Method of quantifying the topographic structure of a surface

Abstract

A fractal-based or 'patchwork' method for analyzing topographic data simulates covering the surface of a specimen surface with triangular patches in order to determine the relative surface area which is a function of patch size or scale of observation or interaction. The specimen surface has X and Y horizontal axes and a vertical Z axis. Height data is obtained for each point of a grid network of points on the surface, the points being arranged in parallel rows and the rows being spaced. The specimen surface is defined with triangles having a surface area equal to a preselected patch area value. The total area of the planar triangles is calculated to obtain a total measured area of value. The area of the specimen surface in the X-Y plane that is defined by the triangles is calculated to obtain a total measured area value. The total measured area value is divided by the total projected area value to obtain a relative area value. The relative values for several patch area values are plotted to obtain a slope and a threshold, or crossover, point. The threshold is indicative of a point which separates the relatively large scales of observation or interaction which are best described by Euclidean geometry from those smaller ones which are best described by fractal geometry.