Bijective spherical parametrization with low distortion.

Computing a bijective spherical parametrization of a genus-0 surface with low distortion is a fundamental task in geometric modeling and processing. Current methods for spherical parametrization cannot, in general, control the worst case distortion of all triangles nor guarantee bijectivity. Given an initial bijective spherical parametrization, with high distortion, we develop a non-linear constrained optimization problem to refine it, with objective penalizing the presence of triangles degeneration and maximal distortion. By using a dynamic adjusting parameter and a constrained, iterative inexact block coordinate descent optimization method, we efficiently and robustly achieve a bijective and low distortion parametrization with an optimal sphere radius. Compared to the state-of-the-art methods, our method is robust to initial parametrization and not sensitive to parameter choice. We demonstrate that our method produces excellent results on numerous models undergoing simple to complex shapes, in comparison to several state-of-the-art methods. Graphical abstractDisplay Omitted HighlightsWe introduce a simple method, including a parameter adjustment scheme and an alternately optimization method, to compute bijective parametrization with low distortion efficiently.Our method achieves both the lowest maximal distortion and average distortion in comparison to several state-of-the-art methods and the computation speed is comparable.Our method is robust to initial parametrization and not sensitive to parameter choice, which is demonstrated in a series of models undergoing simple to complex geometry.