共查询到19条相似文献,搜索用时 62 毫秒
1.
平面三次H-Bézier曲线的形状分析 总被引:6,自引:0,他引:6
本文对平面三次H-Bézier曲线的形状进行分析,讨论其诸如奇点、拐点、局部凸和全局凸的几何特征,得出曲线上含有奇点、拐点和曲线为局部凸或全局凸的用控制多边形边向量相对位置表示的充分必要条件. 相似文献
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基于包络理论与拓扑映射的方法对四次带参Ball曲线进行了形状分析,得出了曲线上含有奇点,拐点和曲线为局部凸或全局凸的充分必要条件,这些条件完全由控制多边形和形状参数所决定;并进一步讨论了形状参数对形状分布图的影响及其对曲线形状的调节能力.研究表明,四次带参Ball曲线的形状调控能力要优于四次带参Bezier曲线. 相似文献
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关于平面四次Bézier曲线的拐点与奇点 总被引:1,自引:0,他引:1
在计算几何中,已给出了三次Bezier曲线的保凸性的充要条件,并进行了几何解释。本文则是导出形式简洁的拐点和奇点方程并对四次Bezier曲线的拐点和奇点的分布进行讨论。按Bezier曲线的拐点个数进行分类,还得到了四次Bezier曲线有奇点的充分必要条件,并给出几个数值实例,实例说明,不但非凸的单纯特征多角形可以有凸的Bezier曲线段,而且非单纯特征多角形也可以有凸的Bezier曲线段。四次Bezier曲线的奇点和拐点是可以共存的。 相似文献
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王国瑾 《高校应用数学学报(A辑)》1997,(1):1-8
本文用计算几何学的观点对A.A.Ball在前英车航空公司研制成功的CONSURF系统进行分析,证明了这一系统的机身造型曲线具有包络性质,分段性质,变差缩减性质,奇点拐点分布性质和保凸性质。 相似文献
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平面C-Bézier曲线的奇拐点分析 总被引:8,自引:0,他引:8
本文完全地讨论了平面C-曲线和平面C-Bezier曲线的奇拐点和凸性性质:曲线段为且必为下列情形之一:有一各拐点,两个拐点,一个尖点,一个二重结点,处处为凸;并给出了相应的用控制多边形相对位置表示的充分必要条件. 相似文献
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局部凸空间的K强凸性与K强光滑性 总被引:3,自引:0,他引:3
首先引进了局部凸空间K强凸性的概念,它既是Banach空间K强凸性概念在局部凸空间中的推广,又是局部凸空间强凸性概念的自然推广;其次给出了局部凸空间K强凸性概念的对偶概念,即局部凸空间K强光滑性的概念,并得到了K强凸(K强光滑)的局部凸空间的特征刻画;最后,在P-自反的条件下给出了它们之间的对偶定理,即(X,TP)是K强凸(K强光滑)的当且仅当(X′,TP′)是K强光滑(K强凸)的. 相似文献
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梁奇伟 《数学的实践与认识》1987,(1)
<正> 由[1]可得出平面上正算参数三次均匀 B 样条曲线出现奇点和拐点的充要条件.据已知顶点 V 直接算出曲线值 C 的参数三次均匀 B 样条曲线方程 相似文献
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关于五次有理曲线的注记 总被引:2,自引:0,他引:2
前言 在前文[1]中,我们阐述了三次参数样条曲线的一些性质其中包括这种曲线必定是三次有理整曲线。本文将讨论五次参数样条曲线的类似性质,主要是关于奇点(包括二重点和尖点)以及拐点的性质。一般,n次参数有理整曲线都是n次代数曲线,它具有1/2(n-1)(n-2)个奇点和(2n-4)个拐点(虚点也算在内)。在第一节证明,五次参数样条有理整曲线段通过其两端有关参数适当的调整,常常可使原来具有六个拐点的曲 相似文献
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M.Beltagy 《数学物理学报(B辑英文版)》1995,(3)
LOCALANDGLOBALEXPOSEDPOINTSM.Beltagy(MathematicsDepartment,FacultyofScienceTantaUniversity,Egypt.)Abstract:Inthispaperwederiv... 相似文献
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T. Lachand-Robert M. A. Peletier 《Proceedings of the American Mathematical Society》1999,127(6):1723-1727
We investigate the extremal points of a functional , for a convex or concave function . The admissible functions are convex themselves and satisfy a condition . We show that the extremal points are exactly and if these functions are convex and coincide on the boundary . No explicit regularity condition is imposed on , , or . Subsequently we discuss a number of extensions, such as the case when or are non-convex or do not coincide on the boundary, when the function also depends on , etc.
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On the Coefficients of Some Subclasses of Univalent Functions 总被引:1,自引:0,他引:1
H. E. Darwish 《Southeast Asian Bulletin of Mathematics》2001,25(1):75-86
In this paper we consider the class Lc*(,,) consisting of analytic and univlent functions with negative coefficients and with fixed second coefficient. The object of the present paper is to show coefficient estimates, convex linear combinations, some distortion theoems and radii of starlikeness and convexity for f(z) in the class Lc*(,,). The results are generalized to families with finitely many fixed coefficients.AMS Subject Classification (1991) 30C45 相似文献
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Monika Budzynska 《Proceedings of the American Mathematical Society》2003,131(9):2771-2777
If is the open unit ball in the Cartesian product furnished with the -norm , where and , then a holomorphic self-mapping of has a fixed point if and only if for some
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C. Singh 《Journal of Optimization Theory and Applications》1981,33(2):287-294
Optimality conditions of Kuhn-Tucker and Fritz John, with and without differentiability requirements, are established for a nonlinear fractional programming problem. The transformation introduced by Manas and Schaible plays a key role. 相似文献
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Charles D. Horvath 《Topology and its Applications》2008,155(8):830-850
A convexity on a set X is a family of subsets of X which contains the whole space and the empty set as well as the singletons and which is closed under arbitrary intersections and updirected unions. A uniform convex space is a uniform topological space endowed with a convexity for which the convex hull operator is uniformly continuous. Uniform convex spaces with homotopically trivial polytopes (convex hulls of finite sets) are absolute extensors for the class of metric spaces; if they are completely metrizable then a continuous selection theorem à la Michael holds. Upper semicontinuous maps have approximate selections and fixed points, under the usual assumptions. 相似文献
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The aim of this paper is to prove the existence of equilibrium for generalized games or abstract economies in contexts where the convexity conditions on strategy spaces and preference correspondences are relaxed and an arbitrary number of agents is considered. The results are based on a fixed-point theorem in which the convexity condition on sets and images of correspondences is replaced by a general notion of abstract convexity, called mc-spaces, generalizing the notions of simplicial convexity, H-spaces, and G-convex spaces. 相似文献
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In this paper, necessary and sufficient conditions for solvability of nonlinear inequality systems are given using certain generalized convexity concepts. Our results imply some theorems of Kirszbraun, Fan, Minty, Simons, Sebestyén, and Gwinner-Oettli.The authors are grateful to the referees for their helpful comments. They thank one of the referees, who emphasized the connection between the Wald minimax theorem and Theorem 2.1, and suggested an alternative proof of Theorem 2.1 in Section 4. 相似文献