摘要
利用代数双曲三角函数空间Γn=span{1,sin t,cos t,sinh t,cosh t,t,t2,…,tn-4}中拟Bézier基的对称性构造了一组正交基,并给出该正交基和拟B啨zier基之间的转换矩阵.进一步,应用最小二乘法对代数双曲三角B啨zier曲线进行了保端点降阶逼近.
In the space Гn = span {1, sin t, cos t, sinh t, cosh t, t, t2, …, tn-4 } , a kind of algebraic trigonometric hyperbolic basis called ATH Bézier basis is constructed by an integral approach. By the symmetry of the ATH Bézier basis, we construct an orthogonal basis called quasi-Lengendre basis, then we present the conversion formula between the ATH Bézier basis and the orthogonal basis. In addition, the optimal lower degree approximation of the ATH Bézier curves is investigated.
出处
《计算机辅助设计与图形学学报》
EI
CSCD
北大核心
2008年第4期464-468,共5页
Journal of Computer-Aided Design & Computer Graphics
基金
国家自然科学基金(60473130)
国家“九七三”重点基础研究发展规划项目(2004CB318000)
杭州电子科技大学校科研启动项目(KYS091507070)
关键词
代数双曲三角Bézier基
正交基
基转化
保端点
降阶逼近
algebraic trigonometric hyperbolic Bézier basis
orthogonal basis
basis transformations
endpoint preservation
least square approximation
