Fractal fabrication for aesthetic product design

Abstract

The contemporary computer-aided design (CAD) and computer-aided manufacturing (CAM) theories and systems are well developed for analytical objects and free-form objects, but neither of them can deal with aesthetic appealing objects efficiently. Not all the manufacturing of aesthetically appealing objects can reap the benefit of CAD/CAM technology. An important area for aesthetic appealing design is in the jewellery industry. Therefore, it is valuable to find an effective CAD/CAM method for aesthetic appealing object. Fractal geometry has been proposed for modelling natural objects that cannot be easily described by Euclidean geometry. In this thesis, the research centres on using fractal geometry to model aesthetic appealing objects in computational form while layered manufacturing (LM) technology is used for the producing physical prototypes of such fractal objects. The method involves proposing two new data structures to bridge the gaps among CAD, LM and fractal geometry. The first one called Radial-Annular Tree data structure is used for two-dimensional fractal modelling and the second one called Radial-Blossoming Tree data structure is for the three-dimensional fractal modelling. Based on the two data structure representations, fractal object information can be properly organised for fabrication by LM. Traversal algorithms are also devised to obtain information for generating the LM tool path. The toolpath can then be used to build physical fractal objects. Some case studies are presented to verify the proposed method.