Improved Mesh Processing using Distorted Pole Spherical Coordinates

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.