/*
    * 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
    *
    *      https://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.
   */
  
  /*
   * This is not the original file distributed by the Apache Software Foundation
   * It has been modified by the Hipparchus project
   */
  package org.hipparchus.geometry.euclidean.twod;
  
  import java.text.NumberFormat;
  
  import org.hipparchus.exception.LocalizedCoreFormats;
  import org.hipparchus.exception.MathIllegalArgumentException;
  import org.hipparchus.exception.MathRuntimeException;
  import org.hipparchus.geometry.Point;
  import org.hipparchus.geometry.Space;
  import org.hipparchus.geometry.Vector;
  import org.hipparchus.util.FastMath;
  import org.hipparchus.util.MathArrays;
  import org.hipparchus.util.MathUtils;
  
  /** This class represents a 2D vector.
   * <p>Instances of this class are guaranteed to be immutable.</p>
   */
  public class Vector2D implements Vector<Euclidean2D, Vector2D> {
  
      /** Origin (coordinates: 0, 0). */
      public static final Vector2D ZERO   = new Vector2D(0, 0);
  
      /** First canonical vector (coordinates: 1, 0).
       * @since 1.6
       */
      public static final Vector2D PLUS_I = new Vector2D(1, 0);
  
      /** Opposite of the first canonical vector (coordinates: -1, 0).
       * @since 1.6
       */
      public static final Vector2D MINUS_I = new Vector2D(-1, 0);
  
      /** Second canonical vector (coordinates: 0, 1).
       * @since 1.6
       */
      public static final Vector2D PLUS_J = new Vector2D(0, 1);
  
      /** Opposite of the second canonical vector (coordinates: 0, -1).
       * @since 1.6
       */
      public static final Vector2D MINUS_J = new Vector2D(0, -1);
  
      // CHECKSTYLE: stop ConstantName
      /** A vector with all coordinates set to NaN. */
      public static final Vector2D NaN = new Vector2D(Double.NaN, Double.NaN);
      // CHECKSTYLE: resume ConstantName
  
      /** A vector with all coordinates set to positive infinity. */
      public static final Vector2D POSITIVE_INFINITY =
          new Vector2D(Double.POSITIVE_INFINITY, Double.POSITIVE_INFINITY);
  
      /** A vector with all coordinates set to negative infinity. */
      public static final Vector2D NEGATIVE_INFINITY =
          new Vector2D(Double.NEGATIVE_INFINITY, Double.NEGATIVE_INFINITY);
  
      /** Serializable UID. */
      private static final long serialVersionUID = 266938651998679754L;
  
      /** Abscissa. */
      private final double x;
  
      /** Ordinate. */
      private final double y;
  
      /** Simple constructor.
       * Build a vector from its coordinates
       * @param x abscissa
       * @param y ordinate
       * @see #getX()
       * @see #getY()
       */
      public Vector2D(double x, double y) {
          this.x = x;
          this.y = y;
      }
  
      /** Simple constructor.
       * Build a vector from its coordinates
      * @param v coordinates array
      * @exception MathIllegalArgumentException if array does not have 2 elements
      * @see #toArray()
      */
     public Vector2D(double[] v) throws MathIllegalArgumentException {
         if (v.length != 2) {
             throw new MathIllegalArgumentException(LocalizedCoreFormats.DIMENSIONS_MISMATCH,
                                                    v.length, 2);
         }
         this.x = v[0];
         this.y = v[1];
     }
 
     /** Multiplicative constructor
      * Build a vector from another one and a scale factor.
      * The vector built will be a * u
      * @param a scale factor
      * @param u base (unscaled) vector
      */
     public Vector2D(double a, Vector2D u) {
         this.x = a * u.x;
         this.y = a * u.y;
     }
 
     /** Linear constructor
      * Build a vector from two other ones and corresponding scale factors.
      * The vector built will be a1 * u1 + a2 * u2
      * @param a1 first scale factor
      * @param u1 first base (unscaled) vector
      * @param a2 second scale factor
      * @param u2 second base (unscaled) vector
      */
     public Vector2D(double a1, Vector2D u1, double a2, Vector2D u2) {
         this.x = a1 * u1.x + a2 * u2.x;
         this.y = a1 * u1.y + a2 * u2.y;
     }
 
     /** Linear constructor
      * Build a vector from three other ones and corresponding scale factors.
      * The vector built will be a1 * u1 + a2 * u2 + a3 * u3
      * @param a1 first scale factor
      * @param u1 first base (unscaled) vector
      * @param a2 second scale factor
      * @param u2 second base (unscaled) vector
      * @param a3 third scale factor
      * @param u3 third base (unscaled) vector
      */
     public Vector2D(double a1, Vector2D u1, double a2, Vector2D u2,
                    double a3, Vector2D u3) {
         this.x = a1 * u1.x + a2 * u2.x + a3 * u3.x;
         this.y = a1 * u1.y + a2 * u2.y + a3 * u3.y;
     }
 
     /** Linear constructor
      * Build a vector from four other ones and corresponding scale factors.
      * The vector built will be a1 * u1 + a2 * u2 + a3 * u3 + a4 * u4
      * @param a1 first scale factor
      * @param u1 first base (unscaled) vector
      * @param a2 second scale factor
      * @param u2 second base (unscaled) vector
      * @param a3 third scale factor
      * @param u3 third base (unscaled) vector
      * @param a4 fourth scale factor
      * @param u4 fourth base (unscaled) vector
      */
     public Vector2D(double a1, Vector2D u1, double a2, Vector2D u2,
                    double a3, Vector2D u3, double a4, Vector2D u4) {
         this.x = a1 * u1.x + a2 * u2.x + a3 * u3.x + a4 * u4.x;
         this.y = a1 * u1.y + a2 * u2.y + a3 * u3.y + a4 * u4.y;
     }
 
     /** Get the abscissa of the vector.
      * @return abscissa of the vector
      * @see #Vector2D(double, double)
      */
     public double getX() {
         return x;
     }
 
     /** Get the ordinate of the vector.
      * @return ordinate of the vector
      * @see #Vector2D(double, double)
      */
     public double getY() {
         return y;
     }
 
     /** Get the vector coordinates as a dimension 2 array.
      * @return vector coordinates
      * @see #Vector2D(double[])
      */
     public double[] toArray() {
         return new double[] { x, y };
     }
 
     /** {@inheritDoc} */
     @Override
     public Space getSpace() {
         return Euclidean2D.getInstance();
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D getZero() {
         return ZERO;
     }
 
     /** {@inheritDoc} */
     @Override
     public double getNorm1() {
         return FastMath.abs(x) + FastMath.abs(y);
     }
 
     /** {@inheritDoc} */
     @Override
     public double getNorm() {
         return FastMath.sqrt (x * x + y * y);
     }
 
     /** {@inheritDoc} */
     @Override
     public double getNormSq() {
         return x * x + y * y;
     }
 
     /** {@inheritDoc} */
     @Override
     public double getNormInf() {
         return FastMath.max(FastMath.abs(x), FastMath.abs(y));
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D add(Vector<Euclidean2D, Vector2D> v) {
         Vector2D v2 = (Vector2D) v;
         return new Vector2D(x + v2.getX(), y + v2.getY());
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D add(double factor, Vector<Euclidean2D, Vector2D> v) {
         Vector2D v2 = (Vector2D) v;
         return new Vector2D(x + factor * v2.getX(), y + factor * v2.getY());
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D subtract(Vector<Euclidean2D, Vector2D> p) {
         Vector2D p3 = (Vector2D) p;
         return new Vector2D(x - p3.x, y - p3.y);
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D subtract(double factor, Vector<Euclidean2D, Vector2D> v) {
         Vector2D v2 = (Vector2D) v;
         return new Vector2D(x - factor * v2.getX(), y - factor * v2.getY());
     }
 
     /** Compute the angular separation between two vectors.
      * <p>This method computes the angular separation between two
      * vectors using the dot product for well separated vectors and the
      * cross product for almost aligned vectors. This allows to have a
      * good accuracy in all cases, even for vectors very close to each
      * other.</p>
      * @param v1 first vector
      * @param v2 second vector
      * @return angular separation between v1 and v2
      * @exception MathRuntimeException if either vector has a null norm
      */
     public static double angle(Vector2D v1, Vector2D v2) throws MathRuntimeException {
 
         double normProduct = v1.getNorm() * v2.getNorm();
         if (normProduct == 0) {
             throw new MathRuntimeException(LocalizedCoreFormats.ZERO_NORM);
         }
 
         double dot = v1.dotProduct(v2);
         double threshold = normProduct * 0.9999;
         if (FastMath.abs(dot) > threshold) {
             // the vectors are almost aligned, compute using the sine
             final double n = FastMath.abs(MathArrays.linearCombination(v1.x, v2.y, -v1.y, v2.x));
             if (dot >= 0) {
                 return FastMath.asin(n / normProduct);
             }
             return FastMath.PI - FastMath.asin(n / normProduct);
         }
 
         // the vectors are sufficiently separated to use the cosine
         return FastMath.acos(dot / normProduct);
 
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D negate() {
         return new Vector2D(-x, -y);
     }
 
     /** {@inheritDoc} */
     @Override
     public Vector2D scalarMultiply(double a) {
         return new Vector2D(a * x, a * y);
     }
 
     /** {@inheritDoc} */
     @Override
     public boolean isNaN() {
         return Double.isNaN(x) || Double.isNaN(y);
     }
 
     /** {@inheritDoc} */
     @Override
     public boolean isInfinite() {
         return !isNaN() && (Double.isInfinite(x) || Double.isInfinite(y));
     }
 
     /** {@inheritDoc} */
     @Override
     public double distance1(Vector<Euclidean2D, Vector2D> p) {
         Vector2D p3 = (Vector2D) p;
         final double dx = FastMath.abs(p3.x - x);
         final double dy = FastMath.abs(p3.y - y);
         return dx + dy;
     }
 
     /** {@inheritDoc} */
     @Override
     public double distance(Point<Euclidean2D> p) {
         Vector2D p3 = (Vector2D) p;
         final double dx = p3.x - x;
         final double dy = p3.y - y;
         return FastMath.sqrt(dx * dx + dy * dy);
     }
 
     /** {@inheritDoc} */
     @Override
     public double distanceInf(Vector<Euclidean2D, Vector2D> p) {
         Vector2D p3 = (Vector2D) p;
         final double dx = FastMath.abs(p3.x - x);
         final double dy = FastMath.abs(p3.y - y);
         return FastMath.max(dx, dy);
     }
 
     /** {@inheritDoc} */
     @Override
     public double distanceSq(Vector<Euclidean2D, Vector2D> p) {
         Vector2D p3 = (Vector2D) p;
         final double dx = p3.x - x;
         final double dy = p3.y - y;
         return dx * dx + dy * dy;
     }
 
     /** {@inheritDoc} */
     @Override
     public double dotProduct(final Vector<Euclidean2D, Vector2D> v) {
         final Vector2D v2 = (Vector2D) v;
         return MathArrays.linearCombination(x, v2.x, y, v2.y);
     }
 
     /**
      * Compute the cross-product of the instance and the given points.
      * <p>
      * The cross product can be used to determine the location of a point
      * with regard to the line formed by (p1, p2) and is calculated as:
      * \[
      *    P = (x_2 - x_1)(y_3 - y_1) - (y_2 - y_1)(x_3 - x_1)
      * \]
      * with \(p3 = (x_3, y_3)\) being this instance.
      * <p>
      * If the result is 0, the points are collinear, i.e. lie on a single straight line L;
      * if it is positive, this point lies to the left, otherwise to the right of the line
      * formed by (p1, p2).
      *
      * @param p1 first point of the line
      * @param p2 second point of the line
      * @return the cross-product
      *
      * @see <a href="http://en.wikipedia.org/wiki/Cross_product">Cross product (Wikipedia)</a>
      */
     public double crossProduct(final Vector2D p1, final Vector2D p2) {
         final double x1 = p2.getX() - p1.getX();
         final double y1 = getY() - p1.getY();
         final double x2 = getX() - p1.getX();
         final double y2 = p2.getY() - p1.getY();
         return MathArrays.linearCombination(x1, y1, -x2, y2);
     }
 
     /** Compute the distance between two vectors according to the L<sub>1</sub> norm.
      * <p>Calling this method is equivalent to calling:
      * <code>p1.subtract(p2).getNorm1()</code> except that no intermediate
      * vector is built</p>
      * @param p1 first vector
      * @param p2 second vector
      * @return the distance between p1 and p2 according to the L<sub>1</sub> norm
      * @since 1.6
      */
     public static double distance1(Vector2D p1, Vector2D p2) {
         return p1.distance1(p2);
     }
 
     /** Compute the distance between two vectors according to the L<sub>2</sub> norm.
      * <p>Calling this method is equivalent to calling:
      * <code>p1.subtract(p2).getNorm()</code> except that no intermediate
      * vector is built</p>
      * @param p1 first vector
      * @param p2 second vector
      * @return the distance between p1 and p2 according to the L<sub>2</sub> norm
      */
     public static double distance(Vector2D p1, Vector2D p2) {
         return p1.distance(p2);
     }
 
     /** Compute the distance between two vectors according to the L<sub>&infin;</sub> norm.
      * <p>Calling this method is equivalent to calling:
      * <code>p1.subtract(p2).getNormInf()</code> except that no intermediate
      * vector is built</p>
      * @param p1 first vector
      * @param p2 second vector
      * @return the distance between p1 and p2 according to the L<sub>&infin;</sub> norm
      */
     public static double distanceInf(Vector2D p1, Vector2D p2) {
         return p1.distanceInf(p2);
     }
 
     /** Compute the square of the distance between two vectors.
      * <p>Calling this method is equivalent to calling:
      * <code>p1.subtract(p2).getNormSq()</code> except that no intermediate
      * vector is built</p>
      * @param p1 first vector
      * @param p2 second vector
      * @return the square of the distance between p1 and p2
      */
     public static double distanceSq(Vector2D p1, Vector2D p2) {
         return p1.distanceSq(p2);
     }
 
     /** Compute the orientation of a triplet of points.
      * @param p first vector of the triplet
      * @param q second vector of the triplet
      * @param r third vector of the triplet
      * @return a positive value if (p, q, r) defines a counterclockwise oriented
      * triangle, a negative value if (p, q, r) defines a clockwise oriented
      * triangle, and 0 if (p, q, r) are collinear or some points are equal
      * @since 1.2
      */
     public static double orientation(final Vector2D p, final Vector2D q, final Vector2D r) {
         return MathArrays.linearCombination(new double[] {
             p.getX(), -p.getX(), q.getX(), -q.getX(), r.getX(), -r.getX()
         }, new double[] {
             q.getY(),  r.getY(), r.getY(),  p.getY(), p.getY(),  q.getY()
         });
     }
 
     /**
      * Test for the equality of two 2D vectors.
      * <p>
      * If all coordinates of two 2D vectors are exactly the same, and none are
      * {@code Double.NaN}, the two 2D vectors are considered to be equal.
      * </p>
      * <p>
      * {@code 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 {@code Double.NaN}, the 2D vector is equal to
      * {@link #NaN}.
      * </p>
      *
      * @param other Object to test for equality to this
      * @return true if two 2D vector objects are equal, false if
      *         object is null, not an instance of Vector2D, or
      *         not equal to this Vector2D instance
      */
     @Override
     public boolean equals(Object other) {
 
         if (this == other) {
             return true;
         }
 
         if (other instanceof Vector2D) {
             final Vector2D rhs = (Vector2D)other;
             return x == rhs.x && y == rhs.y || isNaN() && rhs.isNaN();
         }
 
         return false;
 
     }
 
     /**
      * Test for the equality of two 2D vectors.
      * <p>
      * If all coordinates of two 2D vectors are exactly the same, and none are
      * {@code NaN}, the two 2D vectors are considered to be equal.
      * </p>
      * <p>
      * In compliance with IEEE754 handling, if any coordinates of any of the
      * two vectors are {@code NaN}, then the vectors are considered different.
      * This implies that {@link #NaN Vector2D.NaN}.equals({@link #NaN Vector2D.NaN})
      * returns {@code false} despite the instance is checked against itself.
      * </p>
      *
      * @param other Object to test for equality to this
      * @return true if two 2D vector objects are equal, false if
      *         object is null, not an instance of Vector2D, or
      *         not equal to this Vector2D instance
      * @since 2.1
      */
     public boolean equalsIeee754(Object other) {
 
         if (this == other && !isNaN()) {
             return true;
         }
 
         if (other instanceof Vector2D) {
             final Vector2D rhs = (Vector2D) other;
             return x == rhs.x && y == rhs.y;
         }
         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 122 * (76 * MathUtils.hash(x) +  MathUtils.hash(y));
     }
 
     /** Get a string representation of this vector.
      * @return a string representation of this vector
      */
     @Override
     public String toString() {
         return Vector2DFormat.getVector2DFormat().format(this);
     }
 
     /** {@inheritDoc} */
     @Override
     public String toString(final NumberFormat format) {
         return new Vector2DFormat(format).format(this);
     }
 
 }