@ARTICLE{ClLiRu04, author = {Clarenz, Ulrich and Litke, Nathan and Rumpf, Martin}, title = {Axioms and Variational Problems in Surface Parameterization}, journal = {Comput. Aided Geom. Design}, year = {2004}, volume = {21}, pages = {727--749}, number = {8}, abstract = {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.}, pdf = {http://numod.ins.uni-bonn.de/research/papers/public/ClLiRu04.pdf}, fjournal = {Computer Aided Geometric Design} }