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Extraction of tori from minimal point sets

Laurent Busé 1 André Galligo 1, 2 
1 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
CRISAM - Inria Sophia Antipolis - Méditerranée , NKUA - National and Kapodistrian University of Athens
Abstract : A new algebraic method for extracting tori from a minimal point set, made of two oriented points and a simple point, is proposed. We prove a degree bound on the number of such tori; this bound is reached on examples, even when we restrict to smooth tori. Our method is based on pre-computed closed formulae well suited for numerical computations with approximate input data.
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Laurent Busé, André Galligo. Extraction of tori from minimal point sets. Computer Aided Geometric Design, Elsevier, 2017, 58, pp.1 - 7. ⟨10.1016/j.cagd.2017.10.004⟩. ⟨hal-01553065v2⟩

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