Axioms and variational problems in surface parameterization

For a surface patch on a smooth, two-dimensional surface in IR, low-distortion parameterizations are described in terms of minimizers of suitable energy functionals. Appropriate distortion measures are derived from principles of rational mechanics, closely related to the theory of non-linear elasticity. The parameterization can be optimized with respect to the varying importance of conformality, length preservation and area preservation. A finite element discretization is introduced and a constrained Newton method is used to minimize a corresponding discrete energy. Results of the new approach are compared with other recent parameterization methods.