/*
* Copyright (c) 2016 Martin Davis.
*
* All rights reserved. This program and the accompanying materials
* are made available under the terms of the Eclipse Public License v1.0
* and Eclipse Distribution License v. 1.0 which accompanies this distribution.
* The Eclipse Public License is available at http://www.eclipse.org/legal/epl-v10.html
* and the Eclipse Distribution License is available at
*
* http://www.eclipse.org/org/documents/edl-v10.php.
*/
package org.locationtech.jts.algorithm;
import org.locationtech.jts.geom.Coordinate;
import org.locationtech.jts.math.DD;
/**
* Implements basic computational geometry algorithms using {@link DD} arithmetic.
*
* @author Martin Davis
*
*/
public class CGAlgorithmsDD
{
private CGAlgorithmsDD() {}
/**
* Returns the index of the direction of the point <code>q</code> relative to
* a vector specified by <code>p1-p2</code>.
*
* @param p1 the origin point of the vector
* @param p2 the final point of the vector
* @param q the point to compute the direction to
*
* @return 1 if q is counter-clockwise (left) from p1-p2
* @return -1 if q is clockwise (right) from p1-p2
* @return 0 if q is collinear with p1-p2
*/
public static int orientationIndex(Coordinate p1, Coordinate p2, Coordinate q)
{
// fast filter for orientation index
// avoids use of slow extended-precision arithmetic in many cases
int index = orientationIndexFilter(p1, p2, q);
if (index <= 1) return index;
// normalize coordinates
DD dx1 = DD.valueOf(p2.x).selfAdd(-p1.x);
DD dy1 = DD.valueOf(p2.y).selfAdd(-p1.y);
DD dx2 = DD.valueOf(q.x).selfAdd(-p2.x);
DD dy2 = DD.valueOf(q.y).selfAdd(-p2.y);
// sign of determinant - unrolled for performance
return dx1.selfMultiply(dy2).selfSubtract(dy1.selfMultiply(dx2)).signum();
}
/**
* Computes the sign of the determinant of the 2x2 matrix
* with the given entries.
*
* @return -1 if the determinant is negative,
* @return 1 if the determinant is positive,
* @return 0 if the determinant is 0.
*/
public static int signOfDet2x2(DD x1, DD y1, DD x2, DD y2)
{
DD det = x1.multiply(y2).selfSubtract(y1.multiply(x2));
return det.signum();
}
/**
* A value which is safely greater than the
* relative round-off error in double-precision numbers
*/
private static final double DP_SAFE_EPSILON = 1e-15;
/**
* A filter for computing the orientation index of three coordinates.
* <p>
* If the orientation can be computed safely using standard DP
* arithmetic, this routine returns the orientation index.
* Otherwise, a value i > 1 is returned.
* In this case the orientation index must
* be computed using some other more robust method.
* The filter is fast to compute, so can be used to
* avoid the use of slower robust methods except when they are really needed,
* thus providing better average performance.
* <p>
* Uses an approach due to Jonathan Shewchuk, which is in the public domain.
*
* @param pa a coordinate
* @param pb a coordinate
* @param pc a coordinate
* @return the orientation index if it can be computed safely
* @return i > 1 if the orientation index cannot be computed safely
*/
private static int orientationIndexFilter(Coordinate pa, Coordinate pb, Coordinate pc)
{
double detsum;
double detleft = (pa.x - pc.x) * (pb.y - pc.y);
double detright = (pa.y - pc.y) * (pb.x - pc.x);
double det = detleft - detright;
if (detleft > 0.0) {
if (detright <= 0.0) {
return signum(det);
}
else {
detsum = detleft + detright;
}
}
else if (detleft < 0.0) {
if (detright >= 0.0) {
return signum(det);
}
else {
detsum = -detleft - detright;
}
}
else {
return signum(det);
}
double errbound = DP_SAFE_EPSILON * detsum;
if ((det >= errbound) || (-det >= errbound)) {
return signum(det);
}
return 2;
}
private static int signum(double x)
{
if (x > 0) return 1;
if (x < 0) return -1;
return 0;
}
/**
* Computes an intersection point between two lines
* using DD arithmetic.
* Currently does not handle case of parallel lines.
*
* @param p1
* @param p2
* @param q1
* @param q2
* @return
*/
public static Coordinate intersection(
Coordinate p1, Coordinate p2,
Coordinate q1, Coordinate q2)
{
DD denom1 = DD.valueOf(q2.y).selfSubtract(q1.y)
.selfMultiply(DD.valueOf(p2.x).selfSubtract(p1.x));
DD denom2 = DD.valueOf(q2.x).selfSubtract(q1.x)
.selfMultiply(DD.valueOf(p2.y).selfSubtract(p1.y));
DD denom = denom1.subtract(denom2);
/**
* Cases:
* - denom is 0 if lines are parallel
* - intersection point lies within line segment p if fracP is between 0 and 1
* - intersection point lies within line segment q if fracQ is between 0 and 1
*/
DD numx1 = DD.valueOf(q2.x).selfSubtract(q1.x)
.selfMultiply(DD.valueOf(p1.y).selfSubtract(q1.y));
DD numx2 = DD.valueOf(q2.y).selfSubtract(q1.y)
.selfMultiply(DD.valueOf(p1.x).selfSubtract(q1.x));
DD numx = numx1.subtract(numx2);
double fracP = numx.selfDivide(denom).doubleValue();
double x = DD.valueOf(p1.x).selfAdd(DD.valueOf(p2.x).selfSubtract(p1.x).selfMultiply(fracP)).doubleValue();
DD numy1 = DD.valueOf(p2.x).selfSubtract(p1.x)
.selfMultiply(DD.valueOf(p1.y).selfSubtract(q1.y));
DD numy2 = DD.valueOf(p2.y).selfSubtract(p1.y)
.selfMultiply(DD.valueOf(p1.x).selfSubtract(q1.x));
DD numy = numy1.subtract(numy2);
double fracQ = numy.selfDivide(denom).doubleValue();
double y = DD.valueOf(q1.y).selfAdd(DD.valueOf(q2.y).selfSubtract(q1.y).selfMultiply(fracQ)).doubleValue();
return new Coordinate(x,y);
}
}