The Constrained Optimal Multi-degree Reduction of Tensor Product Bézier Surfaces

To transfer and store the data in different modeling systems,an optimization algorithm for multi-degree reduction of tensor product Bézier surfaces is proposed with some restrained conditions.Firstly,by interpolating four corners of high degree,the optimal multi-degree reduction of Bézier surfaces is achieved by applying dimension reduction method in surface control points in a least squares minimization manner.Secondly,by interpolating four boundary curves with a degree-reduced surface,the optimal degree reduction of the surface is obtained by least-squares subtracting the degree-reduced surface from the original surface.After using the degree reduction to the piecewise surfaces with the interpolation conditions of boundary curves,the resulting piecewise approximating surfaces are globally C 0.Numerical examples and theoretical approximation results suggest that the proposed method is more precise and efficient when compared to previous methods.