张量积B&#233;zier曲面降阶逼近的新方法

张量积Bézier曲面降阶逼近的新方法

摘要: 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,并利用曲面离散算法减少降阶逼近误差.

Abstract: 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．