Dergiler / Mathematical and Computational Applications / 2013 / Cilt: 18 - Sayı: 3

THE TIME SCALE CALCULUS APPROACH TO THE GEODESIC PROBLEM IN 3D DYNAMIC DATA SETS

Sayfa
421–427
DOI
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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.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Geodesics have a fundamental role in the geometry of curved surfaces, as well as in discrete geometry.
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Temel Bulgular & Veri:We present the time scale analogy of the dynamic data sets parameterized by a tensor product of two times scales.
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Sonuç & Katkı: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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

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.

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Bu Makaleye Atıf Yap

ATMACA, S. P., AKGÜLLER, Ö. (2013). THE TIME SCALE CALCULUS APPROACH TO THE GEODESIC PROBLEM IN 3D DYNAMIC DATA SETS. Mathematical and Computational Applications, Cilt: 18 - Sayı: 3, 421–427. https://ajindex.com/articles/279803

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  1. K. Hildebrandt, K. Polthier, M. Wardetzky, On the convergence of metric and geometric properties of polyhedral surfaces, Geom Dedicata 123, 89-112, 2006 2. R. Kimmel, A. Amir, A.M. Bruckstein, Finding shortest paths on surfaces. In: P.J. Laurent, A. LeMéhauté, L.L. Schumaker, (Eds.), Curves and Surfaces in Geometric Design. A.K. Peters, Wellesley, MA, 259-268, 1994 3. R. Kimmel, J. Sethian, Computing geodesic paths on manifolds, Proc. Natl. Acad. Sci. 95(15), 8431-8435, 1995. 4. T. Maekawa, Computation of shortest paths on free-form parametric surfaces, Journal of Mechanical Design 118, 499-508, 1996. 5. F. Memoli, G. Sapiro, Distance functions and geodesics on submanifolds of Rd and point clouds, SIAM Journal on Applied Mathematics 65(4), 1227-1260, 2005. 6. Jr. D.D. Streeter, Gross morphology and fiber geometry of the heart. In: Berne, R.M., Sperelakis, N. (Eds.), Handbook of Physiology, The Heart. American Physiology Society, Williams and Wilkins, Baltimore, pp. 61-112, 1979. 7. M. Schmies, K. Polthier, Straightest geodesics on polyhedral surfaces, Mathematical Visualization, 1998. 8. M. Bohner and G. Sh. Guseinov, Partial differentiation on time scales, Dynamic Systems and Applications 13(3-4), pp. 351379, 2004. 9. M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhauser, Boston, Mass, USA, 2001. 10. G. Sh. Guseinov and E. Ozyilmaz, Tangent lines of generalized regular curves parametrized by time scales, Turkish Journal of Mathematics 25(4) 553562, 2001. 11. E. Ozyilmaz, Directional Derivative of Vector Field and Regular Curves on Time Scales, Applied Mathematics and Mechanics (English Edition) 27(10) 1349-1360, 2006. 12. S. P. Atmaca, Normal and Osculating Planes of Regular Curves, Abstract and Applied Analysis 2010, doi:10.1155/2010/923916, 2010.