Toolpath generation for layer manufacturing of fractal objects

Purpose – Fractal geometry can be used to model natural objects which cannot be easily represented by the euclidean geometry. However, contemporary computer-aided design (CAD) and computer-aided manufacturing (CAM) systems cannot be used to model a fractal object efficiently. In a general layer manufacturing (LM) workflow, a model described by the euclidean geometry is required in order to generate the necessary toolpath information. So this workflow cannot be applied for a fractal object. In this paper, to realize the fabrication of a fractal represented object by the LM technology, a methodology is proposed. Design/methodology/approach – In the proposed methodology, a slab grid is generated in each layer of the object and it consists of a number of pixels. The interior property (corresponding to the fractal object) of each pixel in the slab grid is checked so that slab models of the fractal are created. The boundary of each slab is traced and refined so that the toolpath of the object can be generated from these boundaries. Findings – Applying the proposed methodology, the LM toolpath information can be extracted from the mathematical model of the fractal and the tessellating or slicing processes are not needed to be performed. The problem of representing a fractal in a CAD platform can be eliminated. Research limitations/implications – The proposed methodology can be applied to iterative function system (IFS) or complex fractal. However, for some fractals constructed from more than one kind of fractal objects, such as multi-IFS fractals, the methodology must be further developed. Originality/value – The proposed methodology is a novel development for realizing the fabrication of fractal objects by the LM technology.