Patent ID: 8884954
Filing Date: 2014-11-11
Classification: G06F,G06T

Abstract:
1. A computer software product for directly determining parameters defining a Weierstrass-Mandelbrot (W-M) analytical representation of a rough surface scalar field with fractal character, embedded in a three dimensional space, utilizing pre-existing measured elevation data of a rough surface in the form of a discrete collection of data describing a scalar field at distinct spatial coordinates, the product comprising a non-transitory physical computer-readable medium including stored instructions that, when executed by a computer, cause the computer to apply an inverse algorithm to the elevation data to thereby determine the parameters that define the analytical and continuous W-M representation of the rough surface, and wherein the surface has an array of elevation or height measurements z ij e , i, j=1 . . . K over a square region of size L×L and the parameters are γ and φ mn of the surface z(x, y) and the surface is represented by the complex Weierstrass-Mandelbrot (W-M) function W as: where x is a real variable, and where a two dimensional profile obtained from the real part of Eq. 1 is: and where D is the fractal dimension (1<D<2 for line profiles), φ and wherein the instructions include applying a Singular Value Decomposition (SVD) algorithm to a refactoring of Eq. (1), thereby determining said parameters of the Weierstrass-Mandelbrot (W-M) function describing the surface originally given in terms of measured elevation data.