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Geometric primitives for spherical space.
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/*
* 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.geometry.spherical.twod;
import java.util.Comparator;
import org.apache.commons.geometry.core.Point;
import org.apache.commons.geometry.core.internal.SimpleTupleFormat;
import org.apache.commons.geometry.euclidean.threed.SphericalCoordinates;
import org.apache.commons.geometry.euclidean.threed.Vector3D;
import org.apache.commons.geometry.euclidean.threed.rotation.QuaternionRotation;
import org.apache.commons.numbers.core.Precision;
/** This class represents a point on the 2-sphere.
* Instances of this class are guaranteed to be immutable.
*/
public final class Point2S implements Point {
/** +I (coordinates: ( azimuth = 0, polar = pi/2 )). */
public static final Point2S PLUS_I = new Point2S(0, 0.5 * Math.PI, Vector3D.Unit.PLUS_X);
/** +J (coordinates: ( azimuth = pi/2, polar = pi/2 ))). */
public static final Point2S PLUS_J = new Point2S(0.5 * Math.PI, 0.5 * Math.PI, Vector3D.Unit.PLUS_Y);
/** +K (coordinates: ( azimuth = any angle, polar = 0 )). */
public static final Point2S PLUS_K = new Point2S(0, 0, Vector3D.Unit.PLUS_Z);
/** -I (coordinates: ( azimuth = pi, polar = pi/2 )). */
public static final Point2S MINUS_I = new Point2S(Math.PI, 0.5 * Math.PI, Vector3D.Unit.MINUS_X);
/** -J (coordinates: ( azimuth = 3pi/2, polar = pi/2 )). */
public static final Point2S MINUS_J = new Point2S(1.5 * Math.PI, 0.5 * Math.PI, Vector3D.Unit.MINUS_Y);
/** -K (coordinates: ( azimuth = any angle, polar = pi )). */
public static final Point2S MINUS_K = new Point2S(0, Math.PI, Vector3D.Unit.MINUS_Z);
/** A point with all coordinates set to NaN. */
public static final Point2S NaN = new Point2S(Double.NaN, Double.NaN, null);
/** Comparator that sorts points in component-wise ascending order, first sorting
* by polar value and then by azimuth value. Points are only considered equal if
* their components match exactly. Null arguments are evaluated as being greater
* than non-null arguments.
*/
public static final Comparator POLAR_AZIMUTH_ASCENDING_ORDER = (a, b) -> {
int cmp = 0;
if (a != null && b != null) {
cmp = Double.compare(a.getPolar(), b.getPolar());
if (cmp == 0) {
cmp = Double.compare(a.getAzimuth(), b.getAzimuth());
}
} else if (a != null) {
cmp = -1;
} else if (b != null) {
cmp = 1;
}
return cmp;
};
/** Azimuthal angle in the x-y plane. */
private final double azimuth;
/** Polar angle. */
private final double polar;
/** Corresponding 3D normalized vector. */
private final Vector3D.Unit vector;
/** Build a point from its internal components.
* @param azimuth azimuthal angle in the x-y plane
* @param polar polar angle
* @param vector corresponding vector; if null, the vector is computed
*/
private Point2S(final double azimuth, final double polar, final Vector3D.Unit vector) {
this.azimuth = SphericalCoordinates.normalizeAzimuth(azimuth);
this.polar = SphericalCoordinates.normalizePolar(polar);
this.vector = (vector != null) ?
vector :
computeVector(azimuth, polar);
}
/** Get the azimuth angle in the x-y plane in the range {@code [0, 2pi)}.
* @return azimuth angle in the x-y plane in the range {@code [0, 2pi)}.
* @see Point2S#of(double, double)
*/
public double getAzimuth() {
return azimuth;
}
/** Get the polar angle in the range {@code [0, pi)}.
* @return polar angle in the range {@code [0, pi)}.
* @see Point2S#of(double, double)
*/
public double getPolar() {
return polar;
}
/** Get the corresponding normalized vector in 3D Euclidean space.
* This value will be null if the spherical coordinates of the point
* are infinite or NaN.
* @return normalized vector
*/
public Vector3D.Unit getVector() {
return vector;
}
/** {@inheritDoc} */
@Override
public int getDimension() {
return 2;
}
/** {@inheritDoc} */
@Override
public boolean isNaN() {
return Double.isNaN(azimuth) || Double.isNaN(polar);
}
/** {@inheritDoc} */
@Override
public boolean isInfinite() {
return !isNaN() && (Double.isInfinite(azimuth) || Double.isInfinite(polar));
}
/** {@inheritDoc} */
@Override
public boolean isFinite() {
return Double.isFinite(azimuth) && Double.isFinite(polar);
}
/** Get the point exactly opposite this point on the sphere. The returned
* point is {@code pi} distance away from the current instance.
* @return the point exactly opposite this point on the sphere
*/
public Point2S antipodal() {
return from(vector.negate());
}
/** {@inheritDoc} */
@Override
public double distance(final Point2S point) {
return distance(this, point);
}
/** Spherically interpolate a point along the shortest arc between this point and
* the given point. The parameter {@code t} controls the interpolation and is expected
* to be in the range {@code [0, 1]}, with {@code 0} returning a point equivalent to the
* current instance {@code 1} returning a point equivalent to the given instance. If the
* points are antipodal, then an arbitrary arc is chosen from the infinite number available.
* @param other other point to interpolate with
* @param t interpolation parameter
* @return spherically interpolated point
* @see QuaternionRotation#slerp(QuaternionRotation)
* @see QuaternionRotation#createVectorRotation(Vector3D, Vector3D)
*/
public Point2S slerp(final Point2S other, final double t) {
final QuaternionRotation start = QuaternionRotation.identity();
final QuaternionRotation end = QuaternionRotation.createVectorRotation(getVector(), other.getVector());
final QuaternionRotation quat = start.slerp(end).apply(t);
return Point2S.from(quat.apply(getVector()));
}
/** Return true if this point should be considered equivalent to the argument using the
* given precision context. This will be true if the distance between the points is
* equivalent to zero as evaluated by the precision context.
* @param point point to compare with
* @param precision precision context used to perform floating point comparisons
* @return true if this point should be considered equivalent to the argument using the
* given precision context
*/
public boolean eq(final Point2S point, final Precision.DoubleEquivalence precision) {
return precision.eqZero(distance(point));
}
/** Get a hashCode for the point.
* .
* 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 * Double.hashCode(azimuth) + Double.hashCode(polar));
}
/** Test for the equality of two points.
*
* If all spherical coordinates of two points are exactly the same, and none are
* Double.NaN, the two points are considered to be equal. Note
* that the comparison is made using the azimuth and polar coordinates only; the
* corresponding 3D vectors are not compared. This is significant at the poles,
* where an infinite number of points share the same underlying 3D vector but may
* have different spherical coordinates. For example, the points {@code (0, 0)}
* and {@code (1, 0)} (both located at a pole but with different azimuths) will
* not be considered equal by this method, even though they share the
* exact same underlying 3D vector.
*
*
* NaN coordinates are considered to affect the point globally
* and be equals to each other - i.e, if either (or all) coordinates of the
* point are equal to Double.NaN, the point 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 exactly equal, false if
* object is null, not an instance of Point2S, or
* not equal to this Point2S instance
*/
@Override
public boolean equals(final Object other) {
if (this == other) {
return true;
}
if (!(other instanceof Point2S)) {
return false;
}
final Point2S rhs = (Point2S) other;
if (rhs.isNaN()) {
return this.isNaN();
}
return Double.compare(azimuth, rhs.azimuth) == 0 &&
Double.compare(polar, rhs.polar) == 0;
}
/** {@inheritDoc} */
@Override
public String toString() {
return SimpleTupleFormat.getDefault().format(getAzimuth(), getPolar());
}
/** Build a vector from its spherical coordinates.
* @param azimuth azimuthal angle in the x-y plane
* @param polar polar angle
* @return point instance with the given coordinates
* @see #getAzimuth()
* @see #getPolar()
*/
public static Point2S of(final double azimuth, final double polar) {
return new Point2S(azimuth, polar, null);
}
/** Build a point from its underlying 3D vector.
* @param vector 3D vector
* @return point instance with the coordinates determined by the given 3D vector
* @exception IllegalStateException if vector norm is zero
*/
public static Point2S from(final Vector3D vector) {
final SphericalCoordinates coords = SphericalCoordinates.fromCartesian(vector);
return new Point2S(coords.getAzimuth(), coords.getPolar(), vector.normalize());
}
/** Parses the given string and returns a new point instance. The expected string
* format is the same as that returned by {@link #toString()}.
* @param str the string to parse
* @return point instance represented by the string
* @throws IllegalArgumentException if the given string has an invalid format
*/
public static Point2S parse(final String str) {
return SimpleTupleFormat.getDefault().parse(str, Point2S::of);
}
/** 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(final Point2S p1, final Point2S p2) {
return p1.vector.angle(p2.vector);
}
/** Compute the 3D Euclidean vector associated with the given spherical coordinates.
* Null is returned if the coordinates are infinite or NaN.
* @param azimuth azimuth value
* @param polar polar value
* @return the 3D Euclidean vector associated with the given spherical coordinates
* or null if either of the arguments are infinite or NaN.
*/
private static Vector3D.Unit computeVector(final double azimuth, final double polar) {
if (Double.isFinite(azimuth) && Double.isFinite(polar)) {
return SphericalCoordinates.toCartesian(1, azimuth, polar).normalize();
}
return null;
}
}