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

Sibel Paşalı Atmaca; Ömer Akgüller

doi:10.3390/mca18030421

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1 December 2013

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

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Department of Mathematics, Mugla Sitki Kocman University, 48000, Merkez, Mugla, Turkey

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Math. Comput. Appl.2013, 18(3), 421-427;https://doi.org/10.3390/mca18030421

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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

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