Geometric Modeling of Vitrified Superabrasive Stone Surface

Abstract

A geometric modeling technique of the complex vitrified superabrasive stone surfaces has been developed for the purpose of describing their topographies with desired characteristics. It is based on the generating algorithms for random fractals, such as midpoint displacement and successive random additions, and yields a three-dimensional topographic map of the stone surface. Compari-sons between the simulated topographic map and the measured one show a good match ; the spatial distribution of abrasives on both the stone surfaces exhibits a fractal structure, indicating that the simulated stone surface is a good representation of the real one. Therefore, the computer modeling could be used advantageously when the designer makes drawings of stone surfaces