerance, y1 -+
		 * tolerance, x2 +- tolerance, y2 +- tolerance)
		 */
		Rectangle lineBounds = Rectangle.SINGLETON;
		lineBounds.setSize(0, 0);
		lineBounds.setLocation(x1, y1);
		lineBounds.union(x2, y2);
		lineBounds.expand(tolerance, tolerance);
		if (!lineBounds.contains(px, py)) {
			return false;
		}

		/*
		 * If this is horizontal, vertical line or dot then the distance between
		 * specified point and segment is not more then tolerance (due to the
		 * lineBounds check above)
		 */
		if (x1 == x2 || y1 == y2) {
			return true;
		}

		/*
		 * Calculating square distance from specified point to this segment
		 * using formula for Dot product of two vectors.
		 */
		long v1x = x2 - x1;
		long v1y = y2 - y1;
		long v2x = px - x1;
		long v2y = py - y1;
		long numerator = v2x * v1y - v1x * v2y;
		long denominator = v1x * v1x + v1y * v1y;
		long squareDistance = numerator * numerator / denominator;
		return squareDistance <= tolerance * tolerance;
	}

	/**
	 * One simple way of finding whether the point is inside or outside a simple
	 * polygon is to test how many times a ray starting from the point
	 * intersects the edges of the polygon. If the point in question is not on
	 * the boundary of the polygon, the number of intersections is an even
	 * number if the point is outside, and it is odd if inside.
	 * 
	 * @see PointList#polygonContainsPoint(int, int)
	 * @since 3.5
	 */
	public static boolean polygonContainsPoint(PointList points, int x, int y) {
		boolean isOdd = false;
		int coordinates[] = points.toIntArray();
		int n = coordinates.length;
		if (n > 3) { // If there are at least 2 Points (4 ints)
			int x1, y1;
			int x0 = coordinates[n - 2];
			int y0 = coordinates[n - 1];

			for (int i = 0; i < n; x0 = x1, y0 = y1) {
				x1 = coordinates[i++];
				y1 = coordinates[i++];
				if (!segmentContaintPoint(y0, y1, y)) {
					// Current edge has no intersection with the point by Y
					// coordinates
					continue;
				}
				int crossProduct = crossProduct(x1, y1, x0, y0, x, y);
				if (crossProduct == 0) {
					// cross product == 0 only if this point is on the line
					// containing selected edge
					if (segmentContaintPoint(x0, x1, x)) {
						// This point is on the edge
						return true;
					}
					// This point is outside the edge - simply skipping possible
					// intersection (no parity changes)
				} else if ((y0 <= y && y < y1 && crossProduct > 0)
						|| (y1 <= y && y < y0 && crossProduct < 0)) {
					// has intersection
					isOdd = !isOdd;
				}
			}
			return isOdd;
		}
		return false;
	}

	/**
	 * @return true if segment with two ends x0, x1 contains point x
	 */
	private static boolean segmentContaintPoint(int x0, int x1, int x) {
		return !((x < x0 && x < x1) || (x > x0 && x > x1));
	}

	/**
	 * Calculating cross product of two vectors: 1. [ax - cx, ay - cx] 2. [bx -
	 * cx, by - cy]
	 */
	private static int crossProduct(int ax, int ay, int bx, int by, int cx,
			int cy) {
		return (ax - cx) * (by - cy) - (ay - cy) * (bx - cx);
	}

}