Angle.java
/*
* Copyright (c) 2016 Vivid Solutions.
*
* All rights reserved. This program and the accompanying materials
* are made available under the terms of the Eclipse Public License 2.0
* and Eclipse Distribution License v. 1.0 which accompanies this distribution.
* The Eclipse Public License is available at http://www.eclipse.org/legal/epl-v20.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;
/**
* Utility functions for working with angles.
* Unless otherwise noted, methods in this class express angles in radians.
*/
@SuppressWarnings("DuplicatedCode") public class Angle
{
/**
* The value of 2*Pi
*/
public static final double PI_TIMES_2 = 2.0 * Math.PI;
/**
* The value of Pi/2
*/
public static final double PI_OVER_2 = Math.PI / 2.0;
/**
* The value of Pi/4
*/
public static final double PI_OVER_4 = Math.PI / 4.0;
/** Constant representing counterclockwise orientation */
public static final int COUNTERCLOCKWISE = Orientation.COUNTERCLOCKWISE;
/** Constant representing clockwise orientation */
public static final int CLOCKWISE = Orientation.CLOCKWISE;
/** Constant representing no orientation */
public static final int NONE = Orientation.COLLINEAR;
private Angle() {}
/**
* Converts from radians to degrees.
* @param radians an angle in radians
* @return the angle in degrees
*/
public static double toDegrees(double radians) {
return (radians * 180) / (Math.PI);
}
/**
* Converts from degrees to radians.
*
* @param angleDegrees an angle in degrees
* @return the angle in radians
*/
public static double toRadians(double angleDegrees) {
return (angleDegrees * Math.PI) / 180.0;
}
/**
* Returns the angle of the vector from p0 to p1,
* relative to the positive X-axis.
* The angle is normalized to be in the range [ -Pi, Pi ].
*
* @param p0 the initial point of the vector
* @param p1 the terminal point of the vector
* @return the normalized angle (in radians) that p0-p1 makes with the positive x-axis.
*/
public static double angle(Coordinate p0, Coordinate p1) {
double dx = p1.x - p0.x;
double dy = p1.y - p0.y;
return Math.atan2(dy, dx);
}
/**
* Returns the angle of the vector from (0,0) to p,
* relative to the positive X-axis.
* The angle is normalized to be in the range ( -Pi, Pi ].
*
* @param p the terminal point of the vector
* @return the normalized angle (in radians) that p makes with the positive x-axis.
*/
public static double angle(Coordinate p) {
return Math.atan2(p.y, p.x);
}
/**
* Tests whether the angle between p0-p1-p2 is acute.
* An angle is acute if it is less than 90 degrees.
* <p>
* Note: this implementation is not precise (deterministic) for angles very close to 90 degrees.
*
* @param p0 an endpoint of the angle
* @param p1 the base of the angle
* @param p2 the other endpoint of the angle
* @return true if the angle is acute
*/
public static boolean isAcute(Coordinate p0, Coordinate p1, Coordinate p2)
{
// relies on fact that A dot B is positive if A ang B is acute
double dx0 = p0.x - p1.x;
double dy0 = p0.y - p1.y;
double dx1 = p2.x - p1.x;
double dy1 = p2.y - p1.y;
double dotprod = dx0 * dx1 + dy0 * dy1;
return dotprod > 0;
}
/**
* Tests whether the angle between p0-p1-p2 is obtuse.
* An angle is obtuse if it is greater than 90 degrees.
* <p>
* Note: this implementation is not precise (deterministic) for angles very close to 90 degrees.
*
* @param p0 an endpoint of the angle
* @param p1 the base of the angle
* @param p2 the other endpoint of the angle
* @return true if the angle is obtuse
*/
public static boolean isObtuse(Coordinate p0, Coordinate p1, Coordinate p2)
{
// relies on fact that A dot B is negative if A ang B is obtuse
double dx0 = p0.x - p1.x;
double dy0 = p0.y - p1.y;
double dx1 = p2.x - p1.x;
double dy1 = p2.y - p1.y;
double dotprod = dx0 * dx1 + dy0 * dy1;
return dotprod < 0;
}
/**
* Returns the unoriented smallest angle between two vectors.
* The computed angle will be in the range [0, Pi).
*
* @param tip1 the tip of one vector
* @param tail the tail of each vector
* @param tip2 the tip of the other vector
* @return the angle between tail-tip1 and tail-tip2
*/
public static double angleBetween(Coordinate tip1, Coordinate tail,
Coordinate tip2) {
double a1 = angle(tail, tip1);
double a2 = angle(tail, tip2);
return diff(a1, a2);
}
/**
* Returns the oriented smallest angle between two vectors.
* The computed angle will be in the range (-Pi, Pi].
* A positive result corresponds to a counterclockwise
* (CCW) rotation
* from v1 to v2;
* a negative result corresponds to a clockwise (CW) rotation;
* a zero result corresponds to no rotation.
*
* @param tip1 the tip of v1
* @param tail the tail of each vector
* @param tip2 the tip of v2
* @return the angle between v1 and v2, relative to v1
*/
public static double angleBetweenOriented(Coordinate tip1, Coordinate tail,
Coordinate tip2)
{
double a1 = angle(tail, tip1);
double a2 = angle(tail, tip2);
double angDel = a2 - a1;
// normalize, maintaining orientation
if (angDel <= -Math.PI)
return angDel + PI_TIMES_2;
if (angDel > Math.PI)
return angDel - PI_TIMES_2;
return angDel;
}
/**
* Computes the angle of the unoriented bisector
* of the smallest angle between two vectors.
* The computed angle will be in the range (-Pi, Pi].
*
* @param tip1 the tip of v1
* @param tail the tail of each vector
* @param tip2 the tip of v2
* @return the angle of the bisector between v1 and v2
*/
public static double bisector(Coordinate tip1, Coordinate tail,
Coordinate tip2)
{
double angDel = angleBetweenOriented(tip1, tail, tip2);
double angBi = angle(tail, tip1) + angDel / 2;
return normalize(angBi);
}
/**
* Computes the interior angle between two segments of a ring. The ring is
* assumed to be oriented in a clockwise direction. The computed angle will be
* in the range [0, 2Pi]
*
* @param p0
* a point of the ring
* @param p1
* the next point of the ring
* @param p2
* the next point of the ring
* @return the interior angle based at {@code p1}
*/
public static double interiorAngle(Coordinate p0, Coordinate p1, Coordinate p2)
{
double anglePrev = Angle.angle(p1, p0);
double angleNext = Angle.angle(p1, p2);
return normalizePositive(angleNext - anglePrev);
}
/**
* Returns whether an angle must turn clockwise or counterclockwise
* to overlap another angle.
*
* @param ang1 an angle (in radians)
* @param ang2 an angle (in radians)
* @return whether a1 must turn CLOCKWISE, COUNTERCLOCKWISE or NONE to
* overlap a2.
*/
public static int getTurn(double ang1, double ang2) {
double crossproduct = Math.sin(ang2 - ang1);
if (crossproduct > 0) {
return COUNTERCLOCKWISE;
}
if (crossproduct < 0) {
return CLOCKWISE;
}
return NONE;
}
/**
* Computes the normalized value of an angle, which is the
* equivalent angle in the range ( -Pi, Pi ].
*
* @param angle the angle to normalize
* @return an equivalent angle in the range (-Pi, Pi]
*/
public static double normalize(double angle)
{
while (angle > Math.PI)
angle -= PI_TIMES_2;
while (angle <= -Math.PI)
angle += PI_TIMES_2;
return angle;
}
/**
* Computes the normalized positive value of an angle, which is the
* equivalent angle in the range [ 0, 2*Pi ).
* E.g.:
* <ul>
* <li>normalizePositive(0.0) = 0.0
* <li>normalizePositive(-PI) = PI
* <li>normalizePositive(-2PI) = 0.0
* <li>normalizePositive(-3PI) = PI
* <li>normalizePositive(-4PI) = 0
* <li>normalizePositive(PI) = PI
* <li>normalizePositive(2PI) = 0.0
* <li>normalizePositive(3PI) = PI
* <li>normalizePositive(4PI) = 0.0
* </ul>
*
* @param angle the angle to normalize, in radians
* @return an equivalent positive angle
*/
public static double normalizePositive(double angle)
{
if (angle < 0.0) {
while (angle < 0.0)
angle += PI_TIMES_2;
// in case round-off error bumps the value over
if (angle >= PI_TIMES_2)
angle = 0.0;
}
else {
while (angle >= PI_TIMES_2)
angle -= PI_TIMES_2;
// in case round-off error bumps the value under
if (angle < 0.0)
angle = 0.0;
}
return angle;
}
/**
* Computes the unoriented smallest difference between two angles.
* The angles are assumed to be normalized to the range [-Pi, Pi].
* The result will be in the range [0, Pi].
*
* @param ang1 the angle of one vector (in [-Pi, Pi] )
* @param ang2 the angle of the other vector (in range [-Pi, Pi] )
* @return the angle (in radians) between the two vectors (in range [0, Pi] )
*/
public static double diff(double ang1, double ang2) {
double delAngle;
if (ang1 < ang2) {
delAngle = ang2 - ang1;
} else {
delAngle = ang1 - ang2;
}
if (delAngle > Math.PI) {
delAngle = PI_TIMES_2 - delAngle;
}
return delAngle;
}
/**
* Computes sin of an angle, snapping near-zero values to zero.
*
* @param ang the input angle (in radians)
* @return the result of the trigonometric function
*/
public static double sinSnap(double ang) {
double res = Math.sin(ang);
if (Math.abs(res) < 5e-16) return 0.0;
return res;
}
/**
* Computes cos of an angle, snapping near-zero values to zero.
*
* @param ang the input angle (in radians)
* @return the result of the trigonometric function
*/
public static double cosSnap(double ang) {
double res = Math.cos(ang);
if (Math.abs(res) < 5e-16) return 0.0;
return res;
}
/**
* Projects a point by a given angle and distance.
*
* @param p the point to project
* @param angle the angle at which to project
* @param dist the distance to project
* @return the projected point
*/
public static Coordinate project(Coordinate p, double angle, double dist) {
double x = p.getX() + dist * Angle.cosSnap(angle);
double y = p.getY() + dist * Angle.sinSnap(angle);
return new Coordinate(x, y);
}
}