保持几何连续性的曲线形状调配  

SHAPE BLENDING OF CURVES:RESEARCH INTO GEOMETRIC CONTINUITY PRESERVING

作　　者：张宏鑫[1] 王国瑾[1] 

机构地区：[1]浙江大学CAD&CG国家重点实验室,浙江大学数学系浙江杭州310027

出　　处：《高校应用数学学报（A辑）》2001年第2期187-194,共8页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金!(699730 4 1 );浙江省自然科学基金!(6980 2 5);国家重点基础研究 973项目! (G1 9980 30 60 0 )

摘　　要：在形状调配过程中 ,中间过渡曲线的几何连续性往往是不能保证的 .本文从平衡调整的角度出发 ,利用 Bézier曲线的边界性质 ,研究形状调配中曲线的几何连续特征保持问题 .着重讨论了线性混合过程中 ,一阶和二阶几何连续保持条件及相应解决办法 ;并对 n阶情况提出平衡化几何连续条件 ,从而得出一般的Bézier曲线在形状调配中几何连续的保持方法 .In shape blending process,the geometric continuity of blending curves is not always preserved.In this paper,based on a symmetric opinion,the geometric continuity preserving problems of blending curves are investigated by using the boundary properties of Béziercurve.Especially,in the linear blending process,the maintenance conditions of the first order and the second order geometric continuities are derived,and several solutions are discussed.Then an n-th order balance geometric continuity condition and its relative generic preserving algorithm are given.The algorithms can be used in computer animation and industry design.

关 键 词：形状调配 几何连续性 BEZIER曲线 平衡调整 计算机动画 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]