3D triangular mesh optimization in geometry processing for CAD

Geometry processing in CAD proposes rigorous requirements on mesh quality. In this paper an integrated triangular mesh optimization method is proposed. Edge marking function and local edge operations are used to improve the vertex sampling. Modified weighted centroidal Voronoi tessellation is employed to regularize the triangle geometry. A simulated annealing algorithm is proposed for optimizing the vertex connectivity. Finally, a signal processing filter is developed for mesh denoising. In every optimization stage, the shape deviations from original mesh are prevented, and the boundaries and features are well preserved. Since all modifications are performed locally, the error-prone global parameterization is avoided. This technique has been deployed in real-world product design. Its advantage and robustness are verified by many examples implemented in the geometric design software PUM 2.0 developed by Peking University.

[1]  Martin Isenburg,et al.  Isotropic surface remeshing , 2003, 2003 Shape Modeling International..

[2]  Craig Gotsman,et al.  Explicit Surface Remeshing , 2003, Symposium on Geometry Processing.

[3]  David P. Dobkin,et al.  MAPS: multiresolution adaptive parameterization of surfaces , 1998, SIGGRAPH.

[4]  H.-P. Seidel,et al.  Dynamic remeshing and applications , 2003, SM '03.

[5]  Pierre Alliez,et al.  Isotropic Remeshing of Surfaces: A Local Parameterization Approach , 2003, IMR.

[6]  Daniel Cohen-Or,et al.  Bilateral mesh denoising , 2003 .

[7]  Günther Greiner,et al.  Remeshing triangulated surfaces with optimal parameterizations , 2001, Comput. Aided Des..

[8]  Mark Meyer,et al.  Implicit fairing of irregular meshes using diffusion and curvature flow , 1999, SIGGRAPH.

[9]  Ulrich Pinkall,et al.  Computing Discrete Minimal Surfaces and Their Conjugates , 1993, Exp. Math..

[10]  Leif Kobbelt,et al.  A remeshing approach to multiresolution modeling , 2004, SGP '04.

[11]  Paolo Cignoni,et al.  Metro: Measuring Error on Simplified Surfaces , 1998, Comput. Graph. Forum.

[12]  Gabriel Taubin,et al.  A signal processing approach to fair surface design , 1995, SIGGRAPH.

[13]  Frédo Durand,et al.  Non-iterative, feature-preserving mesh smoothing , 2003, ACM Trans. Graph..

[14]  Mark Meyer,et al.  Interactive geometry remeshing , 2002, SIGGRAPH.

[15]  Christian Rössl,et al.  Feature Sensitive Remeshing , 2001, Comput. Graph. Forum.

[16]  Hans-Peter Seidel,et al.  Mesh Smoothing by Adaptive and Anisotropic Gaussian Filter Applied to Mesh Normals , 2002, VMV.

[17]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[18]  Qiang Du,et al.  Centroidal Voronoi Tessellations: Applications and Algorithms , 1999, SIAM Rev..

[19]  Peter Schröder,et al.  Normal meshes , 2000, SIGGRAPH.

[20]  Steven J. Gortler,et al.  Geometry images , 2002, SIGGRAPH.

[21]  Jonathan Richard Shewchuk,et al.  What is a Good Linear Element? Interpolation, Conditioning, and Quality Measures , 2002, IMR.

[22]  H. Borouchaki,et al.  Geometric surface mesh optimization , 1998 .

[23]  Pierre Alliez,et al.  Anisotropic polygonal remeshing , 2003, ACM Trans. Graph..

[24]  M. Floater.  Mean value coordinates , 2003, Computer Aided Geometric Design.