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Authors: Sheng-Gwo Chen 1 ; Mei-Hsiu Chi 1 and Jyh-Yang Wu 2

Affiliations: 1 National Chia-Yi University; National Chung-Cheng University, Taiwan ; 2 National Chung-Cheng University, Taiwan

Keyword(s): Digital curves, heat equation, the Frenet formulas.

Related Ontology Subjects/Areas/Topics: CAGD/CAD/CAM Systems ; Computer Vision, Visualization and Computer Graphics ; Geometric Computing ; Geometry and Modeling

Abstract: Abstract：In this note we shall discuss the heat equation and the eigenvalue problem for digital curves in the 3D Euclidean space. First, we shall introduce the derivative of a function along a digital curve by the weighted combination method. Then, we can define the Laplace of a function on a digital curve. The Frenet formulas for digital curves will also be discussed. Numerical simulations show our method will provide good estimations for the curvature and torsion.

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Paper citation in several formats:
Chen, S.; Chi, M. and Wu, J. (2007). THE HEAT EQUATION AND THE FRENET FORMULAS FOR DIGITAL CURVES. In Proceedings of the Second International Conference on Computer Graphics Theory and Applications (VISIGRAPP 2007) - Volume 2: GRAPP; ISBN 978-972-8865-71-9; ISSN 2184-4321, SciTePress, pages 97-102. DOI: 10.5220/0002072900970102

@conference{grapp07,
author={Sheng{-}Gwo Chen. and Mei{-}Hsiu Chi. and Jyh{-}Yang Wu.},
title={THE HEAT EQUATION AND THE FRENET FORMULAS FOR DIGITAL CURVES},
booktitle={Proceedings of the Second International Conference on Computer Graphics Theory and Applications (VISIGRAPP 2007) - Volume 2: GRAPP},
year={2007},
pages={97-102},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002072900970102},
isbn={978-972-8865-71-9},
issn={2184-4321},
}

TY - CONF

JO - Proceedings of the Second International Conference on Computer Graphics Theory and Applications (VISIGRAPP 2007) - Volume 2: GRAPP
TI - THE HEAT EQUATION AND THE FRENET FORMULAS FOR DIGITAL CURVES
SN - 978-972-8865-71-9
IS - 2184-4321
AU - Chen, S.
AU - Chi, M.
AU - Wu, J.
PY - 2007
SP - 97
EP - 102
DO - 10.5220/0002072900970102
PB - SciTePress

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