Modelling of fractal objects using layered manufacturing techniques

Abstract

Fractal object is a promising area for aesthetic product and decoration design of natural objects (e.g. landscape, surf, snowflake, coral, etc.), physiology and antenna system. Contemporary computer-aided design (CAD) and computer-aided manufacturing (CAM) systems can use non-uniform rational B-spline (NURBS) surface modeling and solid modeling methods for creating Euclidean analytical objects and free-form objects. But neither can model fractal objects efficiently. Some researchers have proposed a new method to manufacture fractal objects that are mainly described by iterated function system (IFS). However, they were restricted to IFS connected and single contour fractal objects. Therefore, investigation of fractal objects in this area begins to emerge. The thesis investigates a novel method to extend layer manufacturing (LM) technologies to making three dimension (3D) physical fractal objects. First, the fractal geometry is tentatively classified and the manufacturability of fractal geometry is then evaluated. Afterwards, the voxel-based conversion mechanism is proposed to model complex fractal objects, this method can produce n-dimensional colored fractal objects. Then, a data structure called colored generative quadtree encoding (CGQE) is proposed. This data structure is devised to reduce the amount of space necessary to store the data in a computational efficient way. Besides, the CGQE can easily dispose a disconnected dust of fractal object in order to obtain a fractal pattern represented by a simple polygonal chain. These conversion methods can provide a communication bridge between fractal geometry and CAD/CAM systems to LM the colored fractal objects. Finally, a grid-based navigation algorithm and a multi-resolution toolpath generation of fractal objects are proposed. The proposed mechanism and enhanced data structure can be validated via 3D colored printer (Z-Corp machine), which uses layer manufacturing (LM) process to fabricate physical prototypes out of plaster based or starch based material. The proposed methods for toolpath generation are validated by the physical realization of a typical IFS multiply connected fractal objects, produced on a Stratasys Fused Deposition Modeling (FDM) machine. It is a typical LM process that can fabricate prototypes out of amorphous thermoplastic. The method can also be extended for generating toolpaths in the natural fractal domains.