package org.djutils.draw;
   
   import java.util.Arrays;
   import java.util.Iterator;
   
   import org.djutils.draw.bounds.Bounds2d;
   import org.djutils.draw.point.Point2d;
   
   /**
   * Transform2d contains a MUTABLE transformation object that can transform points (x,y) based on e.g, rotation and translation.
   * It uses an affine transform matrix that can be built up from different components (translation, rotation, scaling,
   * reflection, shearing).
   * <p>
   * Copyright (c) 2020-2021 Delft University of Technology, PO Box 5, 2600 AA, Delft, the Netherlands. All rights reserved. <br>
   * BSD-style license. See <a href="https://djutils.org/docs/current/djutils/licenses.html">DJUTILS License</a>.
   * </p>
   * @author <a href="https://www.tudelft.nl/averbraeck">Alexander Verbraeck</a>
   * @author <a href="https://www.tudelft.nl/pknoppers">Peter Knoppers</a>
   */
  public class Transform2d implements Cloneable
  {
      /** The 3x3 transformation matrix, initialized as the Identity matrix. */
      private double[] mat = new double[] {1, 0, 0, 0, 1, 0, 0, 0, 1};
  
      /**
       * Multiply a 3x3 matrix (stored as a 9-value array by row) with a 4-value vector.
       * @param m double[]; the matrix
       * @param v double[]; the vector
       * @return double[3]; the result of m x v
       */
      protected static double[] mulMatVec(final double[] m, final double[] v)
      {
          double[] result = new double[3];
          for (int i = 0; i < 3; i++)
          {
              result[i] = m[3 * i] * v[0] + m[3 * i + 1] * v[1] + m[3 * i + 2] * v[2];
          }
          return result;
      }
  
      /**
       * Multiply a 3x3 matrix (stored as a 9-value array by row) with a 3-value vector and a 1 for the 3rd value.
       * @param m double[]; the matrix
       * @param v double[]; the vector
       * @return double[2]; the result of m x (v1, v2, 1), with the last value left out
       */
      protected static double[] mulMatVec2(final double[] m, final double[] v)
      {
          double[] result = new double[2];
          for (int i = 0; i < 2; i++)
          {
              result[i] = m[3 * i] * v[0] + m[3 * i + 1] * v[1] + m[3 * i + 2];
          }
          return result;
      }
  
      /**
       * Multiply a 3x3 matrix (stored as a 9-value array by row) with another 3x3-matrix.
       * @param m1 double[]; the first matrix
       * @param m2 double[]; the second matrix
       * @return double[9]; the result of m1 x m2
       */
      protected static double[] mulMatMat(final double[] m1, final double[] m2)
      {
          double[] result = new double[9];
          for (int i = 0; i < 3; i++)
          {
              for (int j = 0; j < 3; j++)
              {
                  result[3 * i + j] = m1[3 * i] * m2[j] + m1[3 * i + 1] * m2[j + 3] + +m1[3 * i + 2] * m2[j + 6];
              }
          }
          return result;
      }
  
      /**
       * Get a safe copy of the affine transformation matrix.
       * @return double[]; a safe copy of the affine transformation matrix
       */
      public double[] getMat()
      {
          return this.mat.clone();
      }
  
      /**
       * Transform coordinates by a vector (tx, ty). Note that to carry out multiple operations, the steps have to be built in the
       * OPPOSITE order since matrix multiplication operates from RIGHT to LEFT.
       * @param tx double; the translation value for the x-coordinates
       * @param ty double; the translation value for the y-coordinates
       * @return Transform2d; the new transformation matrix after applying this transform
       */
      public Transform2d translate(final double tx, final double ty)
      {
          if (tx == 0.0 && ty == 0.0)
          {
              return this;
          }
          this.mat = mulMatMat(this.mat, new double[] {1, 0, tx, 0, 1, ty, 0, 0, 1});
          return this;
     }
 
     /**
      * Translate coordinates by a the x and y values contained in a Point2d. Note that to carry out multiple operations, the
      * steps have to be built in the OPPOSITE order since matrix multiplication operates from RIGHT to LEFT.
      * @param point Point2d; the point containing the x and y translation values
      * @return Transform2d; the new transformation matrix after applying this transform
      */
     public Transform2d translate(final Point2d point)
     {
         if (point.x == 0.0 && point.y == 0.0)
         {
             return this;
         }
         this.mat = mulMatMat(this.mat, new double[] {1, 0, point.x, 0, 1, point.y, 0, 0, 1});
         return this;
     }
 
     /**
      * Scale all coordinates with a factor for x, and y. A scale factor of 1 leaves the coordinate unchanged. Note that to carry
      * out multiple operations, the steps have to be built in the OPPOSITE order since matrix multiplication operates from RIGHT
      * to LEFT.
      * @param sx double; the scale factor for the x-coordinates
      * @param sy double; the scale factor for the y-coordinates
      * @return Transform2d; the new transformation matrix after applying this transform
      */
     public Transform2d scale(final double sx, final double sy)
     {
         if (sx == 1.0 && sy == 1.0)
         {
             return this;
         }
         this.mat = mulMatMat(this.mat, new double[] {sx, 0, 0, 0, sy, 0, 0, 0, 1});
         return this;
     }
 
     /**
      * The rotation around the origin with an angle in radians. Note that to carry out multiple operations, the steps have to be
      * built in the OPPOSITE order since matrix multiplication operates from RIGHT to LEFT.
      * @param angle double; the angle to rotate the coordinates with with around the origin
      * @return Transform2d; the new transformation matrix after applying this transform
      */
     public Transform2d rotation(final double angle)
     {
         if (angle == 0.0)
         {
             return this;
         }
         double c = Math.cos(angle);
         double s = Math.sin(angle);
         this.mat = mulMatMat(this.mat, new double[] {c, -s, 0, s, c, 0, 0, 0, 1});
         return this;
     }
 
     /**
      * The 2d shear leaves the xy-coordinate plane for z=0 untouched. An x-coordinate with a value of 1 is translated by sx, and
      * an x-coordinate with another value is translated by x*sx. Similarly, a y-coordinate with a value of 1 is translated by xy
      * and a y-coordinate with another value is translated by y*sy. Note that to carry out multiple operations, the steps have
      * to be built in the OPPOSITE order since matrix multiplication operates from RIGHT to LEFT.
      * @param sx double; the shear factor in the x-direction
      * @param sy double; the shear factor in the y-direction
      * @return Transform2d; the new transformation matrix after applying this transform
      */
     public Transform2d shear(final double sx, final double sy)
     {
         if (sx == 0.0 && sy == 0.0)
         {
             return this;
         }
         this.mat = mulMatMat(this.mat, new double[] {1, sx, 0, sy, 1, 0, 0, 0, 1});
         return this;
     }
 
     /**
      * The reflection of the x-coordinate, by mirroring it in the yz-plane (the plane with x=0). Note that to carry out multiple
      * operations, the steps have to be built in the OPPOSITE order since matrix multiplication operates from RIGHT to LEFT.
      * @return Transform2d; the new transformation matrix after applying this transform
      */
     public Transform2d reflectX()
     {
         this.mat = mulMatMat(this.mat, new double[] {-1, 0, 0, 0, 1, 0, 0, 0, 1});
         return this;
     }
 
     /**
      * The reflection of the y-coordinate, by mirroring it in the xz-plane (the plane with y=0). Note that to carry out multiple
      * operations, the steps have to be built in the OPPOSITE order since matrix multiplication operates from RIGHT to LEFT.
      * @return Transform2d; the new transformation matrix after applying this transform
      */
     public Transform2d reflectY()
     {
         this.mat = mulMatMat(this.mat, new double[] {1, 0, 0, 0, -1, 0, 0, 0, 1});
         return this;
     }
 
     /**
      * Apply the stored transform on the xy-vector and return the transformed vector. For speed reasons, no checks on correct
      * size of the vector is done.
      * @param xy double[]; double[2] the provided vector
      * @return double[2]; the transformed vector
      */
     public double[] transform(final double[] xy)
     {
         return mulMatVec2(this.mat, xy);
     }
 
     /**
      * Apply the stored transform on the provided point and return a point with the transformed coordinate.
      * @param point Point2d; the point to be transformed
      * @return Point2d; a point with the transformed coordinates
      */
     public Point2d#Point2d">Point2d transform(final Point2d point)
     {
         return new Point2d(mulMatVec2(this.mat, new double[] {point.x, point.y}));
     }
 
     /**
      * Apply the stored transform on the provided point and return a point with the transformed coordinate.
      * @param pointIterator Iterator&lt;Point2d&gt;; generates the points to be transformed
      * @return Iterator&lt;Point2d&gt;; an iterator that will generator all transformed points
      */
     public Iterator<Point2d> transform(final Iterator<Point2d> pointIterator)
     {
         return new Iterator<Point2d>()
         {
 
             @Override
             public boolean hasNext()
             {
                 return pointIterator.hasNext();
             }
 
             @Override
             public Point2d next()
             {
                 return transform(pointIterator.next());
             }
         };
     }
 
     /**
      * Apply the stored transform on the provided Bounds2d and return a new Bounds2d with the bounds of the transformed
      * coordinates. All 4 corner points have to be transformed, since we do not know which of the 4 points will result in the
      * lowest and highest x and y coordinates.
      * @param boundingRectangle Bounds2d; the bounds to be transformed
      * @return Bounds2d; the new bounds based on the transformed coordinates
      */
     public Bounds2dl#Bounds2d">Bounds2d transform(final Bounds2d boundingRectangle)
     {
         return new Bounds2d(transform(boundingRectangle.getPoints()));
     }
 
     /** {@inheritDoc} */
     @Override
     public int hashCode()
     {
         final int prime = 31;
         int result = 1;
         result = prime * result + Arrays.hashCode(this.mat);
         return result;
     }
 
     /** {@inheritDoc} */
     @Override
     @SuppressWarnings("checkstyle:needbraces")
     public boolean equals(final Object obj)
     {
         if (this == obj)
             return true;
         if (obj == null)
             return false;
         if (getClass() != obj.getClass())
             return false;
         Transform2d./../org/djutils/draw/Transform2d.html#Transform2d">Transform2d other = (Transform2d) obj;
         if (!Arrays.equals(this.mat, other.mat))
             return false;
         return true;
     }
 
     /** {@inheritDoc} */
     @Override
     public String toString()
     {
         return "Transform2d [mat=" + Arrays.toString(this.mat) + "]";
     }
 
 }