  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.

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