C-Bézier曲线分割算法及G^1拼接条件

Subdivision Algorithm and G^1 Condition for C-Bézier Curves

在对 C- Bézier基函数及曲线端点特性分析的基础上 ,提出 C- Bézier曲线任意分割算法及曲线间 G1拼接的几何条件 .所得结论具有明确的几何意义 ,有效地增强了 C- Bézier方法控制及表达曲线形状的能力 ,并可进一步推广到 C-

C Bézier curves are an extension of cubic Bézier curves. In addition to having many properties that Bézier curves have, they have the adjustable shape parameter α , and can represent arcs precisely. This paper presents the subdivision algorithm and G 1 condition of C Bézier curves based on the analysis of C Bézier basis functions and terminal properties. The results have definite geometric meanings that are useful for the shape modification and representation of C Bézier curves. The results can also be extended to surface modeling with C Bézier.