Class AlgorithmEllipseToRectangle

  • All Implemented Interfaces:
    java.awt.event.ActionListener, java.awt.event.WindowListener, java.lang.Runnable, java.util.EventListener

    public class AlgorithmEllipseToRectangle
    extends AlgorithmBase
    This program performs the conformal mapping of an ellipse to a rectangle. Consider the original ellipse as having a tilt theta with the x axis. From problem 9 in Nehari: w = sin z maps the rectangle -pi/2 < Re |z| < pi/2, -c < Im |z| < c onto the interior of the ellipse u**2/(cosh c)**2 + v**2/(sinh c)**2 = 1 which has been cut along the linear segments -cosh c <= w <= -1, 1 <= w <= cosh c Then the conformal mapping is done in 3 steps. 1.) Translate the center of the rectangular image to the origin, and divide down the rectangle size by ((xDim - 1)/3.1). 2.) Map from the rectangle to a standard ellipse on the x axis with foci at +- 1 and with the same major axis/minor axis ratio as the original ellipse. 3.) Map from the standard ellipse to the original ellipse by rotating, scaling, and translating.

    References: 1.) Advanced Calculus For Applications Second Edition by F. B. Hildebrand, Section 10.4 Analytic Functions of a Complex Variable pages 550-554 and Section 11.4 Conformal Mapping pages 628-632, Prentice-Hall, Inc., 1976. 2.) Conformal Mapping from Zeev Nehari, Chapter VI, Mapping Properties of Special Functions, Section 2, Exponential and Trigonometric Functions, pp. 273-280. See Porblem 9 on page 279.

    • Field Detail

      • xDimDest

        private int xDimDest
    • Constructor Detail

      • AlgorithmEllipseToRectangle

        public AlgorithmEllipseToRectangle()
        AlgorithmEllipseToRectangle - default constructor.
      • AlgorithmEllipseToRectangle

        public AlgorithmEllipseToRectangle​(ModelImage srcImg,
                                           int xDimDest)
        AlgorithmEllipseToRectangle.
        Parameters:
        srcImg - DOCUMENT ME!
        xDimDest -
    • Method Detail

      • getResultImage

        public ModelImage getResultImage()
      • selfTest

        private void selfTest()