An optimization-driven approach for computing geodesic paths on triangle meshes. (September 2017)

• Record Type: Journal Article
• Authors: Liu, Bangquan; Chen, Shuangmin; Xin, Shi-Qing; He, Ying; Liu, Zhen; Zhao, Jieyu
• Is Part Of: Computer aided design. Volume 90(2017)
• Page Start: 105
• Page End: 112
• Publication Date: 2017-09
• Subjects: Geodesic paths -- Geodesic helical curves -- Optimization -- Anisotropic metric -- Non-uniform density; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2017.05.022
• Languages: English
• ISSNs: 0010-4485

Abstract

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. Graphical abstract: Highlights: An optimization driven geodesic approach is proposed. Our task is to minimize the total path length guided by the closed-form formula of the gradients. We exhibit its flexibility to handle anisotropic metric, non-uniform density function, as well as additional user-specified constraints.