Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
Acoustics Scattering on Arbitrary Manifold Surfaces
GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
Particle-based Sampling and Meshing of Surfaces in Multimaterial Volumes
IEEE Transactions on Visualization and Computer Graphics
Delaunay Refinement for Piecewise Smooth Complexes
Discrete & Computational Geometry
Feature preserving Delaunay mesh generation from 3D multi-material images
SGP '09 Proceedings of the Symposium on Geometry Processing
Tetrahedral mesh generation for medical images with multiple regions using active surfaces
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
Meshing interfaces of multi-label data with Delaunay refinement
Engineering with Computers
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This paper presents an efficient and novel geometric flow-driven method for mesh optimization of multi-component tetrahedral meshes with non-manifold boundaries. The presented method is composed of geometric optimization and topological transformation techniques, so that both location and topology of mesh vertices are optimized. Due to the complexity of non-manifold boundaries, we categorize the boundary vertices into three groups: surface vertices, curve vertices, and fixed vertices. Each group of boundary vertices is modified by different shape-preserving geometric flows in order to smooth and regularize boundary meshes. Meanwhile, all vertices are relocated by minimizing an energy functional which is relevant to the quality measure of tetrahedra. In addition, face-swapping and edge-removal operations are employed to eliminate poorly-shaped elements. Finally, the performance of our method is compared with a state of the art technique, named Stellar, for a dozen single-component meshes. We obtain similar or even better results with much less running time. Moreover, we validate the presented method on several multi-component tetrahedral meshes, and the results demonstrate that the mesh quality is improved significantly.