椭圆密度等化映射用于亏格为0的闭合曲面
Ellipsoidal Density-Equalizing Map for Genus-0 Closed Surfaces
AI总结：
本文提出了一种用于亏格为0闭合曲面的椭圆密度等化映射方法，通过能量最小化结合密度等化和准共形映射，实现面积保持或可控面积变化的参数化，提升曲面重新网格化性能。
摘要：
曲面参数化是几何处理中的基本任务，在许多科学和工程应用中起重要作用。近年来，基于密度扩散物理原理的密度等化映射技术已被用于简单连通和多重连通开放曲面的参数化。更近期，一种球形密度等化映射方法已被开发用于亏格为0的闭合曲面参数化。然而，对于具有极端几何的亏格为0闭合曲面，使用球形域进行参数化可能会引起较大的几何失真。在本工作中，我们开发了一种新的方法，用于将亏格为0的闭合曲面计算到椭球域上的密度等化映射。这使我们能够实现椭球面积保持参数化和具有可控面积变化的椭球参数化。我们进一步提出了一种能量最小化方法，结合密度等化映射和准共形映射，从而产生椭球密度等化准共形映射，以在密度等化和准共形性之间取得平衡。使用我们提出的方法，我们能够显著提高亏格为0闭合曲面的表面重新网格化性能。在大量不同亏格为0闭合曲面上的实验结果展示了我们提出方法的有效性。
英文摘要：
Surface parameterization is a fundamental task in geometry processing and plays an important role in many science and engineering applications. In recent years, the density-equalizing map, a shape deformation technique based on the physical principle of density diffusion, has been utilized for the parameterization of simply connected and multiply connected open surfaces. More recently, a spherical density-equalizing mapping method has been developed for the parameterization of genus-0 closed surfaces. However, for genus-0 closed surfaces with extreme geometry, using a spherical domain for the parameterization may induce large geometric distortion. In this work, we develop a novel method for computing density-equalizing maps of genus-0 closed surfaces onto an ellipsoidal domain. This allows us to achieve ellipsoidal area-preserving parameterizations and ellipsoidal parameterizations with controlled area change. We further propose an energy minimization approach that combines density-equalizing maps and quasi-conformal maps, which allows us to produce ellipsoidal density-equalizing quasi-conformal maps for achieving a balance between density-equalization and quasi-conformality. Using our proposed methods, we can significantly improve the performance of surface remeshing for genus-0 closed surfaces. Experimental results on a large variety of genus-0 closed surfaces are presented to demonstrate the effectiveness of our proposed methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
