/*******************************************************************************
* Copyright (c) 2005, 2008 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
* @since 3.1
*/
public class Geometry
{
/**
* Determines whether the two line segments formed by the given coordinates intersect. If
* one of the two line segments starts or ends on the other line, then they are considered
* to be intersecting.
*
* @param ux x coordinate of starting point of line 1
* @param uy y coordinate of starting point of line 1
* @param vx x coordinate of ending point of line 1
* @param vy y coordinate of endpoing point of line 1
* @param sx x coordinate of the starting point of line 2
* @param sy y coordinate of the starting point of line 2
* @param tx x coordinate of the ending point of line 2
* @param ty y coordinate of the ending point of line 2
* @return <code>true</code> if the two line segments formed by the given coordinates
* cross
* @since 3.1
*/
public static boolean linesIntersect(int ux, int uy, int vx, int vy,
int sx, int sy, int tx, int ty) {
/*
* Given the segments: u-------v. s-------t. If s->t is inside the triangle u-v-s,
* then check whether the line u->u splits the line s->t.
*/
/* Values are casted to long to avoid integer overflows */
long usX = (long) ux - sx;
long usY = (long) uy - sy;
long vsX = (long) vx - sx;
long vsY = (long) vy - sy;
long stX = (long) sx - tx;
long stY = (long) sy - ty;
if (productSign(cross(vsX, vsY, stX, stY), cross(stX, stY, usX, usY)) >= 0) {
long vuX = (long) vx - ux;
long vuY = (long) vy - uy;
long utX = (long) ux - tx;
long utY = (long) uy - ty;
return productSign(cross(-usX, -usY, vuX, vuY), cross(vuX, vuY, utX, utY)) <= 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 cross(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.
*/
int v1x = x2 - x1;
int v1y = y2 - y1;
int v2x = px - x1;
int v2y = py - y1;
int numerator = v2x * v1y - v1x * v2y;
int denominator = v1x * v1x + v1y * v1y;
int squareDistance = (int) ((long) 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);
}
}