平面三次混合双曲多项式曲线的特征图判别  

On the Characterization Diagrams of Planar Cubic Hybrid Hyperbolic Polynomial Curve

作　　者：魏永伟[1,2] 曹娟[3] 汪国昭[1] 

机构地区：[1]浙江大学数学系计算机图象图形研究所,杭州310027 [2]上海海事大学应用数学系,上海201306 [3]厦门大学数学科学学院,厦门361005

出　　处：《计算机辅助设计与图形学学报》2010年第5期833-837,共5页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(60773179;60970079;60933008)

摘　　要：根据文献[9](Wang G Z,Yang Q M.Planar cubic hybrid hyperbolic polynomial curve and its shape classification.Progress in Natural Science,2004,14(1):41-46)中提出的H-曲线带奇点或拐点的条件,利用H-曲线奇点、拐点的仿射不变性,给出H-曲线几何特征图的判别法,并找到了不同特征图在三维空间中的关系.该判别法完善了H-曲线的奇异点检测理论,提升了几何特征图维数.In this paper,we propose the geometric characterization diagrams of planar cubic H-curves based on the conditions of singularities for planar cubic H-curves presented by Reference（Wang G Z,Yang Q M.Planar cubic hybrid hyperbolic polynomial curve and its shape classification.Progress In Natural Science,2004,14（1）： 41-46） Since inflection points and singularities（loops or cusps） of curves are affinely invariant,we find out the geometrically intuitive relationship of these different geometric characterization diagrams in a common 3-dimension characterization space.This approach completes the theory of detecting singularities of H-curves in the point of elevating geometric characterization diagrams dimension.

关 键 词：平面三次混合双曲多项式曲线 H-曲线 H-Bézier曲线 特征图 奇点 拐点 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]