平面双线性映射的伸缩率分析  

Analysis of Dilatation of Planar Bilinear Mapping

作　　者：李倩 王旭辉[1] LI Qian;WANG Xu-hui(School of Mathematics, Hefei University of Technology, Hefei 230601, China)

机构地区：[1]合肥工业大学数学学院,合肥230601

出　　处：《大学数学》2021年第5期1-8,共8页College Mathematics

基　　金：国家自然科学基金项目(61772167)。

摘　　要：拟共形映射能较好地保持角度,在形状编辑等几何处理领域有着广泛应用.但该类映射不易构造,特别是复杂区域之间的拟共形映射构造,是一个困难且重要的问题.本文研究了一类简单的拟共形映射,即双线性映射,讨论了其伸缩率的分布情况,证明了伸缩率的最大值一定在四边形区域的顶点上取得.相关结论为复杂区域之间拟共形映射的构造提供了良好的理论基础.数值实验验证了结论的正确性.Quasi-conformal mapping can maintain angles well and is widely used in the field of geometric processing,e.g.,plane deformations.However,it is hard to construct a quasi-conformal mapping between two complex regions.Hence,it is a complex and important problem.The dilatation function of the bilinear mapping,which is a simple case of quasi-conformal mapping,is discussed.The dilatation function of a bilinear mapping attains its maximum at the corner of the quadrilateral.Numerical experiments verify the correctness of the conclusions.

关 键 词：拟共形映射 双线性函数 伸缩率函数 

分 类 号：O241[理学—计算数学]