Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Direct methods in the calculus of variations
Direct methods in the calculus of variations
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
On the Nonlinear Inexact Uzawa Algorithm for Saddle-Point Problems
SIAM Journal on Numerical Analysis
Texture mapping progressive meshes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Least squares conformal maps for automatic texture atlas generation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Bounded-distortion piecewise mesh parameterization
Proceedings of the conference on Visualization '02
Computer Aided Geometric Design
Multilevel Solvers for Unstructured Surface Meshes
SIAM Journal on Scientific Computing
ACM SIGGRAPH Asia 2009 papers
Computing Extremal Quasiconformal Maps
Computer Graphics Forum
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For a surface patch on a smooth, two-dimensional surface in R^3, 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.