An optimization-driven approach for computing geodesic paths on triangle meshes
There are many application scenarios where we need to refine an initial path lying on a surface to be as short as possible. A typical way to solve this problem is to iteratively shorten one segment of the path at a time. As local approaches, they are conceptually simple and easy to implement, but th...
| Main Authors: | , , , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/89439 http://hdl.handle.net/10220/46218 |
| _version_ | 1824455542968418304 |
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| author | Liu, Bangquan Chen, Shuangmin Xin, Shi-Qing He, Ying Liu, Zhen Zhao, Jieyu |
| author2 | School of Computer Science and Engineering |
| author_facet | School of Computer Science and Engineering Liu, Bangquan Chen, Shuangmin Xin, Shi-Qing He, Ying Liu, Zhen Zhao, Jieyu |
| author_sort | Liu, Bangquan |
| collection | NTU |
| description | There are many application scenarios where we need to refine an initial path lying on a surface to be as short as possible. A typical way to solve this problem is to iteratively shorten one segment of the path at a time. As local approaches, they are conceptually simple and easy to implement, but they converge slowly and have poor performance on large scale models. In this paper, we develop an optimization driven approach to improve the performance of computing geodesic paths. We formulate the objective function as the total length and adopt the L-BFGS solver to minimize it. Computational results show that our method converges with super-linear rate, which significantly outperforms the existing methods. Moreover, our method is flexible to handle anisotropic
metric, non-uniform density function, as well as additional user-specified constraints, such as coplanar geodesics and equally-spaced geodesic helical curves, which are challenging to the existing local methods. |
| first_indexed | 2025-02-19T03:39:52Z |
| format | Journal Article |
| id | ntu-10356/89439 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T03:39:52Z |
| publishDate | 2018 |
| record_format | dspace |
| spelling | ntu-10356/894392020-03-07T11:49:00Z An optimization-driven approach for computing geodesic paths on triangle meshes Liu, Bangquan Chen, Shuangmin Xin, Shi-Qing He, Ying Liu, Zhen Zhao, Jieyu School of Computer Science and Engineering Geodesic Helical Curves Geodesic Paths DRNTU::Engineering::Computer science and engineering There are many application scenarios where we need to refine an initial path lying on a surface to be as short as possible. A typical way to solve this problem is to iteratively shorten one segment of the path at a time. As local approaches, they are conceptually simple and easy to implement, but they converge slowly and have poor performance on large scale models. In this paper, we develop an optimization driven approach to improve the performance of computing geodesic paths. We formulate the objective function as the total length and adopt the L-BFGS solver to minimize it. Computational results show that our method converges with super-linear rate, which significantly outperforms the existing methods. Moreover, our method is flexible to handle anisotropic metric, non-uniform density function, as well as additional user-specified constraints, such as coplanar geodesics and equally-spaced geodesic helical curves, which are challenging to the existing local methods. Accepted version 2018-10-04T02:07:35Z 2019-12-06T17:25:31Z 2018-10-04T02:07:35Z 2019-12-06T17:25:31Z 2017 Journal Article Liu, B., Chen, S., Xin, S.-Q., He, Y., Liu, Z., & Zhao, J. (2017). An optimization-driven approach for computing geodesic paths on triangle meshes. Computer-Aided Design, 90105-112. 0010-4485 https://hdl.handle.net/10356/89439 http://hdl.handle.net/10220/46218 10.1016/j.cad.2017.05.022 en Computer-Aided Design © 2017 Elsevier. This is the author created version of a work that has been peer reviewed and accepted for publication by Computer-Aided Design, Elsevier. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1016/j.cad.2017.05.022]. 8 p. application/pdf |
| spellingShingle | Geodesic Helical Curves Geodesic Paths DRNTU::Engineering::Computer science and engineering Liu, Bangquan Chen, Shuangmin Xin, Shi-Qing He, Ying Liu, Zhen Zhao, Jieyu An optimization-driven approach for computing geodesic paths on triangle meshes |
| title | An optimization-driven approach for computing geodesic paths on triangle meshes |
| title_full | An optimization-driven approach for computing geodesic paths on triangle meshes |
| title_fullStr | An optimization-driven approach for computing geodesic paths on triangle meshes |
| title_full_unstemmed | An optimization-driven approach for computing geodesic paths on triangle meshes |
| title_short | An optimization-driven approach for computing geodesic paths on triangle meshes |
| title_sort | optimization driven approach for computing geodesic paths on triangle meshes |
| topic | Geodesic Helical Curves Geodesic Paths DRNTU::Engineering::Computer science and engineering |
| url | https://hdl.handle.net/10356/89439 http://hdl.handle.net/10220/46218 |
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