Constrained multi-degree reduction of triangular Bézier surfaces

摘要

This paper proposes and applies a method to sort two-dimensional control points of triangular B'ezier surfaces in a row vector.Using the property of bivariate Jacobi basis functions,it further presents two algorithms for multi-degree reduction of triangular B'ezier surfaces with constraints,providing explicit degree-reduced surfaces.The first algorithm can obtain the explicit representation of the optimal degree-reduced surfaces and the approximating error in both boundary curve constraints and corner constraints.But it has to solve the inversion of a matrix whose degree is related with the original surface.The second algorithm entails no matrix inversion to bring about computational instability,gives stable degree-reduced surfaces quickly,and presents the error bound.In the end,the paper proves the efficiency of the two algorithms through examples and error analysis.