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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Main Authors: Yi, Ran, Liu, Yong-Jin, He, Ying
Other Authors: School of Computer Science and Engineering
Format: Article
Language:English
Published: 2020
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Online Access:https://hdl.handle.net/10356/144750
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Institution: Nanyang Technological University
Language: English
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spelling 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.
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Engineering::Computer science and engineering
Computing Methodologies
Computer Graphics
spellingShingle Engineering::Computer science and engineering
Computing Methodologies
Computer Graphics
Yi, Ran
Liu, Yong-Jin
He, Ying
Delaunay mesh simplification with differential evolution
description 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.
author2 School of Computer Science and Engineering
author_facet School of Computer Science and Engineering
Yi, Ran
Liu, Yong-Jin
He, Ying
format Article
author Yi, Ran
Liu, Yong-Jin
He, Ying
author_sort 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
publishDate 2020
url https://hdl.handle.net/10356/144750
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