Feature-based modeling for variable fractal geometry design integrated into CAD system

Abstract

Fractal geometry has been widely applied in computer graphics to visually represent natural objects, which cannot be easily represented by Euclidean geometry. Other than visual representation, parametric fractal-like CAD models have been used in industry for the design and manufacture of products with self-similarity geometric features. However, contemporary CAD systems cannot construct CAD fractal models efficiently, as most CAD fractal models are still built manually by designers. The construction and modifications for such CAD fractal models are tedious and time-consuming.This paper aims to build and modify CAD fractal models more efficiently in CAD systems. A method for automatically modeling parametric fractal-like geometry objects in CAD systems is proposed. Feature-based modeling methods have been applied for realizing algorithm-based CAD fractal model generation. A new type of feature, called CAD fractal feature is proposed and implemented to bridge the gap between CAD and fractal geometry. The fractal-like CAD model is constructed iteratively with a dynamic generator for each iteration cycle. Design parameters are extracted as inputs for dynamic fractal generators, which allows users to define, parameterize, generate and edit a fractal design with variable parameters. The parameters of the fractal generator can also take different values for different model construction iterations, which makes the generated models not necessarily to be strictly fractal but can also be fractal-like. The iterative generation method (IGM) is proposed as a built-in method in a CAD fractal feature for modeling complex but self-similar geometric models in an objected-oriented approach with high efficiency and sufficient design flexibility. As a result, designers do not need advanced knowledge of fractal geometry to build and modify CAD models with self-similar features. An extruded Koch Snowflake CAD model with parametric geometric variants has been built as a case study for demonstration of the proposed modeling method.