Class AffineTransformation

  • All Implemented Interfaces:
    java.lang.Cloneable, CoordinateSequenceFilter

    public class AffineTransformation
    extends java.lang.Object
    implements java.lang.Cloneable, CoordinateSequenceFilter
    Represents an affine transformation on the 2D Cartesian plane. It can be used to transform a Coordinate or Geometry. An affine transformation is a mapping of the 2D plane into itself via a series of transformations of the following basic types:
    • reflection (through a line)
    • rotation (around the origin)
    • scaling (relative to the origin)
    • shearing (in both the X and Y directions)
    • translation
    In general, affine transformations preserve straightness and parallel lines, but do not preserve distance or shape.

    An affine transformation can be represented by a 3x3 matrix in the following form:

     T = | m00 m01 m02 |
         | m10 m11 m12 |
         |  0   0   1  |
     
    A coordinate P = (x, y) can be transformed to a new coordinate P' = (x', y') by representing it as a 3x1 matrix and using matrix multiplication to compute:
     | x' |  = T x | x |
     | y' |        | y |
     | 1  |        | 1 |
     

    Transformation Composition

    Affine transformations can be composed using the compose(org.locationtech.jts.geom.util.AffineTransformation) method. Composition is computed via multiplication of the transformation matrices, and is defined as:
    A.compose(B) = TB x TA
    This produces a transformation whose effect is that of A followed by B. The methods reflect(double, double, double, double), rotate(double), scale(double, double), shear(double, double), and translate(double, double) have the effect of composing a transformation of that type with the transformation they are invoked on.

    The composition of transformations is in general not commutative.

    Transformation Inversion

    Affine transformations may be invertible or non-invertible. If a transformation is invertible, then there exists an inverse transformation which when composed produces the identity transformation. The getInverse() method computes the inverse of a transformation, if one exists.
    Author:
    Martin Davis
    • Constructor Detail

      • AffineTransformation

        public AffineTransformation()
        Constructs a new identity transformation
      • AffineTransformation

        public AffineTransformation​(double[] matrix)
        Constructs a new transformation whose matrix has the specified values.
        Parameters:
        matrix - an array containing the 6 values { m00, m01, m02, m10, m11, m12 }
        Throws:
        java.lang.NullPointerException - if matrix is null
        java.lang.ArrayIndexOutOfBoundsException - if matrix is too small
      • AffineTransformation

        public AffineTransformation​(double m00,
                                    double m01,
                                    double m02,
                                    double m10,
                                    double m11,
                                    double m12)
        Constructs a new transformation whose matrix has the specified values.
        Parameters:
        m00 - the entry for the [0, 0] element in the transformation matrix
        m01 - the entry for the [0, 1] element in the transformation matrix
        m02 - the entry for the [0, 2] element in the transformation matrix
        m10 - the entry for the [1, 0] element in the transformation matrix
        m11 - the entry for the [1, 1] element in the transformation matrix
        m12 - the entry for the [1, 2] element in the transformation matrix
      • AffineTransformation

        public AffineTransformation​(AffineTransformation trans)
        Constructs a transformation which is a copy of the given one.
        Parameters:
        trans - the transformation to copy
      • AffineTransformation

        public AffineTransformation​(Coordinate src0,
                                    Coordinate src1,
                                    Coordinate src2,
                                    Coordinate dest0,
                                    Coordinate dest1,
                                    Coordinate dest2)
        Constructs a transformation which maps the given source points into the given destination points.
        Parameters:
        src0 - source point 0
        src1 - source point 1
        src2 - source point 2
        dest0 - the mapped point for source point 0
        dest1 - the mapped point for source point 1
        dest2 - the mapped point for source point 2
    • Method Detail

      • reflectionInstance

        public static AffineTransformation reflectionInstance​(double x0,
                                                              double y0,
                                                              double x1,
                                                              double y1)
        Creates a transformation for a reflection about the line (x0,y0) - (x1,y1).
        Parameters:
        x0 - the x-ordinate of a point on the reflection line
        y0 - the y-ordinate of a point on the reflection line
        x1 - the x-ordinate of a another point on the reflection line
        y1 - the y-ordinate of a another point on the reflection line
        Returns:
        a transformation for the reflection
      • reflectionInstance

        public static AffineTransformation reflectionInstance​(double x,
                                                              double y)
        Creates a transformation for a reflection about the line (0,0) - (x,y).
        Parameters:
        x - the x-ordinate of a point on the reflection line
        y - the y-ordinate of a point on the reflection line
        Returns:
        a transformation for the reflection
      • rotationInstance

        public static AffineTransformation rotationInstance​(double theta)
        Creates a transformation for a rotation about the origin by an angle theta. Positive angles correspond to a rotation in the counter-clockwise direction.
        Parameters:
        theta - the rotation angle, in radians
        Returns:
        a transformation for the rotation
      • rotationInstance

        public static AffineTransformation rotationInstance​(double sinTheta,
                                                            double cosTheta)
        Creates a transformation for a rotation by an angle theta, specified by the sine and cosine of the angle. This allows providing exact values for sin(theta) and cos(theta) for the common case of rotations of multiples of quarter-circles.
        Parameters:
        sinTheta - the sine of the rotation angle
        cosTheta - the cosine of the rotation angle
        Returns:
        a transformation for the rotation
      • rotationInstance

        public static AffineTransformation rotationInstance​(double theta,
                                                            double x,
                                                            double y)
        Creates a transformation for a rotation about the point (x,y) by an angle theta. Positive angles correspond to a rotation in the counter-clockwise direction.
        Parameters:
        theta - the rotation angle, in radians
        x - the x-ordinate of the rotation point
        y - the y-ordinate of the rotation point
        Returns:
        a transformation for the rotation
      • rotationInstance

        public static AffineTransformation rotationInstance​(double sinTheta,
                                                            double cosTheta,
                                                            double x,
                                                            double y)
        Creates a transformation for a rotation about the point (x,y) by an angle theta, specified by the sine and cosine of the angle. This allows providing exact values for sin(theta) and cos(theta) for the common case of rotations of multiples of quarter-circles.
        Parameters:
        sinTheta - the sine of the rotation angle
        cosTheta - the cosine of the rotation angle
        x - the x-ordinate of the rotation point
        y - the y-ordinate of the rotation point
        Returns:
        a transformation for the rotation
      • scaleInstance

        public static AffineTransformation scaleInstance​(double xScale,
                                                         double yScale)
        Creates a transformation for a scaling relative to the origin.
        Parameters:
        xScale - the value to scale by in the x direction
        yScale - the value to scale by in the y direction
        Returns:
        a transformation for the scaling
      • scaleInstance

        public static AffineTransformation scaleInstance​(double xScale,
                                                         double yScale,
                                                         double x,
                                                         double y)
        Creates a transformation for a scaling relative to the point (x,y).
        Parameters:
        xScale - the value to scale by in the x direction
        yScale - the value to scale by in the y direction
        x - the x-ordinate of the point to scale around
        y - the y-ordinate of the point to scale around
        Returns:
        a transformation for the scaling
      • shearInstance

        public static AffineTransformation shearInstance​(double xShear,
                                                         double yShear)
        Creates a transformation for a shear.
        Parameters:
        xShear - the value to shear by in the x direction
        yShear - the value to shear by in the y direction
        Returns:
        a transformation for the shear
      • translationInstance

        public static AffineTransformation translationInstance​(double x,
                                                               double y)
        Creates a transformation for a translation.
        Parameters:
        x - the value to translate by in the x direction
        y - the value to translate by in the y direction
        Returns:
        a transformation for the translation
      • setToIdentity

        public AffineTransformation setToIdentity()
        Sets this transformation to be the identity transformation. The identity transformation has the matrix:
         | 1 0 0 |
         | 0 1 0 |
         | 0 0 1 |
         
        Returns:
        this transformation, with an updated matrix
      • setTransformation

        public AffineTransformation setTransformation​(double m00,
                                                      double m01,
                                                      double m02,
                                                      double m10,
                                                      double m11,
                                                      double m12)
        Sets this transformation's matrix to have the given values.
        Parameters:
        m00 - the entry for the [0, 0] element in the transformation matrix
        m01 - the entry for the [0, 1] element in the transformation matrix
        m02 - the entry for the [0, 2] element in the transformation matrix
        m10 - the entry for the [1, 0] element in the transformation matrix
        m11 - the entry for the [1, 1] element in the transformation matrix
        m12 - the entry for the [1, 2] element in the transformation matrix
        Returns:
        this transformation, with an updated matrix
      • setTransformation

        public AffineTransformation setTransformation​(AffineTransformation trans)
        Sets this transformation to be a copy of the given one
        Parameters:
        trans - a transformation to copy
        Returns:
        this transformation, with an updated matrix
      • getMatrixEntries

        public double[] getMatrixEntries()
        Gets an array containing the entries of the transformation matrix. Only the 6 non-trivial entries are returned, in the sequence:
         m00, m01, m02, m10, m11, m12
         
        Returns:
        an array of length 6
      • getDeterminant

        public double getDeterminant()
        Computes the determinant of the transformation matrix. The determinant is computed as:
         | m00 m01 m02 |
         | m10 m11 m12 | = m00 * m11 - m01 * m10
         |  0   0   1  |
         
        If the determinant is zero, the transform is singular (not invertible), and operations which attempt to compute an inverse will throw a NoninvertibleTransformException.
        Returns:
        the determinant of the transformation
        See Also:
        getInverse()
      • getInverse

        public AffineTransformation getInverse()
                                        throws NoninvertibleTransformationException
        Computes the inverse of this transformation, if one exists. The inverse is the transformation which when composed with this one produces the identity transformation. A transformation has an inverse if and only if it is not singular (i.e. its determinant is non-zero). Geometrically, an transformation is non-invertible if it maps the plane to a line or a point. If no inverse exists this method will throw a NoninvertibleTransformationException.

        The matrix of the inverse is equal to the inverse of the matrix for the transformation. It is computed as follows:

          
                         1    
         inverse(A)  =  ---   x  adjoint(A) 
                        det 
        
        
                     =   1       |  m11  -m01   m01*m12-m02*m11  |
                        ---   x  | -m10   m00  -m00*m12+m10*m02  |
                        det      |  0     0     m00*m11-m10*m01  |
        
        
        
                     = |  m11/det  -m01/det   m01*m12-m02*m11/det |
                       | -m10/det   m00/det  -m00*m12+m10*m02/det |
                       |   0           0          1               |
        
         
        Returns:
        a new inverse transformation
        Throws:
        NoninvertibleTransformationException
        See Also:
        getDeterminant()
      • setToReflectionBasic

        public AffineTransformation setToReflectionBasic​(double x0,
                                                         double y0,
                                                         double x1,
                                                         double y1)
        Explicitly computes the math for a reflection. May not work.
        Parameters:
        x0 - the X ordinate of one point on the reflection line
        y0 - the Y ordinate of one point on the reflection line
        x1 - the X ordinate of another point on the reflection line
        y1 - the Y ordinate of another point on the reflection line
        Returns:
        this transformation, with an updated matrix
      • setToReflection

        public AffineTransformation setToReflection​(double x0,
                                                    double y0,
                                                    double x1,
                                                    double y1)
        Sets this transformation to be a reflection about the line defined by a line (x0,y0) - (x1,y1).
        Parameters:
        x0 - the X ordinate of one point on the reflection line
        y0 - the Y ordinate of one point on the reflection line
        x1 - the X ordinate of another point on the reflection line
        y1 - the Y ordinate of another point on the reflection line
        Returns:
        this transformation, with an updated matrix
      • setToReflection

        public AffineTransformation setToReflection​(double x,
                                                    double y)
        Sets this transformation to be a reflection about the line defined by vector (x,y). The transformation for a reflection is computed by:
        d = sqrt(x2 + y2)
        sin = y / d;
        cos = x / d;

        Tref = Trot(sin, cos) x Tscale(1, -1) x Trot(-sin, cos)
        Parameters:
        x - the x-component of the reflection line vector
        y - the y-component of the reflection line vector
        Returns:
        this transformation, with an updated matrix
      • setToRotation

        public AffineTransformation setToRotation​(double theta)
        Sets this transformation to be a rotation around the origin. A positive rotation angle corresponds to a counter-clockwise rotation. The transformation matrix for a rotation by an angle theta has the value:
          
         |  cos(theta)  -sin(theta)   0 |
         |  sin(theta)   cos(theta)   0 |
         |           0            0   1 |
         
        Parameters:
        theta - the rotation angle, in radians
        Returns:
        this transformation, with an updated matrix
      • setToRotation

        public AffineTransformation setToRotation​(double sinTheta,
                                                  double cosTheta)
        Sets this transformation to be a rotation around the origin by specifying the sin and cos of the rotation angle directly. The transformation matrix for the rotation has the value:
          
         |  cosTheta  -sinTheta   0 |
         |  sinTheta   cosTheta   0 |
         |         0          0   1 |
         
        Parameters:
        sinTheta - the sine of the rotation angle
        cosTheta - the cosine of the rotation angle
        Returns:
        this transformation, with an updated matrix
      • setToRotation

        public AffineTransformation setToRotation​(double theta,
                                                  double x,
                                                  double y)
        Sets this transformation to be a rotation around a given point (x,y). A positive rotation angle corresponds to a counter-clockwise rotation. The transformation matrix for a rotation by an angle theta has the value:
          
         |  cosTheta  -sinTheta   x-x*cos+y*sin |
         |  sinTheta   cosTheta   y-x*sin-y*cos |
         |           0            0   1 |
         
        Parameters:
        theta - the rotation angle, in radians
        x - the x-ordinate of the rotation point
        y - the y-ordinate of the rotation point
        Returns:
        this transformation, with an updated matrix
      • setToRotation

        public AffineTransformation setToRotation​(double sinTheta,
                                                  double cosTheta,
                                                  double x,
                                                  double y)
        Sets this transformation to be a rotation around a given point (x,y) by specifying the sin and cos of the rotation angle directly. The transformation matrix for the rotation has the value:
          
         |  cosTheta  -sinTheta   x-x*cos+y*sin |
         |  sinTheta   cosTheta   y-x*sin-y*cos |
         |         0          0         1       |
         
        Parameters:
        sinTheta - the sine of the rotation angle
        cosTheta - the cosine of the rotation angle
        x - the x-ordinate of the rotation point
        y - the y-ordinate of the rotation point
        Returns:
        this transformation, with an updated matrix
      • setToScale

        public AffineTransformation setToScale​(double xScale,
                                               double yScale)
        Sets this transformation to be a scaling. The transformation matrix for a scale has the value:
          
         |  xScale      0  dx |
         |  0      yScale  dy |
         |  0           0   1 |
         
        Parameters:
        xScale - the amount to scale x-ordinates by
        yScale - the amount to scale y-ordinates by
        Returns:
        this transformation, with an updated matrix
      • setToShear

        public AffineTransformation setToShear​(double xShear,
                                               double yShear)
        Sets this transformation to be a shear. The transformation matrix for a shear has the value:
          
         |  1      xShear  0 |
         |  yShear      1  0 |
         |  0           0  1 |
         
        Note that a shear of (1, 1) is not equal to shear(1, 0) composed with shear(0, 1). Instead, shear(1, 1) corresponds to a mapping onto the line x = y.
        Parameters:
        xShear - the x component to shear by
        yShear - the y component to shear by
        Returns:
        this transformation, with an updated matrix
      • setToTranslation

        public AffineTransformation setToTranslation​(double dx,
                                                     double dy)
        Sets this transformation to be a translation. For a translation by the vector (x, y) the transformation matrix has the value:
          
         |  1  0  dx |
         |  1  0  dy |
         |  0  0   1 |
         
        Parameters:
        dx - the x component to translate by
        dy - the y component to translate by
        Returns:
        this transformation, with an updated matrix
      • reflect

        public AffineTransformation reflect​(double x0,
                                            double y0,
                                            double x1,
                                            double y1)
        Updates the value of this transformation to that of a reflection transformation composed with the current value.
        Parameters:
        x0 - the x-ordinate of a point on the line to reflect around
        y0 - the y-ordinate of a point on the line to reflect around
        x1 - the x-ordinate of a point on the line to reflect around
        y1 - the y-ordinate of a point on the line to reflect around
        Returns:
        this transformation, with an updated matrix
      • reflect

        public AffineTransformation reflect​(double x,
                                            double y)
        Updates the value of this transformation to that of a reflection transformation composed with the current value.
        Parameters:
        x - the x-ordinate of the line to reflect around
        y - the y-ordinate of the line to reflect around
        Returns:
        this transformation, with an updated matrix
      • rotate

        public AffineTransformation rotate​(double theta)
        Updates the value of this transformation to that of a rotation transformation composed with the current value. Positive angles correspond to a rotation in the counter-clockwise direction.
        Parameters:
        theta - the angle to rotate by, in radians
        Returns:
        this transformation, with an updated matrix
      • rotate

        public AffineTransformation rotate​(double sinTheta,
                                           double cosTheta)
        Updates the value of this transformation to that of a rotation around the origin composed with the current value, with the sin and cos of the rotation angle specified directly.
        Parameters:
        sinTheta - the sine of the angle to rotate by
        cosTheta - the cosine of the angle to rotate by
        Returns:
        this transformation, with an updated matrix
      • rotate

        public AffineTransformation rotate​(double theta,
                                           double x,
                                           double y)
        Updates the value of this transformation to that of a rotation around a given point composed with the current value. Positive angles correspond to a rotation in the counter-clockwise direction.
        Parameters:
        theta - the angle to rotate by, in radians
        x - the x-ordinate of the rotation point
        y - the y-ordinate of the rotation point
        Returns:
        this transformation, with an updated matrix
      • rotate

        public AffineTransformation rotate​(double sinTheta,
                                           double cosTheta,
                                           double x,
                                           double y)
        Updates the value of this transformation to that of a rotation around a given point composed with the current value, with the sin and cos of the rotation angle specified directly.
        Parameters:
        sinTheta - the sine of the angle to rotate by
        cosTheta - the cosine of the angle to rotate by
        x - the x-ordinate of the rotation point
        y - the y-ordinate of the rotation point
        Returns:
        this transformation, with an updated matrix
      • scale

        public AffineTransformation scale​(double xScale,
                                          double yScale)
        Updates the value of this transformation to that of a scale transformation composed with the current value.
        Parameters:
        xScale - the value to scale by in the x direction
        yScale - the value to scale by in the y direction
        Returns:
        this transformation, with an updated matrix
      • shear

        public AffineTransformation shear​(double xShear,
                                          double yShear)
        Updates the value of this transformation to that of a shear transformation composed with the current value.
        Parameters:
        xShear - the value to shear by in the x direction
        yShear - the value to shear by in the y direction
        Returns:
        this transformation, with an updated matrix
      • translate

        public AffineTransformation translate​(double x,
                                              double y)
        Updates the value of this transformation to that of a translation transformation composed with the current value.
        Parameters:
        x - the value to translate by in the x direction
        y - the value to translate by in the y direction
        Returns:
        this transformation, with an updated matrix
      • compose

        public AffineTransformation compose​(AffineTransformation trans)
        Updates this transformation to be the composition of this transformation with the given AffineTransformation. This produces a transformation whose effect is equal to applying this transformation followed by the argument transformation. Mathematically,
        A.compose(B) = TB x TA
        Parameters:
        trans - an affine transformation
        Returns:
        this transformation, with an updated matrix
      • composeBefore

        public AffineTransformation composeBefore​(AffineTransformation trans)
        Updates this transformation to be the composition of a given AffineTransformation with this transformation. This produces a transformation whose effect is equal to applying the argument transformation followed by this transformation. Mathematically,
        A.composeBefore(B) = TA x TB
        Parameters:
        trans - an affine transformation
        Returns:
        this transformation, with an updated matrix
      • transform

        public Coordinate transform​(Coordinate src,
                                    Coordinate dest)
        Applies this transformation to the src coordinate and places the results in the dest coordinate (which may be the same as the source).
        Parameters:
        src - the coordinate to transform
        dest - the coordinate to accept the results
        Returns:
        the dest coordinate
      • transform

        public Geometry transform​(Geometry g)
        Creates a new Geometry which is the result of this transformation applied to the input Geometry.
        Parameters:
        g - a Geometry
        Returns:
        a transformed Geometry
      • transform

        public void transform​(CoordinateSequence seq,
                              int i)
        Applies this transformation to the i'th coordinate in the given CoordinateSequence.
        Parameters:
        seq - a CoordinateSequence
        i - the index of the coordinate to transform
      • filter

        public void filter​(CoordinateSequence seq,
                           int i)
        Transforms the i'th coordinate in the input sequence
        Specified by:
        filter in interface CoordinateSequenceFilter
        Parameters:
        seq - a CoordinateSequence
        i - the index of the coordinate to transform
      • isGeometryChanged

        public boolean isGeometryChanged()
        Description copied from interface: CoordinateSequenceFilter
        Reports whether the execution of this filter has modified the coordinates of the geometry. If so, Geometry.geometryChanged() will be executed after this filter has finished being executed.

        Most filters can simply return a constant value reflecting whether they are able to change the coordinates.

        Specified by:
        isGeometryChanged in interface CoordinateSequenceFilter
        Returns:
        true if this filter has changed the coordinates of the geometry
      • isDone

        public boolean isDone()
        Reports that this filter should continue to be executed until all coordinates have been transformed.
        Specified by:
        isDone in interface CoordinateSequenceFilter
        Returns:
        false
      • isIdentity

        public boolean isIdentity()
        Tests if this transformation is the identity transformation.
        Returns:
        true if this is the identity transformation
      • equals

        public boolean equals​(java.lang.Object obj)
        Tests if an object is an AffineTransformation and has the same matrix as this transformation.
        Overrides:
        equals in class java.lang.Object
        Parameters:
        obj - an object to test
        Returns:
        true if the given object is equal to this object
      • hashCode

        public int hashCode()
        Overrides:
        hashCode in class java.lang.Object
      • toString

        public java.lang.String toString()
        Gets a text representation of this transformation. The string is of the form:
         AffineTransformation[[m00, m01, m02], [m10, m11, m12]]
         
        Overrides:
        toString in class java.lang.Object
        Returns:
        a string representing this transformation
      • clone

        public java.lang.Object clone()
        Clones this transformation
        Returns:
        a copy of this transformation