空间Bézier曲线的最小旋转标架构造  

Constructing Rotation-Minimizing Frame of Space Bézier Curve

作　　者：郑志浩[1] 汪国昭[1] 

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

出　　处：《计算机辅助设计与图形学学报》2005年第8期1785-1792,共8页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(10371110);国家重点基础研究发展规划项目(2002CB312101)

摘　　要：最小旋转标架(RMF)是生成扫掠曲面的最理想标架.通过对一空间B啨zier曲线插入参数节点,构造出其对应的G1三次PH样条逼近曲线;然后旋转PH样条曲线的有理形式的Euler-RodriguesFrame(ERF)生成其RMF,该标架同时可作为原空间B啨zier曲线的RMF.The rotation-minimizing frame（RMF） is the most attractive frame for applications such as animation, sweep surface construction, and motion planning. However, it is difficult to construct rational RMF which is compatible with the current CAD system for Bézier and B-spline curves. Since Pythagorean hodograph （PH） curves admit rational Euler-Rodrigues frame （ERF） exactly and cubic PH curve shares optimal geometric properties, in this paper, a cubic PH-spline with G^1 continuity is constructed according to the endpoint conditions of the subdivided segments after inserting knots into the Bézier curve.Correspondingly, the PH-spline is an approximation for the given space Bézier curve. The least number of subdivisions and the bound error can be efficiently controlled by our formula. We construct ERF for every cubic PH curve which belongs to the PH-spline, then the corresponding RMF for each cubic PH curve can be generated by rotating the last two vectors of ERF for the PH-spline on the normal planar. The total RMF in rational form for PH-spline can be regarded as approximate RMF for the Bézier curve. The method can also be used to solve same problem on B-spline curve.

关 键 词：空间Bézier曲线 空间三次PH曲线 扫掠曲面 最小旋转标架 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]