摘要
通过在Hermite插值过程中最优化端点切矢的模长,使最优几何Hermite曲线的曲率变化率最小;得到并证明了使最优几何Hermite曲线达到几何光顺的切矢角约束条件.针对切矢角不满足该约束条件的情况,提出了构造2-分段和3-分段组合最优几何Hermite曲线的方法.最后通过实例及比较表明,该方法与基于应变能最小的方法可相互补充,在整个切矢角区域上达到满意的效果.
The magnitudes of the endpoint tangent vectors are optimized in the process of Hermite interpolation so that the curvature variation of the optimized geometric Hermite curve is a minimum. The tangent angle constraints guaranteeing an optimized geometric Hermite curve geometrically smooth is got and proved. For the cases in which the given tangent vectors do not satisfy the constraints, new methods for constructing 2-segment and 3-segment composite optimized geometric Hermite curves are presented. Examples have been presented to shown that combination of these new methods and those based on strain energy minimization can get satisfying results in all the tangent angle regions.
出处
《计算机辅助设计与图形学学报》
EI
CSCD
北大核心
2008年第7期882-887,共6页
Journal of Computer-Aided Design & Computer Graphics
基金
国家自然科学基金(60603077,60403036,60573181)
山东省自然科学基金(Y2005G15)
