具有反射群对称性的球面图案自动生成

计算机工程与应用 ›› 2013, Vol. 49 ›› Issue (23): 27-30.

具有反射群对称性的球面图案自动生成

王新长1，2，刘满凤1，欧阳培昌2

1.江西财经大学信息管理学院，南昌 330013
2.井冈山大学数理学院，江西吉安 343009

出版日期:2013-12-01 发布日期:2016-06-12

Automatic generation of aesthetical spherical patterns

WANG Xinchang1，2, LIU Manfeng1, OUYANG Peichang2

1.School of Information Management, Jiangxi University of Finance and Economics, Nanchang 330013, China
2.School of Mathematics & Physics, Jinggangshan University, Ji’an, Jiangxi 343009, China

Online:2013-12-01 Published:2016-06-12

摘要/Abstract

摘要： 等变映射方法在生成艺术图案中具有构造困难，受对称群阶数瓶颈限制等缺点。借鉴有限反射群不变论的结论，提出不变映射方法生成具有正多面体反射群对称性的球面艺术图案，建立了一种可生成无穷无尽球面图案的自动化方法。该方法不仅实施容易，且可类似地推广到高维空间中。

关键词: 有限反射群, 正多面体, 不变论, 不变映射

Abstract: Equivariant mapping method is not only difficult to be implemented, but also constrained by the order of symmetry group. Drawn on the experience of the invariant theory of finite reflection group, this paper proposes an invariant mapping method to yield aesthetical spherical patterns and establishes a method to create infinite spherical patterns automatically. This method not only is easy to be implemented, but also can be extended to deal with the cases in the higher dimensional spaces.

Key words: finite reflection group, regular solids, invariant theory, invariant mapping

王新长1，2，刘满凤1，欧阳培昌2. 具有反射群对称性的球面图案自动生成[J]. 计算机工程与应用, 2013, 49(23): 27-30.

WANG Xinchang1，2, LIU Manfeng1, OUYANG Peichang2. Automatic generation of aesthetical spherical patterns[J]. Computer Engineering and Applications, 2013, 49(23): 27-30.