Circular Cylinders by Four or Five Points in Space

Olivier Devillers 1 Bernard Mourrain 2 Franco Preparata 3 Philippe Trebuchet 4, 2
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée
2 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
3 Brown University - Department of Computer Science
4 CALFOR - Calcul formel
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : We are interested in computing effectively cylinders through 5 points, and in other problems involved in metrology. In particular, we consider the cylinders through 4 points with a fix radius and with extremal radius. For these different problems, we give bounds on the number of solutions and exemples show that these bounds are optimal. Finally, we describe two algebraic methods which can be used here to solve efficiently these problems and some experimentation results.
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Olivier Devillers, Bernard Mourrain, Franco Preparata, Philippe Trebuchet. Circular Cylinders by Four or Five Points in Space. Discrete and Computational Geometry, Springer Verlag, 2002, 29 (1), pp.83--104. ⟨10.1007/s00454-002-2811-7⟩. ⟨inria-00090648⟩

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