标题： 半球形参数化和单连通开曲面的调和分解 显示英文标题

标题： Hemispheroidal parameterization and harmonic decomposition of simply connected open surfaces

摘要： 谱分析在开放曲面中的应用正在工程、计算机图形学和医学领域中逐渐兴起，用于研究表面形貌。 这种分析是通过在目标分析域上使用适当的参数化方法实现的。 在本文中，我们提出使用可定制的参数化坐标，这些坐标允许将开放曲面映射到扁球或长球半球面上。 为此，我们提出了使用Tutte映射、共形映射、面积保持映射和平衡映射，将任何给定的单连通开放曲面参数化到最优半球面上。 引入了半球面谐波基函数，通过推广已知的半球面基函数来对这些参数化曲面进行谱展开。 该方法利用半球面的半径作为自由度，以控制开放曲面参数化域的大小，同时提供数值稳定的基函数。 使用不同的映射组合对多个开放曲面进行了测试。 我们还提出了基于优化的映射，以服务于重建问题的各种应用。 总之，我们的工作为表示和分析单连通开放曲面提供了一种有效的方法。 显示英文摘要

摘要： Spectral analysis of open surfaces is gaining momentum for studying surface morphology in engineering, computer graphics, and medical domains. This analysis is enabled using proper parameterization approaches on the target analysis domain. In this paper, we propose the usage of customizable parameterization coordinates that allow mapping open surfaces into oblate or prolate hemispheroidal surfaces. For this, we proposed the usage of Tutte, conformal, area-preserving, and balanced mappings for parameterizing any given simply connected open surface onto an optimal hemispheroid. The hemispheroidal harmonic bases were introduced to spectrally expand these parametric surfaces by generalizing the known hemispherical ones. This approach uses the radius of the hemispheroid as a degree of freedom to control the size of the parameterization domain of the open surfaces while providing numerically stable basis functions. Several open surfaces have been tested using different mapping combinations. We also propose optimization-based mappings to serve various applications on the reconstruction problem. Altogether, our work provides an effective way to represent and analyze simply connected open surfaces.