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Title: An optimization-driven approach for computing geodesic paths on triangle meshes
Authors: Liu, Bangquan
Chen, Shuangmin
Xin, Shi-Qing
He, Ying
Liu, Zhen
Zhao, Jieyu
Keywords: Geodesic Helical Curves
Geodesic Paths
DRNTU::Engineering::Computer science and engineering
Issue Date: 2017
Source: 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.
Series/Report no.: Computer-Aided Design
Abstract: 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.
ISSN: 0010-4485
DOI: 10.1016/j.cad.2017.05.022
Rights: © 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: [].
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SCSE Journal Articles

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