Class Transformation2D


  • public final class Transformation2D
    extends java.lang.Object
    The affine transformation class for 2D. Vector is a row:
    |m11 m12 0|
    | x y 1| * |m21 m22 0| = |m11 * x + m21 * y + m31 m12 * x + m22 * y + m32 1|
    |m31 m32 1|
    Then elements of the Transformation2D are as follows:
    |xx yx 0|
    | x y 1| * |xy yy 0| = |xx * x + xy * y + xd yx * x + yy * y + yd 1|
    |xd yd 1|
    Matrices are used for transformations of the vectors as rows (case 2). That means the math expressions on the Geometry matrix operations should be writen like this:
    v' = v * M1 * M2 * M3 = ( (v * M1) * M2 ) * M3, where v is a vector, Mn are the matrices.
    This is equivalent to the following line of code:
    ResultVector = (M1.mul(M2).mul(M3)).transform(Vector)
    • Field Summary

      Fields 
      Modifier and Type Field Description
      double xd
      X translation component of the transformation.
      double xx
      Matrix coefficient XX of the transformation.
      double xy
      Matrix coefficient XY of the transformation.
      double yd
      Y translation component of the transformation.
      double yx
      Matrix coefficient YX of the transformation.
      double yy
      Matrix coefficient YY of the transformation.
    • Constructor Summary

      Constructors 
      Constructor Description
      Transformation2D()
      Creates a 2D affine transformation with identity transformation.
      Transformation2D​(double scale)
      Creates a 2D affine transformation with a specified scale.
    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      Transformation2D copy()
      Returns a copy of the Transformation2D object.
      boolean equals​(java.lang.Object other)
      Returns True when all members of this transformation are equal to the corresponding members of the other.
      long estimateMemorySize()  
      void extractScaleTransform​(Transformation2D scale, Transformation2D rotateNshearNshift)
      Extracts scaling part of the transformation.
      void flipX​(double x0, double x1)
      Flips the transformation around the X axis.
      void flipY​(double y0, double y1)
      Flips the transformation around the Y axis.
      void getCoefficients​(double[] coefs)
      Writes the matrix coefficients in the order XX, XY, XD, YX, YY, YD into the given array.
      int hashCode()
      Returns the hash code for the 2D transformation.
      (package private) void initializeFromCurveParameters​(Point2D Position, Point2D Tangent, double Offset)
      Initializes transformation from Position, Tangent vector and offset value.
      (package private) void initializeFromRect​(Envelope2D src, Envelope2D dest)
      Initialize transformation from two rectangles.
      (package private) void initializeFromRectIsotropic​(Envelope2D src, Envelope2D dest)
      Initializes an orhtonormal transformation from the Src and Dest rectangles.
      void inverse()
      Inverses the matrix.
      void inverse​(Transformation2D inverse)
      Produces inverse matrix for this matrix and puts result into the inverse parameter.
      boolean isDegenerate​(double tol)
      Returns TRUE if this matrix is degenerated (does not have an inverse) within the given tolerance.
      boolean isIdentity()
      Returns TRUE if this matrix is the identity matrix.
      boolean isIdentity​(double tol)
      Returns TRUE if this matrix is an identity matrix within the given tolerance.
      boolean isOrthonormal​(double tol)
      Returns TRUE if this is an orthonormal transformation with the given tolerance.
      boolean isReflective()
      Returns TRUE for reflective transformations.
      boolean isScaleAndShift​(double tol)
      Returns TRUE, if this transformation does not have rotation and shear within the given tolerance.
      boolean isShift()
      Returns TRUE if this transformation is a shift transformation.
      boolean isShift​(double tol)
      Returns TRUE if this transformation is a shift transformation within the given tolerance.
      boolean isUniform​(double eps)
      Returns TRUE if this transformation is a uniform transformation.
      void mulLeft​(Transformation2D left)
      Multiplies this matrix on the left with the "left" matrix.
      void multiply​(Transformation2D right)
      Multiplies this matrix on the right with the "right" matrix.
      static void multiply​(Transformation2D a, Transformation2D b, Transformation2D result)
      Performs multiplication of matrices a and b and places the result into this matrix.
      void rotate​(double angle_in_Radians)
      Rotates the transformation.
      void rotate​(double cos, double sin)
      Rotates the transformation.
      void rotate​(double cos, double sin, Point2D rotationCenter)
      Rotates the transformation aroung a center point.
      void scale​(double x, double y)
      Scales the transformation.
      void setFlipX​(double x0, double x1)
      Sets the transformation to be a flip around the X axis.
      void setFlipY​(double y0, double y1)
      Sets the transformation to be a flip around the Y axis.
      void setIdentity()
      Sets this matrix to be the identity matrix.
      void setRotate​(double angle_in_Radians)
      Sets this transformation to be a rotation around point (0, 0).
      void setRotate​(double cosA, double sinA)
      Sets rotation for this transformation.
      (package private) void setRotate​(double cosA, double sinA, Point2D rotationCenter)
      Sets this transformation to be a rotation around point rotationCenter.
      (package private) void setRotate​(double angle_in_Radians, Point2D rotationCenter)
      Sets this transformation to be a rotation around point rotationCenter.
      void setScale​(double _scale)
      Set transformation to be a uniform scale.
      void setScale​(double x, double y)
      Set this transformation to be a scale.
      void setShear​(double proportionX, double proportionY)
      Set transformation to a shear.
      void setShift​(double x, double y)
      Set this transformation to be a shift.
      (package private) Transformation2D setSwapCoordinates()
      Produces a transformation that swaps x and y coordinate values.
      void setZero()
      Initializes a zero transformation.
      void shear​(double proportionX, double proportionY)
      Shears the transformation.
      void shift​(double x, double y)
      Shifts the transformation.
      double transform​(double tolerance)
      Transforms a tolerance value.
      void transform​(double[] pointsXYInterleaved, int start, int count)
      Transforms an array of points stored in an array of doubles as interleaved XY coordinates.
      (package private) void transform​(Envelope2D env)
      Transforms envelope
      void transform​(Point[] pointsIn, int count, Point[] pointsOut)
      Transforms an array of points.
      (package private) void transform​(Point2D[] points, int start, int count)  
      (package private) void transform​(Point2D[] pointsIn, Point2D[] pointsOut)  
      (package private) void transform​(Point2D psrc, Point2D pdst)  
      (package private) Point2D transformSize​(Point2D SizeSrc)
      Transforms size.
      (package private) Point2D transformWithoutShift​(Point2D srcPoint)  
      (package private) void transformWithoutShift​(Point2D[] pointsIn, int from, int count, Point2D[] pointsOut)  
      • Methods inherited from class java.lang.Object

        clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait
    • Field Detail

      • xx

        public double xx
        Matrix coefficient XX of the transformation.
      • xy

        public double xy
        Matrix coefficient XY of the transformation.
      • xd

        public double xd
        X translation component of the transformation.
      • yx

        public double yx
        Matrix coefficient YX of the transformation.
      • yy

        public double yy
        Matrix coefficient YY of the transformation.
      • yd

        public double yd
        Y translation component of the transformation.
    • Constructor Detail

      • Transformation2D

        public Transformation2D()
        Creates a 2D affine transformation with identity transformation.
      • Transformation2D

        public Transformation2D​(double scale)
        Creates a 2D affine transformation with a specified scale.
        Parameters:
        scale - The scale to use for the transformation.
    • Method Detail

      • setZero

        public void setZero()
        Initializes a zero transformation. Transforms any coordinate to (0, 0).
      • equals

        public boolean equals​(java.lang.Object other)
        Returns True when all members of this transformation are equal to the corresponding members of the other.
        Overrides:
        equals in class java.lang.Object
      • hashCode

        public int hashCode()
        Returns the hash code for the 2D transformation.
        Overrides:
        hashCode in class java.lang.Object
      • transform

        void transform​(Point2D[] points,
                       int start,
                       int count)
      • transform

        public void transform​(Point[] pointsIn,
                              int count,
                              Point[] pointsOut)
        Transforms an array of points.
        Parameters:
        pointsIn - The points to be transformed.
        count - The number of points to transform.
        pointsOut - The transformed points are returned using this array. It should have the same or greater size as the input array.
      • transform

        public void transform​(double[] pointsXYInterleaved,
                              int start,
                              int count)
        Transforms an array of points stored in an array of doubles as interleaved XY coordinates.
        Parameters:
        pointsXYInterleaved - The array of points with interleaved X, Y values to be transformed.
        start - The start point index to transform from (the actual element index is 2 * start).
        count - The number of points to transform (the actual element count is 2 * count).
      • multiply

        public void multiply​(Transformation2D right)
        Multiplies this matrix on the right with the "right" matrix. Stores the result into this matrix and returns a reference to it.
        Equivalent to this *= right.
        Parameters:
        right - The matrix to be multiplied with.
      • mulLeft

        public void mulLeft​(Transformation2D left)
        Multiplies this matrix on the left with the "left" matrix. Stores the result into this matrix and returns a reference to it.
        Equivalent to this = left * this.
        Parameters:
        left - The matrix to be multiplied with.
      • multiply

        public static void multiply​(Transformation2D a,
                                    Transformation2D b,
                                    Transformation2D result)
        Performs multiplication of matrices a and b and places the result into this matrix. The a, b, and result could point to same objects.
        Equivalent to result = a * b.
        Parameters:
        a - The 2D transformation to be multiplied.
        b - The 2D transformation to be multiplied.
        result - The 2D transformation created by multiplication of matrices.
      • copy

        public Transformation2D copy()
        Returns a copy of the Transformation2D object.
        Returns:
        A copy of this object.
      • getCoefficients

        public void getCoefficients​(double[] coefs)
        Writes the matrix coefficients in the order XX, XY, XD, YX, YY, YD into the given array.
        Parameters:
        coefs - The array into which the coefficients are returned. Should be of size 6 elements.
      • transform

        void transform​(Envelope2D env)
        Transforms envelope
        Parameters:
        env - The envelope that is to be transformed
      • transform

        void transform​(Point2D[] pointsIn,
                       Point2D[] pointsOut)
      • initializeFromRect

        void initializeFromRect​(Envelope2D src,
                                Envelope2D dest)
        Initialize transformation from two rectangles.
      • initializeFromRectIsotropic

        void initializeFromRectIsotropic​(Envelope2D src,
                                         Envelope2D dest)
        Initializes an orhtonormal transformation from the Src and Dest rectangles. The result transformation proportionally fits the Src into the Dest. The center of the Src will be in the center of the Dest.
      • initializeFromCurveParameters

        void initializeFromCurveParameters​(Point2D Position,
                                           Point2D Tangent,
                                           double Offset)
        Initializes transformation from Position, Tangent vector and offset value. Tangent vector must have unity length
      • transformSize

        Point2D transformSize​(Point2D SizeSrc)
        Transforms size. Creates an AABB with width of SizeSrc.x and height of SizeSrc.y. Transforms that AABB and gets a quadrangle in new coordinate system. The result x contains the length of the quadrangle edge, which were parallel to X in the original system, and y contains the length of the edge, that were parallel to the Y axis in the original system.
      • transform

        public double transform​(double tolerance)
        Transforms a tolerance value.
        Parameters:
        tolerance - The tolerance value.
      • transformWithoutShift

        void transformWithoutShift​(Point2D[] pointsIn,
                                   int from,
                                   int count,
                                   Point2D[] pointsOut)
      • transformWithoutShift

        Point2D transformWithoutShift​(Point2D srcPoint)
      • setIdentity

        public void setIdentity()
        Sets this matrix to be the identity matrix.
      • isIdentity

        public boolean isIdentity()
        Returns TRUE if this matrix is the identity matrix.
      • isIdentity

        public boolean isIdentity​(double tol)
        Returns TRUE if this matrix is an identity matrix within the given tolerance.
        Parameters:
        tol - The tolerance value.
      • isReflective

        public boolean isReflective()
        Returns TRUE for reflective transformations. It inverts the sign of vector cross product.
      • isUniform

        public boolean isUniform​(double eps)
        Returns TRUE if this transformation is a uniform transformation. The uniform transformation is a transformation, which transforms a square to a square.
      • isShift

        public boolean isShift()
        Returns TRUE if this transformation is a shift transformation. The shift transformation performs shift only.
      • isShift

        public boolean isShift​(double tol)
        Returns TRUE if this transformation is a shift transformation within the given tolerance.
        Parameters:
        tol - The tolerance value.
      • isOrthonormal

        public boolean isOrthonormal​(double tol)
        Returns TRUE if this is an orthonormal transformation with the given tolerance. The orthonormal: Rotation or rotoinversion and shift (preserves lengths of vectors and angles between vectors).
        Parameters:
        tol - The tolerance value.
      • isDegenerate

        public boolean isDegenerate​(double tol)
        Returns TRUE if this matrix is degenerated (does not have an inverse) within the given tolerance.
        Parameters:
        tol - The tolerance value.
      • isScaleAndShift

        public boolean isScaleAndShift​(double tol)
        Returns TRUE, if this transformation does not have rotation and shear within the given tolerance.
        Parameters:
        tol - The tolerance value.
      • setShift

        public void setShift​(double x,
                             double y)
        Set this transformation to be a shift.
        Parameters:
        x - The X coordinate to shift to.
        y - The Y coordinate to shift to.
      • setScale

        public void setScale​(double x,
                             double y)
        Set this transformation to be a scale.
        Parameters:
        x - The X coordinate to scale to.
        y - The Y coordinate to scale to.
      • setScale

        public void setScale​(double _scale)
        Set transformation to be a uniform scale.
        Parameters:
        _scale - The scale of the transformation.
      • setFlipX

        public void setFlipX​(double x0,
                             double x1)
        Sets the transformation to be a flip around the X axis. Flips the X coordinates so that the x0 becomes x1 and vice verse.
        Parameters:
        x0 - The X coordinate to flip.
        x1 - The X coordinate to flip to.
      • setFlipY

        public void setFlipY​(double y0,
                             double y1)
        Sets the transformation to be a flip around the Y axis. Flips the Y coordinates so that the y0 becomes y1 and vice verse.
        Parameters:
        y0 - The Y coordinate to flip.
        y1 - The Y coordinate to flip to.
      • setShear

        public void setShear​(double proportionX,
                             double proportionY)
        Set transformation to a shear.
        Parameters:
        proportionX - The proportion of shearing in x direction.
        proportionY - The proportion of shearing in y direction.
      • setRotate

        public void setRotate​(double angle_in_Radians)
        Sets this transformation to be a rotation around point (0, 0). When the axis Y is directed up and X is directed to the right, the positive angle corresponds to the anti-clockwise rotation. When the axis Y is directed down and X is directed to the right, the positive angle corresponds to the clockwise rotation.
        Parameters:
        angle_in_Radians - The rotation angle in radian.
      • setSwapCoordinates

        Transformation2D setSwapCoordinates()
        Produces a transformation that swaps x and y coordinate values. xx = 0.0; xy = 1.0; xd = 0; yx = 1.0; yy = 0.0; yd = 0;
      • setRotate

        void setRotate​(double angle_in_Radians,
                       Point2D rotationCenter)
        Sets this transformation to be a rotation around point rotationCenter. When the axis Y is directed up and X is directed to the right, the positive angle corresponds to the anti-clockwise rotation. When the axis Y is directed down and X is directed to the right, the positive angle corresponds to the clockwise rotation.
        Parameters:
        angle_in_Radians - The rotation angle in radian.
        rotationCenter - The center point of the rotation.
      • setRotate

        public void setRotate​(double cosA,
                              double sinA)
        Sets rotation for this transformation. When the axis Y is directed up and X is directed to the right, the positive angle corresponds to the anti-clockwise rotation. When the axis Y is directed down and X is directed to the right, the positive angle corresponds to the clockwise rotation.
        Parameters:
        cosA - The rotation angle.
        sinA - The rotation angle.
      • setRotate

        void setRotate​(double cosA,
                       double sinA,
                       Point2D rotationCenter)
        Sets this transformation to be a rotation around point rotationCenter. When the axis Y is directed up and X is directed to the right, the positive angle corresponds to the anti-clockwise rotation. When the axis Y is directed down and X is directed to the right, the positive angle corresponds to the clockwise rotation.
        Parameters:
        cosA - The cos of the rotation angle.
        sinA - The sin of the rotation angle.
        rotationCenter - The center point of the rotation.
      • shift

        public void shift​(double x,
                          double y)
        Shifts the transformation.
        Parameters:
        x - The shift factor in X direction.
        y - The shift factor in Y direction.
      • scale

        public void scale​(double x,
                          double y)
        Scales the transformation.
        Parameters:
        x - The scale factor in X direction.
        y - The scale factor in Y direction.
      • flipX

        public void flipX​(double x0,
                          double x1)
        Flips the transformation around the X axis.
        Parameters:
        x0 - The X coordinate to flip.
        x1 - The X coordinate to flip to.
      • flipY

        public void flipY​(double y0,
                          double y1)
        Flips the transformation around the Y axis.
        Parameters:
        y0 - The Y coordinate to flip.
        y1 - The Y coordinate to flip to.
      • shear

        public void shear​(double proportionX,
                          double proportionY)
        Shears the transformation.
        Parameters:
        proportionX - The proportion of shearing in x direction.
        proportionY - The proportion of shearing in y direction.
      • rotate

        public void rotate​(double angle_in_Radians)
        Rotates the transformation.
        Parameters:
        angle_in_Radians - The rotation angle in radian.
      • rotate

        public void rotate​(double cos,
                           double sin)
        Rotates the transformation.
        Parameters:
        cos - The cos angle of the rotation.
        sin - The sin angle of the rotation.
      • rotate

        public void rotate​(double cos,
                           double sin,
                           Point2D rotationCenter)
        Rotates the transformation aroung a center point.
        Parameters:
        cos - The cos angle of the rotation.
        sin - sin angle of the rotation.
        rotationCenter - The center point of the rotation.
      • inverse

        public void inverse​(Transformation2D inverse)
        Produces inverse matrix for this matrix and puts result into the inverse parameter.
        Parameters:
        inverse - The result inverse matrix.
      • inverse

        public void inverse()
        Inverses the matrix.
      • extractScaleTransform

        public void extractScaleTransform​(Transformation2D scale,
                                          Transformation2D rotateNshearNshift)
        Extracts scaling part of the transformation. this == scale * rotateNshearNshift.
        Parameters:
        scale - The destination matrix where the scale part is copied.
        rotateNshearNshift - The destination matrix where the part excluding rotation is copied.
      • estimateMemorySize

        public long estimateMemorySize()