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.
出处
《机械科学与技术》
CSCD
北大核心
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
关键词
流曲线
细分
四元数
stream curve
non-uniform subdivision
quatemion
