Piecewise surface flattening for non-distorted texture mapping
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
SIAM Journal on Scientific and Statistical Computing
Shape transformation for polyhedral objects
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
MAPS: multiresolution adaptive parameterization of surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Non-distorted texture mapping for sheared triangulated meshes
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
How to morph tilings injectively
Journal of Computational and Applied Mathematics
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Texture mapping progressive meshes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Constrained texture mapping for polygonal meshes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Interactive geometry remeshing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Proceedings of the 29th 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
Smoothing an overlay grid to minimize linear distortion in texture mapping
ACM Transactions on Graphics (TOG)
Signal-specialized parametrization
EGRW '02 Proceedings of the 13th Eurographics workshop on Rendering
Bounded-distortion piecewise mesh parameterization
Proceedings of the conference on Visualization '02
Conformal Surface Parameterization for Texture Mapping
IEEE Transactions on Visualization and Computer Graphics
Computer Aided Geometric Design
Spherical parametrization and remeshing
ACM SIGGRAPH 2003 Papers
Fundamentals of spherical parameterization for 3D meshes
ACM SIGGRAPH 2003 Papers
A Fast and Simple Stretch-Minimizing Mesh Parameterization
SMI '04 Proceedings of the Shape Modeling International 2004
Computing Length-Preserved Free Boundary for Quasi-Developable Mesh Segmentation
IEEE Transactions on Visualization and Computer Graphics
A local/global approach to mesh parameterization
SGP '08 Proceedings of the Symposium on Geometry Processing
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The parameterization of a 3D mesh into a planar domain requires a distortion metric and a minimizing process. Most previous work has sought to minimize the average area distortion, the average angle distortion, or a combination of these. Typical distortion metrics can reflect the overall performance of parameterizations but discount high local deformations. This affects the performance of postprocessing operations such as uniform remeshing and texture mapping. This paper introduces a new metric that synthesizes the average distortions and the variances of both the area deformations and the angle deformations over an entire mesh. Experiments show that, when compared with previous work, the use of synthesized distortion metric performs satisfactorily in terms of both the average area deformation and the average angle deformation; furthermore, the area and angle deformations are distributed more uniformly. This paper also develops a new iterative process for minimizing the synthesized distortion, the coefficient-optimizing algorithm. At each iteration, rather than updating the positions immediately after the local optimization, the coefficient-optimizing algorithm first update the coefficients for the linear convex combination and then globally updates the positions by solving the Laplace system. The high performance of the coefficient-optimizing algorithm has been demonstrated in many experiments.