Feature-preserving surface mesh smoothing via suboptimal Delaunay triangulation

• Published in: Graphical models Vol. 75; no. 1; pp. 23 - 38
• Main Authors: Gao, Zhanheng, Yu, Zeyun, Holst, Michael
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01-01-2013; Elsevier
• 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; Optimal Delaunay triangulation; Surface mesh denoising; Mesh quality improvement; Feature-preserving; Capability index; Linear interpolation; Error function; Delaunay triangulation; Quadratic programming; Automatic mesh generation; Computational geometry; Surface reconstruction; Smoothing; piecewise function; Computer aided design; Mesh generation; Mathematical programming
• ISSN: 1524-0703; 1524-0711
• DOI: 10.1016/j.gmod.2012.10.007

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► 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.