Package org.geotools.referencing.operation.transform

Class ProjectiveTransform

  • All Implemented Interfaces:
    Serializable, MathTransform, LinearTransform
    Direct Known Subclasses:
    GeocentricTranslation
    public class ProjectiveTransform
extends AbstractMathTransform
implements LinearTransform, Serializable
    A usually affine, or otherwise a projective transform. A projective transform is capable of mapping an arbitrary quadrilateral into another arbitrary quadrilateral, while preserving the straightness of lines. In the special case where the transform is affine, the parallelism of lines in the source is preserved in the output.

    Such a coordinate transformation can be represented by a square matrix of an arbitrary size. Point coordinates must have a dimension equals to Matrix.getNumCol()-1. For example, for square matrix of size 4×4, coordinate points are three-dimensional. The transformed points (x',y',z') are computed as below (note that this computation is similar to PerspectiveTransform in Java Advanced Imaging): 

     [ u ]     [ m00  m01  m02  m03 ] [ x ]
 [ v ]  =  [ m10  m11  m12  m13 ] [ y ]
 [ w ]     [ m20  m21  m22  m23 ] [ z ]
 [ t ]     [ m30  m31  m32  m33 ] [ 1 ]

   x' = u/t
   y' = v/t
   y' = w/t
    In the special case of an affine transform, the last row contains only zero values except in the last column, which contains 1.
    Since:
    2.0
    Author:
    Martin Desruisseaux (IRD)
    See Also:
    PerspectiveTransform, AffineTransform, Affine transformation on MathWorld, Serialized Form

    • Constructor Detail

      • ProjectiveTransform

        protected ProjectiveTransform​(Matrix matrix)
        Constructs a transform from the specified matrix. The matrix should be affine, but it will not be verified.
        Parameters:
        matrix - The matrix.

    • Method Detail

      • create

        public static LinearTransform create​(Matrix matrix)
        Creates a transform for the specified matrix. The matrix should be affine, but it is not be verified.
        Parameters:
        matrix - The affine transform as a matrix.
        Returns:
        The transform for the given matrix.

      • create

        public static LinearTransform create​(AffineTransform matrix)
        Creates a transform for the specified matrix as a Java2D object. This method is provided for interoperability with Java2D.
        Parameters:
        matrix - The affine transform as a matrix.
        Returns:
        The transform for the given matrix.

      • createScale

        public static LinearTransform createScale​(int dimension,
                                          double scale)
        Creates a transform that apply a uniform scale along all axis.
        Parameters:
        dimension - The input and output dimensions.
        scale - The scale factor.
        Returns:
        The scale transform.
        Since:
        2.3

      • createTranslation

        public static LinearTransform createTranslation​(int dimension,
                                                double offset)
        Creates a transform that apply the same translation along all axis.
        Parameters:
        dimension - The input and output dimensions.
        offset - The translation.
        Returns:
        The offset transform.
        Since:
        2.3

      • createSelectMatrix

        public static Matrix createSelectMatrix​(int sourceDim,
                                        int[] toKeep)
                                 throws IndexOutOfBoundsException
        Creates a matrix that keep only a subset of the ordinate values. The dimension of source coordinates is sourceDim and the dimension of target coordinates is toKeep.length.
        Parameters:
        sourceDim - the dimension of source coordinates.
        toKeep - the indices of ordinate values to keep.
        Returns:
        The matrix to give to the create(Matrix) method in order to create the transform.
        Throws:
        IndexOutOfBoundsException - if a value of toKeep is lower than 0 or not smaller than sourceDim.

      • getParameterValues

        public ParameterValueGroup getParameterValues()
        Returns the matrix elements as a group of parameters values. The number of parameters depends on the matrix size. Only matrix elements different from their default value will be included in this group.
        Overrides:
        getParameterValues in class AbstractMathTransform
        Returns:
        A copy of the parameter values for this math transform.
        See Also:
        Operation.getParameterValues()

      • transform

        public void transform​(float[] srcPts,
                      int srcOff,
                      float[] dstPts,
                      int dstOff,
                      int numPts)
        Transforms an array of floating point coordinates by this matrix. Point coordinates must have a dimension equals to Matrix.getNumCol()-1. For example, for square matrix of size 4×4, coordinate points are three-dimensional and stored in the arrays starting at the specified offset (srcOff) in the order [x0, y0, z0, x1, y1, z1..., xn, yn, zn].
        Specified by:
        transform in interface MathTransform
        Overrides:
        transform in class AbstractMathTransform
        Parameters:
        srcPts - The array containing the source point coordinates.
        srcOff - The offset to the first point to be transformed in the source array.
        dstPts - The array into which the transformed point coordinates are returned.
        dstOff - The offset to the location of the first transformed point that is stored in the destination array. The source and destination array sections can be overlaps.
        numPts - The number of points to be transformed

      • transform

        public void transform​(double[] srcPts,
                      int srcOff,
                      double[] dstPts,
                      int dstOff,
                      int numPts)
        Transforms an array of floating point coordinates by this matrix. Point coordinates must have a dimension equals to Matrix.getNumCol()-1. For example, for square matrix of size 4×4, coordinate points are three-dimensional and stored in the arrays starting at the specified offset (srcOff) in the order [x0, y0, z0, x1, y1, z1..., xn, yn, zn].
        Specified by:
        transform in interface MathTransform
        Parameters:
        srcPts - The array containing the source point coordinates.
        srcOff - The offset to the first point to be transformed in the source array.
        dstPts - The array into which the transformed point coordinates are returned.
        dstOff - The offset to the location of the first transformed point that is stored in the destination array. The source and destination array sections can be overlaps.
        numPts - The number of points to be transformed

      • derivative

        public Matrix derivative​(Point2D point)
        Gets the derivative of this transform at a point. For a matrix transform, the derivative is the same everywhere.
        Overrides:
        derivative in class AbstractMathTransform
        Parameters:
        point - The coordinate point where to evaluate the derivative.
        Returns:
        The derivative at the specified point as a 2×2 matrix.
        See Also:
        MathTransform2D.derivative(Point2D)

      • derivative

        public Matrix derivative​(Position point)
        Gets the derivative of this transform at a point. For a matrix transform, the derivative is the same everywhere.
        Specified by:
        derivative in interface MathTransform
        Overrides:
        derivative in class AbstractMathTransform
        Parameters:
        point - The coordinate point where to evaluate the derivative.
        Returns:
        The derivative at the specified point (never null).

      • getMatrix

        public Matrix getMatrix()
        Returns a copy of the matrix.
        Specified by:
        getMatrix in interface LinearTransform
        Returns:
        A copy of the underlying matrix.

      • isIdentity

        public boolean isIdentity()
        Tests whether this transform does not move any points.
        Specified by:
        isIdentity in interface MathTransform
        Overrides:
        isIdentity in class AbstractMathTransform
        Returns:
        true if this MathTransform is an identity transform; false otherwise.

      • isIdentity

        public boolean isIdentity​(double tolerance)
        Tests whether this transform does not move any points by using the provided tolerance. This method work in the same way than XMatrix.isIdentity(double).
        Specified by:
        isIdentity in interface LinearTransform
        Parameters:
        tolerance - The tolerance factor.
        Returns:
        true if this transform is the identity one
        Since:
        2.4

      • hashCode

        public int hashCode()
        Returns a hash value for this transform. This value need not remain consistent between different implementations of the same class.
        Overrides:
        hashCode in class AbstractMathTransform

      • equals

        public boolean equals​(Object object)
        Compares the specified object with this math transform for equality.
        Overrides:
        equals in class AbstractMathTransform
        Parameters:
        object - The object to compare with this transform.
        Returns:
        true if the given object is a transform of the same class and if, given identical source position, the transformed position would be the equals.