Feature-preserving surface mesh smoothing via suboptimal Delaunay triangulation

[Display omitted] ► We develop a novel method for triangular surface mesh quality improvement. ► Our method also has capabilities of removing noise and preserving sharp features. ► Our method is proved to preserve volumes for smooth and closed meshes. A method of triangular surface mesh smoothing is...

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Bibliographic Details
Published in:Graphical models 2013-01, Vol.75 (1), p.23-38
Main Authors: Gao, Zhanheng, Yu, Zeyun, Holst, Michael
Format: Article
Language:English
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Approximation
Artificial intelligence
Computer aided design
Computer graphics
Computer science
control theory
systems
Delaunay triangulation
Exact sciences and technology
Exact solutions
Feature-preserving
Finite element method
Interpolation
Mesh quality improvement
Optimal Delaunay triangulation
Optimization
Pattern recognition. Digital image processing. Computational geometry
Smoothing
Software
Surface mesh denoising
Theoretical computing
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Summary:[Display omitted] ► We develop a novel method for triangular surface mesh quality improvement. ► Our method also has capabilities of removing noise and preserving sharp features. ► Our method is proved to preserve volumes for smooth and closed meshes. A method of triangular surface mesh smoothing is presented to improve angle quality by extending the original optimal Delaunay triangulation (ODT) to surface meshes. The mesh quality is improved by solving a quadratic optimization problem that minimizes the approximated interpolation error between a parabolic function and its piecewise linear interpolation defined on the mesh. A suboptimal problem is derived to guarantee a unique, analytic solution that is significantly faster with little loss in accuracy as compared to the optimal one. In addition to the quality-improving capability, the proposed method has been adapted to remove noise while faithfully preserving sharp features such as edges and corners of a mesh. Numerous experiments are included to demonstrate the performance of the method.
ISSN:1524-0703
1524-0711
DOI:10.1016/j.gmod.2012.10.007