Title: Modelling of complex fractal objects for aesthetic product development

Authors: C.L. Li, Y.C. Yeung, W.K. Chiu, K.M. Yu

Addresses: Department of Manufacturing Engineering and Engineering Management, The City University of Hong Kong, Hong Kong. ' Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong. ' Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong. ' Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong

Abstract: Fractal geometry has been used for modelling natural objects that cannot be described by Euclidean geometry, and is also employed in aesthetic product design. However, the contemporary Computer-Aided Design (CAD) and Computer-Aided Manufacturing (CAM) systems are well developed only for semi-analytical and free-form objects, and they cannot deal with aesthetic appealing objects efficiently. As a result, new data structure or representation model has to be introduced in order to model and process the fractal geometry effectively in Euclidean-based CAD/CAM system. In this paper an algorithm is proposed for generating a 3D complex fractal from its mathematical models. To represent the 3D complex fractal object model in a CAD system, a voxel-based model is introduced. To fabricate a physical fractal object, Layered Manufacturing (LM) technology is employed. The geometrical information of the fractal object is extracted from its voxel-based model and the LM tool path can be generated accordingly. Applying the proposed algorithm, the fabrication of a fractal object can be realised.

Keywords: complex fractals; layered manufacturing; voxels; voxel-based models; object modelling; aesthetics; product development; fractal geometry; product design; CADCAM; Euclidean CAD.

DOI: 10.1504/IJPD.2007.012492

International Journal of Product Development, 2007 Vol.4 No.3/4, pp.207 - 224

Published online: 19 Feb 2007 *

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