Rapid prototyping for self-similarity design

Abstract

This paper proposes a method for the rapid prototyping (RP) of self-similar objects. RP technology makes available the physical generation of a solid object. However, the contemporary design capability of a computer-aided design (CAD) system can atmost use the non-uniform rational B-spline (NURBS) modelling method. When the design has a very complicated shape with self-similarity, contemporary CAD systems can no longer handle the object. In fact, most objects in nature are self-similar. It is valuable to develop a method that can fabricate self-similar objects. Natural objects, such as mountains, clouds, and trees have irregular or fragmented features with self-similarity. These natural objects can be realistically described the by fractal geometry method, while Euclidean geometry is mainly used to represent simple man-made objects such as polyhedra. A typical self-similar fractal solid, the Menger sponge, will be used to illustrate the method. In order to represent a self-similar fractal object for RP, the first task is to develop a method to model the object in a computable form. In this paper, a new data structure, called the radial-blossoming tree (RBT) structure, is proposed and implemented in order to bridge the gaps among CAD, RP and fractal geometry. Based on the RBT representation, an RP toolpath can be traced out more efficiently. The Menger sponge will then be produced layer by layer from the RP machine.