基于非均匀细分的流曲线曲面  

Stream Curve and Surface Based on Non-uniform Subdivision

作　　者：李秀娟[1,2] 刘浩[2] 何钢[2] 廖文和[2] 

机构地区：[1]南京航空航天大学理学院,南京210016 [2]南京航空航天大学机电学院,南京210016

出　　处：《机械科学与技术》2008年第10期1216-1219,1224,共5页Mechanical Science and Technology for Aerospace Engineering

基　　金：国防基础科研项目资助

摘　　要：流曲线为切矢的积分曲线。被积函数的计算复杂,引入细分,可将被积函数的计算转化为细分的计算,但被积函数中的曲线事实上是非均匀单位B样条四元数曲线。由此,将细分推广至非均匀细分,从几何的角度推导了计算切矢的线性插值的一种简便算法;给出了和非均匀B样条曲线的细分模式对应的、切矢的线性插值的表达式和计算;提出了基于非均匀细分的流曲线曲面生成算法,并给出了实例。未来可以研究基于此算法的曲面拼接、混合等,将其推广应用于CAD软件和计算机动画中。Stream curves are by blending tangent vectors. It is difficult to calculate the integrands By subdivision, calculations of integrands are simplified. But the curves in the are non-uniform unit Bspline quaternion curves. Therefore, non-uniform subdivisions are introduced. A simple method for calculating the blending directions of tangent vectors is presented. Its special expressions corresponding to non-uniform subdivision are given. In addition, the generating algorithm is proposed on stream curve and surface based on non-uniform subdivision, and an example is given. The results can be used in CAD software and computer animation.

关 键 词：流曲线 细分 四元数 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]