论文标题
使用准共构理论对多重连接表面进行有效的共形参数化
Efficient conformal parameterization of multiply-connected surfaces using quasi-conformal theory
论文作者
论文摘要
共形映射是复杂分析和差异几何形状中的经典主题，在近几十年来，在科学和工程中的各种应用中，在表面参数化领域引起了极大的兴趣。但是，大多数现有的共形参数化算法仅关注简单连接的表面，并且不能直接应用于带有孔的表面。在这项工作中，我们提出了两种新型算法，用于计算多连接表面的共形参数化。我们首先开发了一种有效的方法，用于将一个孔与一个孔一起在平面上的环上进行连接。然后，基于这种方法，我们开发了一种有效的方法，用于将带有$ K $孔的开放表面参数化到带有$ K $圆形孔的单位磁盘上。映射的映射的共形性和射击性是通过准共构理论确保的。提出了数值实验和应用，以证明所提出的方法的有效性。
Conformal mapping, a classical topic in complex analysis and differential geometry, has become a subject of great interest in the area of surface parameterization in recent decades with various applications in science and engineering. However, most of the existing conformal parameterization algorithms only focus on simply-connected surfaces and cannot be directly applied to surfaces with holes. In this work, we propose two novel algorithms for computing the conformal parameterization of multiply-connected surfaces. We first develop an efficient method for conformally parameterizing an open surface with one hole to an annulus on the plane. Based on this method, we then develop an efficient method for conformally parameterizing an open surface with $k$ holes onto a unit disk with $k$ circular holes. The conformality and bijectivity of the mappings are ensured by quasi-conformal theory. Numerical experiments and applications are presented to demonstrate the effectiveness of the proposed methods.
