摘要
为了解决造型设计中复杂曲线难以用单一曲线来表示的问题,研究了一种带形状参数的四次C-Bézier曲线的光滑拼接技术.在对四次C-Bézier曲线基函数及其端点性质分析的基础上,给出了两相邻四次C-Bézier曲线间G1、G2和C1、C2的光滑拼接的充要条件,同时还给出了两相邻四次C-Bézier曲线间光滑拼接的基本步骤和几何造型实例.实例结果表明,所提方法简单有效、易实现,极大地增强了四次C-Bézier曲线表达复杂曲线的能力,可广泛地应用于各种CG/CAD/CAID/CAM造型系统中.
To tackle the problem that the engineering complex curves can not be constructed by using a single curve,the continuity conditions of quartic C-Bézier curves with shape parameter are investigated.Based on the analysis of the basis functions and terminal properties,the necessary and sufficient conditions of G1 and G2 continuity,and C1 and C2 continuity between two adjacent quartic C-Bézier curves are proposed.In addition,some applications in quartic C-Bézier curves design are discussed.The modeling examples show that the proposed method is simple,effective and easy to implement,which greatly enhances the ability to constructing complex curve by using quartic C-Bézier curves.Hence,the continuity conditions of the quartic C-Bézier curves could be widely applied to the complex curves and surfaces modeling system.
出处
《陕西科技大学学报（自然科学版）》
2012年第5期113-117,共5页
Journal of Shaanxi University of Science & Technology
基金
陕西省自然科学基金项目(2011JM1006)
陕西省教育厅科研计划项目(11JK1052)
