ACM Transactions on Graphics (TOG)
Mesh Smoothing Using A Posteriori Error Estimates
SIAM Journal on Numerical Analysis
Smoothing an overlay grid to minimize linear distortion in texture mapping
ACM Transactions on Graphics (TOG)
Computer Aided Geometric Design
Globally smooth parameterizations with low distortion
ACM SIGGRAPH 2003 Papers
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Mesh smoothing (or r-refinement) are used in computer aided design, interpolation, numerical solution of partial differential equations, etc. We derive a new smoothing called parallelogram smoothing. The new smoothing tries to fit a given domain by the parallelograms. We present several numerical examples and compare our results against the traditional Laplacian smoothing. Presented numerical work shows that the new approach is superior to the Laplacian smoothing.