张量积Bézier曲面降阶逼近的新方法

New Method of Approximate Degree Reduction of Bézier Surfaces

基于 L2 范数 ,给出基于曲面间体积极小的约束优化算法 ,将 Bézier曲面的降阶问题转变为线性方程组的求解 ,并给出降阶逼近问题解的存在性证明 .文中还对逼近误差进行了分析 。

By using the contrained optimization method, degree reduction of Bézier surface is achieved by solving systems of linear equations. The existence of solution is proved. The error of degree reduction is analyzed and reduced by using standard subdivision algorithms.