Quasi-isometric surface parameterization

Parameterization of surface is defined by a one-to-one mapping from a planar domain to the surface. Well established methods based on harmonic, conformal and quasi-conformal mappings may create parameterizations with singularities. Singularity-free parameterization technique is suggested based on the concept of quasi-isometric mappings. Well-posed variational formulations for quasi-isometric parameterizations are discussed based on existence theory for hyperelasticity. Distortion minimization, invariance and mesh independence are discussed with numerical examples. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.