三角Bézier曲面快速求交算法  

Efficient Algorithm Getting Intersection Curves for Triangular Bézier Surface

作　　者：孙殿柱[1] 康新才[1] 李延瑞[1] 刘健[1] 

机构地区：[1]山东理工大学机械工程学院,淄博255091

出　　处：《机械工程学报》2011年第3期89-94,共6页Journal of Mechanical Engineering

基　　金：山东省自然科学基金(ZR2010EM008);国家自然科学基金(51075247)资助项目

摘　　要：提出一种三角Bézier曲面快速求交算法,该算法采用R*S-树建立三角Bézier曲面的动态空间索引结构,基于该索引结构快速获取相交区域三角Bézier曲面片集,通过设定离散精度阀值,在逼近精度允许范围内将相交三角Bézier曲面片均匀离散为三角网格,采用R*S-树建立离散后三角网格的动态空间索引结构,通过网格单元间的求交获取交线数据,进而通过查询共端点交线数据跟踪提取三角Bézier曲面的完整交线,实例证明该算法在逼近精度允许范围内可快速、准确获取任意复杂三角Bézier曲面交线,并通过三角Bézier曲面模型的数控刀轨生成验证了该算法的实用性。An algorithm of rapidly getting intersection curves for triangular Bézier surface is proposed,which includes four steps.The intersection regions are obtained rapidly based on the dynamic spatial indexing structure named R＊S-tree of triangular Bézier surface models,so that the sets of intersection triangular Bézier patches are located exactly.Each Bézier patch is subdivided into many triangular planar patches in the scope of the precision by setting the discrete precision.The intersection line data is obtained through the intersection of triangular planar patches.The intersection curves are obtained by tracking extraction of intersection lines which have the common end point on line segments.The experimental results show that the algorithm can obtain the exact intersection curves of two complex triangular Bézier surface models rapidly,and it is proved to be applicable through generating NC tool path for triangular Bézier surface based on this algorithm.

关 键 词：三角BÉZIER曲面 R＊S-树 均匀离散 跟踪提取 曲面求交 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]