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
Geometric modeling based on triangle meshes
ACM SIGGRAPH 2006 Courses
An image processing approach to surface matching
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
Restoring 2D Content from Distorted Documents
IEEE Transactions on Pattern Analysis and Machine Intelligence
Local versus Global in Quasi-Conformal Mapping for Medical Imaging
Journal of Mathematical Imaging and Vision
Edge based parameterization for tubular meshes
VRCAI '08 Proceedings of The 7th ACM SIGGRAPH International Conference on Virtual-Reality Continuum and Its Applications in Industry
A variational approach for automatic generation of panoramic maps
ACM Transactions on Graphics (TOG)
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
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For a surface patch on a smooth, two-dimensional surface in R3, 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.