Abstract
It is a well known fact that the meridian curve of a rotational constant mean curvature (cmc) surface (which determines the surface completely) can be obtained as the trace of a focal point of an ellipse or hyperbola when rolling it on a straight line. In this paper, it will be shown that discrete rotational cmc surfaces can be obtained in a similar way. In fact, the meridian polygons are closely related to the elliptic (or hyberbolic) standard billiard: the discrete analogue of the ellipse or hyperbola will be the trace of a billiard in a continuous one.
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© 1998 Springer-Verlag Berlin Heidelberg
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Hoffmann, T. (1998). Discrete Rotational CMC Surfaces and the Elliptic Billiard. In: Hege, HC., Polthier, K. (eds) Mathematical Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03567-2_9
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DOI: https://doi.org/10.1007/978-3-662-03567-2_9
Publisher Name: Springer, Berlin, Heidelberg
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