三角网格曲面共形参数化研究综述

曲面参数化是计算机图形学和计算机辅助设计中的一个重要问题，有着广泛的应用背景。曲面 参数化旨在谋求从三维曲面到某参数区域变换过程中某些内蕴几何量(例如边长、角度、面积)的变形最小化。 保角参数化前后保持曲面局部形状，又称作共形参数化。本文针对三角网格曲面，介绍了共形参数化领域的研 究现状。根据目标参数域的不同，主要讨论了平面参数化、球面参数化和双曲空间参数化。最后总结了现阶段 共形参数化存在的难点问题和未来可能的研究方向。

Survey on triangular mesh surface conformal parameterization

Surface parameterization is a significant topic in computer graphics and computer-aided design, with a wide range of applications. Surface parameterization aims to seek the minimization of some intrinsic geometry distortion (such as edge length, angle, and area) from 3D surface to a parameterization plane transformation. Angle-preserving parameterization preserves the local shape of the surface before and after parameterization, also known as conformal parameterization. This survey introduced the recent progress on triangular mesh surface conformal parameterization from computer graphics application angle. Based on different parameter domains, it mainly discussed planar parameterization, spherical parameterization, and hyperbolic parameterization. Finally, this survey presented a list of open research problems and possible future research directions.