On curves with constant curvatures

  • Matthijs Ebbens University of Groningen

Abstract

One of the fields of research of Computer Aided Geometric Design is approximating complex curves by simpler curves. Curves with constant curvatures are useful tools for these purposes. However, parametrizations of such curves are not always easily given. In this paper we will derive several necessary and sufficient geometric conditions for a curve to have constant curvatures, both in Euclidean geometry and in affine geometry.

References

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[2] Manfredo P. do Carmo. Differential Geometry of
Curves and Surfaces. Prentice-Hall, Upper Saddle
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[4] Heinrich W. Guggenheimer. Differential Geometry.
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[5] Felix Klein. Vergleichende Betrachtungen uber
neuere geometrische Forschungen. 1872.
How to Cite
EBBENS, Matthijs. On curves with constant curvatures. Student Undergraduate Research E-journal!, [S.l.], v. 1, nov. 2015. ISSN 2468-0443. Available at: <https://journals.open.tudelft.nl/index.php/sure/article/view/1045>. Date accessed: 26 mar. 2019.
Published
2015-11-20