/*
    * 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.core.precision.DoublePrecisionContext;
  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;
  
  /** This class represents a point on the 2-sphere.
   * <p>Instances of this class are guaranteed to be immutable.</p>
   */
  public final class Point2S implements Point<Point2S> {
  
      /** +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);
  
      // CHECKSTYLE: stop ConstantName
      /** A point with all coordinates set to NaN. */
      public static final Point2S NaN = new Point2S(Double.NaN, Double.NaN, null);
      // CHECKSTYLE: resume ConstantName
  
      /** 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<Point2S> 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 DoublePrecisionContext precision) {
         return precision.eqZero(distance(point));
     }
 
     /** Get a hashCode for the point.
      * .
      * <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 * Double.hashCode(azimuth) +  Double.hashCode(polar));
     }
 
     /** Test for the equality of two points.
      *
      * <p>If all spherical coordinates of two points are exactly the same, and none are
      * <code>Double.NaN</code>, 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
      * <em>not</em> be considered equal by this method, even though they share the
      * exact same underlying 3D vector.</p>
      *
      * <p>
      * <code>NaN</code> 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 <code>Double.NaN</code>, the point 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 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;
     }
 }