Process of creating real world objects usually involves usage of more than one CAD/CAM system. Communicating product data between diverse systems that use incompatible internal representation schemes necessitates data conversion and approximation. Main focus of the thesis will be on Bézier curves and surface patches that offer a way of converting data while retaining information about the approximation error made during conversion. We will briefly review basic building blocks such as intervals, interval arithmetic and Bernstein basis functions, and then resume with describing interval Bézier curves and surface patches. Crucial algorithms that allow us to work with Bézier curves, Bézier surface patches and their interval counterparts will be implemented. We will conclude this thesis with short review of a few selected examples of interval Bézier curves and surface patches.
|
