Delaunay mesh simplification with differential evolution
Delaunay meshes (DM) are a special type of manifold triangle meshes --- where the local Delaunay condition holds everywhere --- and find important applications in digital geometry processing. This paper addresses the general DM simplification problem: given an arbitrary manifold triangle mesh M with...
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sg-ntu-dr.10356-1447502020-11-23T06:27:08Z Delaunay mesh simplification with differential evolution Yi, Ran Liu, Yong-Jin He, Ying School of Computer Science and Engineering Engineering::Computer science and engineering Computing Methodologies Computer Graphics Delaunay meshes (DM) are a special type of manifold triangle meshes --- where the local Delaunay condition holds everywhere --- and find important applications in digital geometry processing. This paper addresses the general DM simplification problem: given an arbitrary manifold triangle mesh M with n vertices and the user-specified resolution m (< n), compute a Delaunay mesh M* with m vertices that has the least Hausdorffdistance to M. To solve the problem, we abstract the simplification process using a 2D Cartesian grid model, in which each grid point corresponds to triangle meshes with a certain number of vertices and a simplification process is a monotonic path on the grid. We develop a novel differential-evolution-based method to compute a low-cost path, which leads to a high quality Delaunay mesh. Extensive evaluation shows that our method consistently outperforms the existing methods in terms of approximation error. In particular, our method is highly effective for small-scale CAD models and man-made objects with sharp features but less details. Moreover, our method is fully automatic and can preserve sharp features well and deal with models with multiple components, whereas the existing methods often fail. This work is supported by the National Science Foundation of China (61725204, 61432003, 61521002 and 61661130156) and the Royal Society-Newton Advanced Fellowship (NA150431). 2020-11-23T06:27:08Z 2020-11-23T06:27:08Z 2018 Journal Article Yi, R., Liu, Y.-J., & He, Y. (2018). Delaunay mesh simplification with differential evolution. ACM Transactions on Graphics, 37(6), 263-. doi:10.1145/3272127.3275068 0730-0301 https://hdl.handle.net/10356/144750 10.1145/3272127.3275068 6 37 en ACM Transactions on Graphics © 2018 Copyright held by the owner/author(s). Publication rights licensed to ACM. |
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Engineering::Computer science and engineering Computing Methodologies Computer Graphics Yi, Ran Liu, Yong-Jin He, Ying Delaunay mesh simplification with differential evolution |
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Delaunay meshes (DM) are a special type of manifold triangle meshes --- where the local Delaunay condition holds everywhere --- and find important applications in digital geometry processing. This paper addresses the general DM simplification problem: given an arbitrary manifold triangle mesh M with n vertices and the user-specified resolution m (< n), compute a Delaunay mesh M* with m vertices that has the least Hausdorffdistance to M. To solve the problem, we abstract the simplification process using a 2D Cartesian grid model, in which each grid point corresponds to triangle meshes with a certain number of vertices and a simplification process is a monotonic path on the grid. We develop a novel differential-evolution-based method to compute a low-cost path, which leads to a high quality Delaunay mesh. Extensive evaluation shows that our method consistently outperforms the existing methods in terms of approximation error. In particular, our method is highly effective for small-scale CAD models and man-made objects with sharp features but less details. Moreover, our method is fully automatic and can preserve sharp features well and deal with models with multiple components, whereas the existing methods often fail. |
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School of Computer Science and Engineering |
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School of Computer Science and Engineering Yi, Ran Liu, Yong-Jin He, Ying |
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Article |
author |
Yi, Ran Liu, Yong-Jin He, Ying |
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Yi, Ran |
title |
Delaunay mesh simplification with differential evolution |
title_short |
Delaunay mesh simplification with differential evolution |
title_full |
Delaunay mesh simplification with differential evolution |
title_fullStr |
Delaunay mesh simplification with differential evolution |
title_full_unstemmed |
Delaunay mesh simplification with differential evolution |
title_sort |
delaunay mesh simplification with differential evolution |
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2020 |
url |
https://hdl.handle.net/10356/144750 |
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1688665573530009600 |