流形网格曲面上测地B样条插值  

Interpolation of Geodesic B-spline Curves on Manifold Triangulation

作　　者：刘斌[1] 黄常标[1] 林俊义[1] 江开勇[1] 

机构地区：[1]华侨大学机电及自动化学院,厦门361021

出　　处：《机械工程学报》2011年第19期136-142,共7页Journal of Mechanical Engineering

基　　金：福建省科技计划重点(2009H0032);福建省高等学校新世纪优秀人才支持计划(07176C03);中央高校基本科研业务费(JB-ZR1104)资助项目

摘　　要：针对现有曲面上自由曲线设计方法的不足,提出一种插值于流形网格曲面上给定点列的测地B样条曲线生成方法。用流形网格曲面上两点间的最短测地线代替欧氏空间中的两点间直线,将欧氏空间中的德布尔算法拓展到曲面空间,得到流形网格曲面上的测地B样条表示形式。对于给定的约束于网格曲面上的点列,基于欧氏空间中的B样条插值理论,反算出其控制顶点,将这些控制顶点投影到网格曲面上,作为待求曲线的初始控制顶点,生成初始的测地B样条曲线。为使曲线尽可能逼近于型值点,提出反向误差补偿策略,通过简单迭代求取约束于网格曲面上的控制顶点。根据曲线的凸包性,将曲线所在测地凸包区域与整体网格曲面虚拟分割,使插值测地B样条曲线的计算量仅与曲线所在测地凸包区域内的网格顶点数有关,而与整体网格大小无关,从而大大减少计算量。试验结果表明,所介绍方法健壮、有效,能满足曲面上曲线的交互设计要求。In allusion to the deficiencies of the existing methods of designing free curve on the surface,a generation method for geodesic B-spline curve interpolated from manifold triangulation surface is proposed.The shortest geodesic curve between two points on the manifold triangulation surface is used to substitute for the straight line between the two points in Euclidean space;and de Boor algorithm in Euclidean space is expand to curved space,so that the representation for geodesic B-spline curve on manifold triangulation is obtained.The given range of points constrained on the mesh surface are operated base on the B-spline interpolation theory in Euclidean space;control points are gained by inverse computation,and then projected onto the mesh surface;points on the mesh surface are treated as the initial control points of expected curve,from which the initial geodesic B-spline curve is finally generated.A reverse error compensation strategy which obtains control points constrained onto the mesh by simple iteration is proposed in order to approximate the curve with the data points as much as possible.According to the convex hull property of the curve,the convex hull region is virtual partitioned from the whole mesh surface;and then the computation of interpolating geodesic B-spline curve is only related to the mesh vertices within the convex hull region rather than the overall mesh,which greatly reduces the computational complexity.The results show that,the method is robust,effective,and able to meet the requirements of curve interaction design on surface.

关 键 词：扩展德布尔算法 流形网格 测地B样条 插值 测地凸包 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]