/*
    * 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.euclidean.threed;
  
  import org.apache.commons.geometry.core.Spatial;
  import org.apache.commons.geometry.core.internal.SimpleTupleFormat;
  import org.apache.commons.geometry.euclidean.internal.Vectors;
  import org.apache.commons.geometry.euclidean.twod.PolarCoordinates;
  import org.apache.commons.numbers.angle.PlaneAngleRadians;
  
  /** Class representing <a href="https://en.wikipedia.org/wiki/Spherical_coordinate_system">spherical coordinates</a>
   * in 3 dimensional Euclidean space.
   *
   * <p>Spherical coordinates for a point are defined by three values:
   * <ol>
   *  <li><em>Radius</em> - The distance from the point to a fixed referenced point.</li>
   *  <li><em>Azimuth angle</em> - The angle measured from a fixed reference direction in a plane to
   * the orthogonal projection of the point on that plane.</li>
   *  <li><em>Polar angle</em> - The angle measured from a fixed zenith direction to the point. The zenith
   *direction must be orthogonal to the reference plane.</li>
   * </ol>
   * This class follows the convention of using the origin as the reference point; the positive x-axis as the
   * reference direction for the azimuth angle, measured in the x-y plane with positive angles moving counter-clockwise
   * toward the positive y-axis; and the positive z-axis as the zenith direction. Spherical coordinates are
   * related to Cartesian coordinates as follows:
   * <pre>
   * x = r cos(&theta;) sin(&Phi;)
   * y = r sin(&theta;) sin(&Phi;)
   * z = r cos(&Phi;)
   *
   * r = &radic;(x^2 + y^2 + z^2)
   * &theta; = atan2(y, x)
   * &Phi; = acos(z/r)
   * </pre>
   * where <em>r</em> is the radius, <em>&theta;</em> is the azimuth angle, and <em>&Phi;</em> is the polar angle
   * of the spherical coordinates.
   *
   * <p>There are numerous, competing conventions for the symbols used to represent spherical coordinate values. For
   * example, the mathematical convention is to use <em>(r, &theta;, &Phi;)</em> to represent radius, azimuth angle, and
   * polar angle, whereas the physics convention flips the angle values and uses <em>(r, &Phi;, &theta;)</em>. As such,
   * this class avoids the use of these symbols altogether in favor of the less ambiguous formal names of the values,
   * e.g. {@code radius}, {@code azimuth}, and {@code polar}.</p>
   *
   * <p>In order to ensure the uniqueness of coordinate sets, coordinate values
   * are normalized so that {@code radius} is in the range {@code [0, +Infinity)},
   * {@code azimuth} is in the range {@code [0, 2pi)}, and {@code polar} is in the
   * range {@code [0, pi]}.</p>
   *
   * @see <a href="https://en.wikipedia.org/wiki/Spherical_coordinate_system">Spherical Coordinate System</a>
   */
  public final class SphericalCoordinates implements Spatial {
      /** Radius value. */
      private final double radius;
  
      /** Azimuth angle in radians. */
      private final double azimuth;
  
      /** Polar angle in radians. */
      private final double polar;
  
      /** Simple constructor. The given inputs are normalized.
       * @param radius Radius value.
       * @param azimuth Azimuth angle in radians.
       * @param polar Polar angle in radians.
       */
      private SphericalCoordinates(double radius, double azimuth, double polar) {
          if (radius < 0) {
              // negative radius; flip the angles
              radius = Math.abs(radius);
              azimuth += PlaneAngleRadians.PI;
              polar += PlaneAngleRadians.PI;
          }
  
          this.radius = radius;
          this.azimuth = normalizeAzimuth(azimuth);
          this.polar = normalizePolar(polar);
      }
  
      /** Return the radius value. The value is in the range {@code [0, +Infinity)}.
       * @return the radius value
       */
      public double getRadius() {
          return radius;
      }
  
     /** Return the azimuth angle in radians. This is the angle in the x-y plane measured counter-clockwise from
      * the positive x axis. The angle is in the range {@code [0, 2pi)}.
      * @return the azimuth angle in radians
      */
     public double getAzimuth() {
         return azimuth;
     }
 
     /** Return the polar angle in radians. This is the angle the coordinate ray makes with the positive z axis.
      * The angle is in the range {@code [0, pi]}.
      * @return the polar angle in radians
      */
     public double getPolar() {
         return polar;
     }
 
     /** {@inheritDoc} */
     @Override
     public int getDimension() {
         return 3;
     }
 
     /** {@inheritDoc} */
     @Override
     public boolean isNaN() {
         return Double.isNaN(radius) || Double.isNaN(azimuth) || Double.isNaN(polar);
     }
 
     /** {@inheritDoc} */
     @Override
     public boolean isInfinite() {
         return !isNaN() && (Double.isInfinite(radius) || Double.isInfinite(azimuth) || Double.isInfinite(polar));
     }
 
     /** {@inheritDoc} */
     @Override
     public boolean isFinite() {
         return Double.isFinite(radius) && Double.isFinite(azimuth) && Double.isFinite(polar);
     }
 
     /** Convert this set of spherical coordinates to a Cartesian form.
      * @return A 3-dimensional vector with an equivalent set of
      *      Cartesian coordinates.
      */
     public Vector3D toVector() {
         return toCartesian(radius, azimuth, polar);
     }
 
     /** Get a hashCode for this set of spherical coordinates.
      * <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 127;
         }
         return 449 * (79 * Double.hashCode(radius) + Double.hashCode(azimuth) + Double.hashCode(polar));
     }
 
     /** Test for the equality of two sets of spherical coordinates.
      * <p>
      * If all values of two sets of coordinates are exactly the same, and none are
      * <code>Double.NaN</code>, the two sets are considered to be equal.
      * </p>
      * <p>
      * <code>NaN</code> values are considered to globally affect the coordinates
      * and be equal to each other - i.e, if any (or all) values of the
      * coordinate set are equal to <code>Double.NaN</code>, the set as a whole
      * is considered to equal NaN.
      * </p>
      *
      * @param other Object to test for equality to this
      * @return true if two SphericalCoordinates objects are equal, false if
      *         object is null, not an instance of SphericalCoordinates, or
      *         not equal to this SphericalCoordinates instance
      *
      */
     @Override
     public boolean equals(final Object other) {
         if (this == other) {
             return true;
         }
         if (other instanceof SphericalCoordinates) {
             final SphericalCoordinates rhs = (SphericalCoordinates) other;
             if (rhs.isNaN()) {
                 return this.isNaN();
             }
 
             return Double.compare(radius, rhs.radius) == 0 &&
                     Double.compare(azimuth, rhs.azimuth) == 0 &&
                     Double.compare(polar, rhs.polar) == 0;
         }
         return false;
     }
 
     /** {@inheritDoc} */
     @Override
     public String toString() {
         return SimpleTupleFormat.getDefault().format(radius, azimuth, polar);
     }
 
     /** Return a new instance with the given spherical coordinate values. The values are normalized
      * so that {@code radius} lies in the range {@code [0, +Infinity)}, {@code azimuth} lies in the range
      * {@code [0, 2pi)}, and {@code polar} lies in the range {@code [0, +pi]}.
      * @param radius the length of the line segment from the origin to the coordinate point.
      * @param azimuth the angle in the x-y plane, measured in radians counter-clockwise
      *      from the positive x-axis.
      * @param polar the angle in radians between the positive z-axis and the ray from the origin
      *      to the coordinate point.
      * @return a new {@link SphericalCoordinates} instance representing the same point as the given set of
      *      spherical coordinates.
      */
     public static SphericalCoordinates of(final double radius, final double azimuth, final double polar) {
         return new SphericalCoordinates(radius, azimuth, polar);
     }
 
     /** Convert the given set of Cartesian coordinates to spherical coordinates.
      * @param x X coordinate value
      * @param y Y coordinate value
      * @param z Z coordinate value
      * @return a set of spherical coordinates equivalent to the given Cartesian coordinates
      */
     public static SphericalCoordinates fromCartesian(final double x, final double y, final double z) {
         final double radius = Vectors.norm(x, y, z);
         final double azimuth = Math.atan2(y, x);
 
         // default the polar angle to 0 when the radius is 0
         final double polar = (radius > 0.0) ? Math.acos(z / radius) : 0.0;
 
         return new SphericalCoordinates(radius, azimuth, polar);
     }
 
     /** Convert the given set of Cartesian coordinates to spherical coordinates.
      * @param vec vector containing Cartesian coordinates to convert
      * @return a set of spherical coordinates equivalent to the given Cartesian coordinates
      */
     public static SphericalCoordinates fromCartesian(final Vector3D vec) {
         return fromCartesian(vec.getX(), vec.getY(), vec.getZ());
     }
 
     /** Convert the given set of spherical coordinates to Cartesian coordinates.
      * @param radius The spherical radius value.
      * @param azimuth The spherical azimuth angle in radians.
      * @param polar The spherical polar angle in radians.
      * @return A 3-dimensional vector with an equivalent set of
      *      Cartesian coordinates.
      */
     public static Vector3D toCartesian(final double radius, final double azimuth, final double polar) {
         final double xyLength = radius * Math.sin(polar);
 
         final double x = xyLength * Math.cos(azimuth);
         final double y = xyLength * Math.sin(azimuth);
         final double z = radius * Math.cos(polar);
 
         return Vector3D.of(x, y, z);
     }
 
     /** Parse the given string and return a new {@link SphericalCoordinates} instance. The parsed
      * coordinate values are normalized as in the {@link #of(double, double, double)} method.
      * The expected string format is the same as that returned by {@link #toString()}.
      * @param input the string to parse
      * @return new {@link SphericalCoordinates} instance
      * @throws IllegalArgumentException if the string format is invalid.
      */
     public static SphericalCoordinates parse(final String input) {
         return SimpleTupleFormat.getDefault().parse(input, SphericalCoordinates::new);
     }
 
     /** Normalize an azimuth value to be within the range {@code [0, 2pi)}. This
      * is exactly equivalent to {@link PolarCoordinates#normalizeAzimuth(double)}.
      * @param azimuth azimuth value in radians
      * @return equivalent azimuth value in the range {@code [0, 2pi)}.
      * @see PolarCoordinates#normalizeAzimuth(double)
      */
     public static double normalizeAzimuth(final double azimuth) {
         return PolarCoordinates.normalizeAzimuth(azimuth);
     }
 
     /** Normalize a polar value to be within the range {@code [0, +pi]}. Since the
      * polar angle is the angle between two vectors (the zenith direction and the
      * point vector), the sign of the angle is not significant as in the azimuth angle.
      * For example, a polar angle of {@code -pi/2} and one of {@code +pi/2} will both
      * normalize to {@code pi/2}.
      * @param polar polar value in radians
      * @return equivalent polar value in the range {@code [0, +pi]}
      */
     public static double normalizePolar(double polar) {
         // normalize the polar angle; this is the angle between the polar vector and the point ray
         // so it is unsigned (unlike the azimuth) and should be in the range [0, pi]
         if (Double.isFinite(polar)) {
             polar = Math.abs(PlaneAngleRadians.normalizeBetweenMinusPiAndPi(polar));
         }
 
         return polar;
     }
 }