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Surface parameterization plays a fundamental role in many science andengineering problems. In particular, as genus-0 closed surfaces aretopologically equivalent to a sphere, many spherical parameterization methodshave been developed over the past few decades. However, in practice, mapping agenus-0 closed surface onto a sphere may result in a large distortion due totheir geometric difference. In this work, we propose a new framework forcomputing ellipsoidal conformal and quasi-conformal parameterizations ofgenus-0 closed surfaces, in which the target parameter domain is an ellipsoidinstead of a sphere. By combining simple conformal transformations withdifferent types of quasi-conformal mappings, we can easily achieve a largevariety of ellipsoidal parameterizations with their bijectivity guaranteed byquasi-conformal theory. Numerical experiments are presented to demonstrate theeffectiveness of the proposed framework.

Fast ellipsoidal conformal and quasi-conformal parameterization of genus-0 closed surfaces