One of the key activities in any product design process is to develop a geometric model of the product from the conceptual ideas, which can then be augmented with further engineering information pertaining to the application area. For example, the geometric model of a design may be developed to include material and manufacturing information that can later be used in computer-aided process planning and manufacturing (CAPP/CAM) activities. A geometric model is also a must for any engineering analysis, such as finite elopement analysis (FEA). In mathematic terms, geometric modelling is concerned with defining geometric objects using computational geometry, which is often, represented through computer software or rather a geometric modelling kernel. Geometry may be defined with the help of a wire-frame model, surface model, or solid model. Geometric modelling has now become an integral part of any computer-aided design (CAD) system. In this chapter, various geometric modelling approaches, such as wire-frame, surface, and solid modelling will be discussed. Basic computational geometric methods for defining simple entities such as curves, surfaces, and solids are given. Concepts of parametric, variational, history-based, and history-free CAD systems are explained. These topics are discussed in this opening chapter because (a) CAD was the very first computer-aided technologies developed and (b) its related techniques and methods have been pervasive in the other related subjects like computer-aided manufacturing. This chapter only discusses CAD systems from the application point of view; CAD data formats and data exchange issues are covered in the second chapter.
Geometric Modelling Approaches
The development of geometric modelling is coupled with three departments of sciences and technologies. They are computer graphics techniques, three-dimensional (3D) geometric representation schemes and computer hardware advances. The research started in the 1960’s. The basic geometric modelling approaches used in today’s CAD/CAM systems are wire-frame, surface and solid modelling. In the following sections, a basic account of these approaches to geometric modelling is presented.