Synthesis of fractal geometry and CAGD models for multi-scale topography modelling of functional surfaces

Abstract

In order to support the functional design and simulation and the final fabrication processes for functional surfaces, it is necessary to obtain a multi-scale modelling approach representing both macro geometry and micro details of the surface in one unified model. Based on the fractal geometry theory, a synthesized model is proposed by mathematically combining Weierstrass-Mandelbrot fractal function in micro space and freeform CAGD model in macro space. Key issues of the synthesis, such as algorithms for fractal interpolation of freeform profiles, and visualization optimization for fractal details, are addressed. A prototype of the integration solution is developed based on the platform of AutoCAD’s Object ARX, and a few multi-scale modelling examples are used as case studies. With the consistent mathematic model, multi-scale surface geometries can be represented precisely. Moreover, the visualization result of the functional surfaces shows that the visualization optimization strategies developed are efficient.

Keywords

surface roughness / microtopography / fractal geometry / functional surface