The Cartesian coordinate system is the most commonly used system in computer visualization. This is due to its ease of use and processing speed. However, it is not always suitable for a given problem. Angular measures often allow us to operate more efficiently on a three-dimensional model. When dealing with issues related to the processing of three-dimensional objects described using polygon meshes, it often happens that these standard systems do not satisfy specific properties that are crucial to us. The topic of the paper is to discuss a specific transformation to spherical coordinates with distorted poles, which allows us to eliminate singular points from the determined subset of the mesh and bypass inconvenient seam lines in its two-dimensional projection, which can hinder further calculations.

翻译：笛卡尔坐标系是计算机可视化中最常用的坐标系，这得益于其易用性和处理速度。然而，它并不总能适用于特定问题。角度度量通常使我们能够更高效地处理三维模型。当处理基于多边形网格描述的三维对象的相关问题时，这些标准坐标系往往无法满足对我们至关重要的特定属性。本文的主题是讨论一种特定的畸变极点球坐标变换，该变换能够从网格的确定子集中消除奇异点，并避开其二维投影中可能阻碍后续计算的不便接缝线。