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.