Abstract

We first derive a theoretical basis for spherical conformal parameterizations between a simply connected closed surface and a unit sphere by minimizing the Dirichlet energy on by stereographic projection. The Dirichlet energy can be rewritten as the sum of the energies associated with the southern and northern hemispheres and can be decreased under an equivalence relation by alternatingly solving the corresponding Laplacian equations. Based on this theoretical foundation, we develop a modified Dirichlet energy minimization with nonequivalence deflation for the computation of the spherical conformal parameterization between and .

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