Class AffineTransformationBuilder


  • public class AffineTransformationBuilder
    extends java.lang.Object
    Builds an AffineTransformation defined by a set of control vectors. A control vector consists of a source point and a destination point, which is the image of the source point under the desired transformation.

    A transformation is well-defined by a set of three control vectors if and only if the source points are not collinear. (In particular, the degenerate situation where two or more source points are identical will not produce a well-defined transformation). A well-defined transformation exists and is unique. If the control vectors are not well-defined, the system of equations defining the transformation matrix entries is not solvable, and no transformation can be determined.

    No such restriction applies to the destination points. However, if the destination points are collinear or non-unique, a non-invertible transformations will be generated.

    This technique of recovering a transformation from its effect on known points is used in the Bilinear Interpolated Triangulation algorithm for warping planar surfaces.

    • Constructor Detail

      • AffineTransformationBuilder

        public AffineTransformationBuilder​(Coordinate src0,
                                           Coordinate src1,
                                           Coordinate src2,
                                           Coordinate dest0,
                                           Coordinate dest1,
                                           Coordinate dest2)
        Constructs a new builder for the transformation defined by the given set of control point mappings.
        Parameters:
        src0 - a control point
        src1 - a control point
        src2 - a control point
        dest0 - the image of control point 0 under the required transformation
        dest1 - the image of control point 1 under the required transformation
        dest2 - the image of control point 2 under the required transformation
    • Method Detail

      • getTransformation

        public AffineTransformation getTransformation()
        Computes the AffineTransformation determined by the control point mappings, or null if the control vectors do not determine a well-defined transformation.
        Returns:
        an affine transformation
      • compute

        private boolean compute()
        Computes the transformation matrix by solving the two systems of linear equations defined by the control point mappings, if this is possible.
        Returns:
        true if the transformation matrix is solvable
      • solve

        private double[] solve​(double[] b)
        Solves the transformation matrix system of linear equations for the given right-hand side vector.
        Parameters:
        b - the vector for the right-hand side of the system
        Returns:
        the solution vector