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The Apache Commons Math project is a library of lightweight, self-contained mathematics and statistics components addressing the most common practical problems not immediately available in the Java programming language or commons-lang.
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.geometry.spherical.twod;
import org.apache.commons.math3.exception.MathArithmeticException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.geometry.Point;
import org.apache.commons.math3.geometry.Space;
import org.apache.commons.math3.geometry.euclidean.threed.Vector3D;
import org.apache.commons.math3.util.FastMath;
import org.apache.commons.math3.util.MathUtils;
/** This class represents a point on the 2-sphere.
*
* We use the mathematical convention to use the azimuthal angle \( \theta \)
* in the x-y plane as the first coordinate, and the polar angle \( \varphi \)
* as the second coordinate (see Spherical
* Coordinates in MathWorld).
*
* Instances of this class are guaranteed to be immutable.
* @since 3.3
*/
public class S2Point implements Point {
/** +I (coordinates: \( \theta = 0, \varphi = \pi/2 \)). */
public static final S2Point PLUS_I = new S2Point(0, 0.5 * FastMath.PI, Vector3D.PLUS_I);
/** +J (coordinates: \( \theta = \pi/2, \varphi = \pi/2 \))). */
public static final S2Point PLUS_J = new S2Point(0.5 * FastMath.PI, 0.5 * FastMath.PI, Vector3D.PLUS_J);
/** +K (coordinates: \( \theta = any angle, \varphi = 0 \)). */
public static final S2Point PLUS_K = new S2Point(0, 0, Vector3D.PLUS_K);
/** -I (coordinates: \( \theta = \pi, \varphi = \pi/2 \)). */
public static final S2Point MINUS_I = new S2Point(FastMath.PI, 0.5 * FastMath.PI, Vector3D.MINUS_I);
/** -J (coordinates: \( \theta = 3\pi/2, \varphi = \pi/2 \)). */
public static final S2Point MINUS_J = new S2Point(1.5 * FastMath.PI, 0.5 * FastMath.PI, Vector3D.MINUS_J);
/** -K (coordinates: \( \theta = any angle, \varphi = \pi \)). */
public static final S2Point MINUS_K = new S2Point(0, FastMath.PI, Vector3D.MINUS_K);
// CHECKSTYLE: stop ConstantName
/** A vector with all coordinates set to NaN. */
public static final S2Point NaN = new S2Point(Double.NaN, Double.NaN, Vector3D.NaN);
// CHECKSTYLE: resume ConstantName
/** Serializable UID. */
private static final long serialVersionUID = 20131218L;
/** Azimuthal angle \( \theta \) in the x-y plane. */
private final double theta;
/** Polar angle \( \varphi \). */
private final double phi;
/** Corresponding 3D normalized vector. */
private final Vector3D vector;
/** Simple constructor.
* Build a vector from its spherical coordinates
* @param theta azimuthal angle \( \theta \) in the x-y plane
* @param phi polar angle \( \varphi \)
* @see #getTheta()
* @see #getPhi()
* @exception OutOfRangeException if \( \varphi \) is not in the [\( 0; \pi \)] range
*/
public S2Point(final double theta, final double phi)
throws OutOfRangeException {
this(theta, phi, vector(theta, phi));
}
/** Simple constructor.
* Build a vector from its underlying 3D vector
* @param vector 3D vector
* @exception MathArithmeticException if vector norm is zero
*/
public S2Point(final Vector3D vector) throws MathArithmeticException {
this(FastMath.atan2(vector.getY(), vector.getX()), Vector3D.angle(Vector3D.PLUS_K, vector),
vector.normalize());
}
/** Build a point from its internal components.
* @param theta azimuthal angle \( \theta \) in the x-y plane
* @param phi polar angle \( \varphi \)
* @param vector corresponding vector
*/
private S2Point(final double theta, final double phi, final Vector3D vector) {
this.theta = theta;
this.phi = phi;
this.vector = vector;
}
/** Build the normalized vector corresponding to spherical coordinates.
* @param theta azimuthal angle \( \theta \) in the x-y plane
* @param phi polar angle \( \varphi \)
* @return normalized vector
* @exception OutOfRangeException if \( \varphi \) is not in the [\( 0; \pi \)] range
*/
private static Vector3D vector(final double theta, final double phi)
throws OutOfRangeException {
if (phi < 0 || phi > FastMath.PI) {
throw new OutOfRangeException(phi, 0, FastMath.PI);
}
final double cosTheta = FastMath.cos(theta);
final double sinTheta = FastMath.sin(theta);
final double cosPhi = FastMath.cos(phi);
final double sinPhi = FastMath.sin(phi);
return new Vector3D(cosTheta * sinPhi, sinTheta * sinPhi, cosPhi);
}
/** Get the azimuthal angle \( \theta \) in the x-y plane.
* @return azimuthal angle \( \theta \) in the x-y plane
* @see #S2Point(double, double)
*/
public double getTheta() {
return theta;
}
/** Get the polar angle \( \varphi \).
* @return polar angle \( \varphi \)
* @see #S2Point(double, double)
*/
public double getPhi() {
return phi;
}
/** Get the corresponding normalized vector in the 3D euclidean space.
* @return normalized vector
*/
public Vector3D getVector() {
return vector;
}
/** {@inheritDoc} */
public Space getSpace() {
return Sphere2D.getInstance();
}
/** {@inheritDoc} */
public boolean isNaN() {
return Double.isNaN(theta) || Double.isNaN(phi);
}
/** Get the opposite of the instance.
* @return a new vector which is opposite to the instance
*/
public S2Point negate() {
return new S2Point(-theta, FastMath.PI - phi, vector.negate());
}
/** {@inheritDoc} */
public double distance(final Point point) {
return distance(this, (S2Point) point);
}
/** Compute the distance (angular separation) between two points.
* @param p1 first vector
* @param p2 second vector
* @return the angular separation between p1 and p2
*/
public static double distance(S2Point p1, S2Point p2) {
return Vector3D.angle(p1.vector, p2.vector);
}
/**
* Test for the equality of two points on the 2-sphere.
*
* If all coordinates of two points are exactly the same, and none are
* Double.NaN, the two points are considered to be equal.
*
*
* NaN coordinates are considered to affect globally the vector
* and be equals to each other - i.e, if either (or all) coordinates of the
* 2D vector are equal to Double.NaN, the 2D vector is equal to
* {@link #NaN}.
*
*
* @param other Object to test for equality to this
* @return true if two points on the 2-sphere objects are equal, false if
* object is null, not an instance of S2Point, or
* not equal to this S2Point instance
*
*/
@Override
public boolean equals(Object other) {
if (this == other) {
return true;
}
if (other instanceof S2Point) {
final S2Point rhs = (S2Point) other;
if (rhs.isNaN()) {
return this.isNaN();
}
return (theta == rhs.theta) && (phi == rhs.phi);
}
return false;
}
/**
* Get a hashCode for the 2D vector.
*
* All NaN values have the same hash code.
*
* @return a hash code value for this object
*/
@Override
public int hashCode() {
if (isNaN()) {
return 542;
}
return 134 * (37 * MathUtils.hash(theta) + MathUtils.hash(phi));
}
}