No Folding Spherical Parameterization Of Closed Mesh

In this paper,we introduce a novel approach to no folding spherical parameterization method for closed genus-zero triangular mesh.Considering the complexity of solving the nonlinear equations by the global parameterization,we use the hemisphere as the parameter domain.The key to the parameterization of the hemisphere is how to find the appropriate line to ensure the validity of the parameterization.The traditional segmentation method is to divided the original mesh surface area into two parts 1and 2,which are approximately equal with each other.1and 2are unilateral bounded areas and disk-shaped,by the help of these poverties the complex spherical parameterization could turn into a Planar parameterization to get the solution.But this method may cause some folding of the parametric result.Based on this traditional method,we find a triangle area to ensure that each sub-mesh is less than half spherical surface,and we use the poverty that any great circle of spherical surface will be projected into straight line in gnomonic projection to extend the existing parametric method on the spherical surface.This method can avoid the folding and ensure the validity of spherical parameterization.At last the feasibility and effectiveness of the algorithm are verified by some model experiments.