# THE HEAT EQUATION AND THE FRENET FORMULAS FOR DIGITAL CURVES

### Sheng-Gwo Chen, Mei-Hsiu Chi, Jyh-Yang Wu

#### 2007

#### 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.

#### References

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#### Paper Citation

#### in Harvard Style

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 - Volume 1: GRAPP,* ISBN 978-972-8865-71-9, pages 97-102. DOI: 10.5220/0002072900970102

#### in Bibtex Style

@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 - Volume 1: GRAPP,},

year={2007},

pages={97-102},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0002072900970102},

isbn={978-972-8865-71-9},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the Second International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP,

TI - THE HEAT EQUATION AND THE FRENET FORMULAS FOR DIGITAL CURVES

SN - 978-972-8865-71-9

AU - Chen S.

AU - Chi M.

AU - Wu J.

PY - 2007

SP - 97

EP - 102

DO - 10.5220/0002072900970102