An Optimization of Square Parameterization

In order to parameterize a three-dimensional surface into a two-dimensional planar domain, we need to convert its polygonal mesh into a disk topology surface. For quality of texturing or re-meshing that uses a parameterization technique, it is more effective if the distortion of two-dimensional manifold planar domain map is as small as possible. Since square planar domain is easily understandable to human or very simple as a computer image file, it has been frequently used in real world applications. We introduce a series of experiments focusing on how to deliver an optimized square parameterization with low-cost calculation and stable result. The result of these experiments shows that our method is a suitable method for optimizing square parameterization.