Axioms and variational problems in surface parameterization

For a surface patch on a smooth, two-dimensional surface in IR3 , 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. Key words: Surface Parameterization, Non-linear Elasticity, Variational Methods, Finite Element Methods

• Type: Journal
• Year: 2004
• Where: CAGD
• Authors: Ulrich Clarenz, Nathan Litke, Martin Rumpf
• Keywords: CAGD 2004, Finite Element, Non-linear Elasticity, Suitable Energy Functionals