/*******************************************************************************
* Copyright (c) 2005, 2010, 2012 IBM Corporation, Gerhardt Informatics Kft. 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
* Gerhardt Informatics Kft. - GEFGWT port
*******************************************************************************/
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);
}
}