Convex Combination Spherical Parameterization

Based on a linear convex combination of spherical vectors, a spherical parameterization method for genus-zero mesh and single boundary mesh is presented. Traditional approach to parameterize triangular mesh onto a planar domain is extended to spherical domain without cutting the mesh into charts. Various barycentric coordinates with convexity and shape-preserving property are introduced to compute the parameterization with low distortion. Existence and uniqueness of the spherical parameterization verified. The presented algorithm is simple and reliable despite of the complicated spherical geometry.