Java tutorial
/* * 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. * <p> * 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 <a * href="http://mathworld.wolfram.com/SphericalCoordinates.html">Spherical * Coordinates</a> in MathWorld). * </p> * <p>Instances of this class are guaranteed to be immutable.</p> * @since 3.3 */ public class S2Point implements Point<Sphere2D> { /** +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<Sphere2D> 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. * <p> * If all coordinates of two points are exactly the same, and none are * <code>Double.NaN</code>, the two points are considered to be equal. * </p> * <p> * <code>NaN</code> 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 <code>Double.NaN</code>, the 2D vector is equal to * {@link #NaN}. * </p> * * @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. * <p> * All NaN values have the same hash code.</p> * * @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)); } }