INSTRUMENTAL TOOLS FOR GEOMETRIC MODELLING USIG PARAMETRIC FUNCTIONS - Al-Athamneh, H. K. M. (Computer Science and Applied Mathematics, 2016)
Computer-aided design (CAD) systems have become important in engineering, architecture, computer graphics etc. These systems use abstract rigid solid to model physical solids. Solid geometry plays significant role in many scientific applications of CAD. Hence, geometry of solids is represented in CAD by special symbol structures. The subsystem which provides tools for entering, storing and editing object representation is called geometric modelling system. In computer-aided design and solid modelling, boundary representation (B-rep) is a method for representing shapes using the limits. A solid is represented as a collection of its boundaries. In this article, parametric functions are used for boundary representation. Solids are represented in terms of parametric curves and surfaces. Particularly, analytical curves and surfaces, and spline patches are used. Ray parity test is used to check whether a point is inside a region defined by parametric functions. This even-odd test also known as the Jordan Curve theorem. Essentially, it says that a point is inside a region if for any ray from this point, there is an odd number of crossings of the ray with the region boundaries. This parity test allows representation of complex solids in logical set operations.