On curves with constant curvatures

Authors

  • 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

Wilhelm Blaschke and Kurt Reidemeister. Vorlesungen

über Differentialgeometrie und Geometrische

Grundlagen von Einsteins Relativitätstheorie:

II Affine Differentialgeometrie. Springer

Berlin Heidelberg, 1923.

Manfredo P. do Carmo. Differential Geometry of

Curves and Surfaces. Prentice-Hall, Upper Saddle

River, New Jersey, 1976.

H. Glück. Higher Curvatures in Euclidean Spaces.

The American Mathematical Monthly, 73:699–704,

Heinrich W. Guggenheimer. Differential Geometry.

McGraw-Hill Book Company, Inc., New York,

Felix Klein. Vergleichende Betrachtungen uber

neuere geometrische Forschungen. 1872.

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Published

2015-11-20

How to Cite

Ebbens, M. (2015). On curves with constant curvatures. Student Undergraduate Research E-Journal!, 1. Retrieved from https://journals.open.tudelft.nl/sure/article/view/1045

Issue

Vol. 1 (2015): Student Research Conference 2015

Section

Economics & Social Sciences

License

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