Degree reduction of parametric curves and surfaces is an important process in the exchange of product model data between various CAD systems. In this paper the degenerate conditions of triangular Bezier surface patch...Degree reduction of parametric curves and surfaces is an important process in the exchange of product model data between various CAD systems. In this paper the degenerate conditions of triangular Bezier surface patches are derived. The degenerate conditions and constrained optimization methods are used to develop a degree reduction method for triangular Bezier surface patches. The error in the degree reduction of a triangular Bezier surface is also shown to depend on some geometric invariants which decrease exponentially in the subdivision process. Therefore, the degree reduction method can be combined with a subdivision algorithm to generate lower degree approximations which are within some preset error tolerance.展开更多
文摘Degree reduction of parametric curves and surfaces is an important process in the exchange of product model data between various CAD systems. In this paper the degenerate conditions of triangular Bezier surface patches are derived. The degenerate conditions and constrained optimization methods are used to develop a degree reduction method for triangular Bezier surface patches. The error in the degree reduction of a triangular Bezier surface is also shown to depend on some geometric invariants which decrease exponentially in the subdivision process. Therefore, the degree reduction method can be combined with a subdivision algorithm to generate lower degree approximations which are within some preset error tolerance.