带G^1连续约束的Bézier曲线显式最佳降多阶  

Matrix Representation for Optimal Multi-degree Reduction of Bézier Curves with G^1 Constraints

作　　者：周联[1,2] 王国瑾[1,2] 

机构地区：[1]浙江大学数学系计算机图象图形研究所,杭州310027 [2]浙江大学CAD＆CG国家重点实验室,杭州310027

出　　处：《计算机辅助设计与图形学学报》2010年第4期735-740,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(60873111,60933007)

摘　　要：为了克服已有Bézier曲线降阶算法在保G1连续约束条件下仅给出数值解的缺陷,提出一种Bézier曲线在端点处保G1连续的最佳显式降阶算法.在求解以逼近误差为目标函数的最小化问题过程中,首先给出了Bernstein多项式在两端点保高阶几何连续条件下降阶的最佳显式解;其次给出了Bézier曲线在两端点处保G1连续条件下降阶的最佳显式解;最后给出了降阶曲线的控制顶点和逼近误差的2个显式矩阵表示.数值实例结果表明,文中算法比其他算法的精度高、效率高.The existing algorithms for multi degree reduction of Bezier curves with G1 constraints only provide numerical solutions. To overcome this flaw, an algorithm for optimal degree reduction of Bezier curves with G1 constraints at the endpoints is presented. By taking the approximation error as the objective function and minimizing this function, the optimal explicit solution to multi-degree reduction of Bernstein polynomials with high-order continuity at the two endpoints is given. And then the optimal explicit solution to multi-degree reduction of B4zier curves with G1 constraints is also given. The control points of the degree reduced curves and the approximation error are derived from two matrix representations respectively. Numerical examples show that the proposed method is more precise and efficient comparing to previous methods.

关 键 词：BÉZIER曲线 降阶 几何连续 矩阵表示 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]