High-quality 2D mesh generation without obtuse and small angles

Khan, Dawar; Yan, Dong‐Ming; Wang, Yiqun; Hu, Kaimo; Ye, Juntao; Zhang, Xiaopeng

doi:10.1016/j.camwa.2017.09.041

Cited by 8 publications

(25 citation statements)

References 23 publications

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“…We select CVT for initialization since it provides a smooth distribution of the vertices in an efficient manner avoiding the major defects. Various methods including [1,[39][40][41] have used CVT either for initializations or to improve it.…”

Section: Initializationmentioning

confidence: 99%

“…10 Making a hole (to be refilled) for obtuse triangle (red color) removal In addition to vertex translation, we also use hole-filling strategy in pentagonal structures to minimize the ratio of obtuse triangles. Inspired by a recent 2D non-obtuse remeshing method [40], we design pentagonal structures around each obtuse triangle [see Fig. 10 (left)].…”

Section: Maximal Angle Improvementmentioning

confidence: 99%

“…Figure 11 shows an example of pentagonal structure design and point insertions for obtuse removal. Unlike 2D meshing [40], we use surface normal to ensure the three triangles are on the same plane. Our method easily eliminates all angles greater than or equal to 120 • and also significantly reduces the ratio of obtuse triangles.…”

Section: Maximal Angle Improvementmentioning

confidence: 99%

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Valence optimization and angle improvement for molecular surface remeshing

et al. 2020

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Molecular surface mesh generation plays a vital role in molecular modeling and visualization. However, meshes extracted directly from Protein Data Bank files have several issues such as small and large triangles, redundant elements, selfintersections, and irregular vertices. The state-of-the-art mesh improvement methods often fail to deal with these issues. In this paper, we present a novel method for valence optimization and angle improvement. For valence optimization, we remove the bad valence vertices with its neighbor triangle making regular holes in the mesh. The holes are filled in a careful manner to improve their valences as well as angle quality. We also use a segmentation-based surface remeshing which segments the mesh into random segments and then each segment is independently remeshed. In addition, a point insertion scheme is applied to minimize the ratio of obtuse triangles. Experimental results show that our method not only improves the maximal and minimal angles to an angle bound of [30 • 120 • ] but also improves the vertices' regularity, reduces the ratio of obtuse triangles, preserves the area and volume, and always succeeds with downstream applications.

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Section: Initializationmentioning

confidence: 99%

Section: Maximal Angle Improvementmentioning

confidence: 99%

Section: Maximal Angle Improvementmentioning

confidence: 99%

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Valence optimization and angle improvement for molecular surface remeshing

et al. 2020

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“…Geometric objects are typically converted to meshes for efficient rendering and numerical solution of partial differential equations. Therefore, mesh generation becomes one of the essential steps for most geometry processing applications [65].…”

Section: Mesh Generation and Surface Remeshing Mesh Generationmentioning

confidence: 99%

“…The main objective of quality meshing is to improve different quality parameters. The parameters used for meshing quality measurements in previous papers [55,65,66,73] are described in the following. The triangle quality calculated for a triangle t is used for the mesh quality analysis which is given as…”

Section: Meshing Quality Measurementsmentioning

confidence: 99%

Frontiers in biomolecular mesh generation and molecular visualization systems

Gui

Khan

Wang

et al. 2018

Vis. Comput. Ind. Biomed. Art

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With the development of biomolecular modeling and simulation, especially implicit solvent modeling, higher requirements are set for the stability, efficiency and mesh quality of molecular mesh generation software. In this review, we summarize the recent works in biomolecular mesh generation and molecular visualization. First, we introduce various definitions of molecular surface and corresponding meshing software. Second, as the mesh quality significantly influences biomolecular simulation, we investigate some remeshing methods in the fields of computer graphics and molecular modeling. Then, we show the application of biomolecular mesh in the boundary element method (BEM) and the finite element method (FEM). Finally, to conveniently visualize the numerical results based on the mesh, we present two types of molecular visualization systems.

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Accelerating surface remeshing through GPU-based computation of the restricted tangent face

Yao

Liu

et al. 2023

Computer Aided Geometric Design

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High-quality 2D mesh generation without obtuse and small angles

Cited by 8 publications

References 23 publications

Valence optimization and angle improvement for molecular surface remeshing

Valence optimization and angle improvement for molecular surface remeshing

Frontiers in biomolecular mesh generation and molecular visualization systems

Accelerating surface remeshing through GPU-based computation of the restricted tangent face

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