Uniform Quasi-Conformal Spherical Parameterization

This paper presents a novel spherical parameterization method for closed genus-zero triangular mesh or single boundary genus-zero triangular mesh.An initial spherical parameterization is firstly constructed by lifting planar parameterization to the sphere through the stereographic projection.Then we introduce an efficient approach based on bary centric coordinate to improve the initial spherical parameterization.At last,a uniform spherical parameterization is generated by a Moebius transformation.Our method can avoid fold-overs by the stereographic projection and always yields bijective mappings.Experiments and comparisons are taken with representative 3D meshes,which reveals that our approach has low distortion,and it has also obvious improvement in uniform texture mapping for complicated meshes than available conformal mapping methods and authalic mapping methods.