Computing smooth quasi-geodesic distance field (QGDF) with quadratic programming
Computing geodesic distances on polyhedral surfaces is an important task in digital geometry processing. Speed and accuracy are two commonly-used measurements of evaluating a discrete geodesic algorithm. In applications, such as parametrization and shape analysis, a smooth distance field is often pr...
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sg-ntu-dr.10356-1522842021-08-05T01:47:58Z Computing smooth quasi-geodesic distance field (QGDF) with quadratic programming Cao, Luming Zhao, Junhao Xu, Jian Chen, Shuangmin Liu, Guozhu Xin, Shiqing Zhou, Yuanfeng He, Ying School of Computer Science and Engineering Engineering::Computer science and engineering Smooth Geodesic Distance Field Quadratic Programming Computing geodesic distances on polyhedral surfaces is an important task in digital geometry processing. Speed and accuracy are two commonly-used measurements of evaluating a discrete geodesic algorithm. In applications, such as parametrization and shape analysis, a smooth distance field is often preferred over the exact, non-smooth geodesic distance field. We use the term Quasi-geodesic Distance Field (QGDF) to denote a smooth scalar field that is as close as possible to an exact geodesic distance field. In this paper, we formulate the problem of computing QGDF into a standard quadratic programming (QP) problem which maintains a trade-off between accuracy and smoothness. The proposed QP formulation is also flexible in that it can be naturally extended to point clouds and tetrahedral meshes, and support various user-specified constraints. We demonstrate the effectiveness of QGDF in defect-tolerant distances and symmetry-constrained distances. The authors would like to thank the anonymous reviewers for their valuable comments and suggestions. This work is supported by National Natural Science Foundation of China (61772016, 61772312), the NSFC-Zhejiang Joint Fund for the Integration of Industrialization and Informatization (U1909210), the Dalian University of Technology 2019 Discipline Platform Fund (1000-82212201), the National Young Talents Program of China, and the Strategic Priority Research Program of Chinese Academy of Science (XDA21010205). 2021-08-05T01:47:58Z 2021-08-05T01:47:58Z 2020 Journal Article Cao, L., Zhao, J., Xu, J., Chen, S., Liu, G., Xin, S., Zhou, Y. & He, Y. (2020). Computing smooth quasi-geodesic distance field (QGDF) with quadratic programming. Computer-Aided Design, 127, 102879-. https://dx.doi.org/10.1016/j.cad.2020.102879 0010-4485 https://hdl.handle.net/10356/152284 10.1016/j.cad.2020.102879 2-s2.0-85085245124 127 102879 en Computer-Aided Design © 2020 Elsevier Ltd. All rights reserved. |
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Engineering::Computer science and engineering Smooth Geodesic Distance Field Quadratic Programming Cao, Luming Zhao, Junhao Xu, Jian Chen, Shuangmin Liu, Guozhu Xin, Shiqing Zhou, Yuanfeng He, Ying Computing smooth quasi-geodesic distance field (QGDF) with quadratic programming |
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Computing geodesic distances on polyhedral surfaces is an important task in digital geometry processing. Speed and accuracy are two commonly-used measurements of evaluating a discrete geodesic algorithm. In applications, such as parametrization and shape analysis, a smooth distance field is often preferred over the exact, non-smooth geodesic distance field. We use the term Quasi-geodesic Distance Field (QGDF) to denote a smooth scalar field that is as close as possible to an exact geodesic distance field. In this paper, we formulate the problem of computing QGDF into a standard quadratic programming (QP) problem which maintains a trade-off between accuracy and smoothness. The proposed QP formulation is also flexible in that it can be naturally extended to point clouds and tetrahedral meshes, and support various user-specified constraints. We demonstrate the effectiveness of QGDF in defect-tolerant distances and symmetry-constrained distances. |
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School of Computer Science and Engineering |
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School of Computer Science and Engineering Cao, Luming Zhao, Junhao Xu, Jian Chen, Shuangmin Liu, Guozhu Xin, Shiqing Zhou, Yuanfeng He, Ying |
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Article |
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Cao, Luming Zhao, Junhao Xu, Jian Chen, Shuangmin Liu, Guozhu Xin, Shiqing Zhou, Yuanfeng He, Ying |
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Cao, Luming |
title |
Computing smooth quasi-geodesic distance field (QGDF) with quadratic programming |
title_short |
Computing smooth quasi-geodesic distance field (QGDF) with quadratic programming |
title_full |
Computing smooth quasi-geodesic distance field (QGDF) with quadratic programming |
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Computing smooth quasi-geodesic distance field (QGDF) with quadratic programming |
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Computing smooth quasi-geodesic distance field (QGDF) with quadratic programming |
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computing smooth quasi-geodesic distance field (qgdf) with quadratic programming |
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2021 |
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https://hdl.handle.net/10356/152284 |
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