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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on mdpi.com as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 2013, 18(3), 421-427; https://doi.org/10.3390/mca18030421

The Time Scale Calculus Approach to the Geodesic Problem in 3D Dynamic Data Sets

Department of Mathematics, Mugla Sitki Kocman University, 48000, Merkez, Mugla, Turkey
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Published: 1 December 2013
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Abstract

Geodesics have a fundamental role in the geometry of curved surfaces, as well as in discrete geometry. We present the time scale analogy of the dynamic data sets parameterized by a tensor product of two times scales. The goal of our study is the find the shortest and straightest path between two points on a point cloud like data sets which also involves continuous data.
Keywords: Discrete Differential Geometry; Time Scale Calculus; Discrete Geodesic Problem; Point Cloud Data Discrete Differential Geometry; Time Scale Calculus; Discrete Geodesic Problem; Point Cloud Data
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Atmaca, S.P.; Akgüller, Ö. The Time Scale Calculus Approach to the Geodesic Problem in 3D Dynamic Data Sets. Math. Comput. Appl. 2013, 18, 421-427.

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