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The intersection problems of parametric curve and surfaces by means of matrix based implicit representations

Ba Thang Luu 1, 2 
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (1965 - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : In this paper, we introduce and study a new implicit representation of parametric curves and parametric surfaces . We show how these representations which we will call the matrix implied, establish a bridge between geometry and linear algebra, thus opening the possibility of a more robust digital processing. The contribution of this approach is discussed and illustrated on important issues of geometric modeling and Computer Aided Geometric Design (CAGD) : The curve/curve, urve/surface and surface/surface intersection problems, the point-on-curve and inversion problems, the computation of singularities points.
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https://hal.inria.fr/hal-00809325
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Submitted on : Wednesday, April 17, 2013 - 5:04:39 AM
Last modification on : Thursday, August 4, 2022 - 4:52:36 PM
Long-term archiving on: : Thursday, July 18, 2013 - 4:03:28 AM

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Ba Thang Luu. The intersection problems of parametric curve and surfaces by means of matrix based implicit representations. 2013. ⟨hal-00809325v2⟩

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