Near-optimal parameterization of the intersection of quadrics: II. A classification of pencils
نویسندگان
چکیده
While Part I [2] of this paper was devoted mainly to quadrics intersecting in a smooth quartic, we now focus on singular intersections. To produce optimal or near-optimal parameterizations in all cases, we first determine the the real type of the intersection before computing the actual parameterization. In this second part, we present the first classification of pencils of quadrics based on the type of the real intersection and we show how this classification can be used to compute efficiently the type of the real intersection. The near-optimal parameterization algorithms in all singular cases will be given in Part III [3]. Key-words: Intersection of surfaces, quadrics, pencils of quadrics, classification, curve parameterization. ∗ Project Vegas, LORIA (UMR CNRS, INPL, INRIA Lorraine, Universités Nancy 1 & 2), Nancy, France; [email protected]. † Project Salsa and LIP6 (UMR Université Pierre et Marie Curie and CNRS), Paris, France; [email protected]. Paramétrisation quasi-optimale de l’intersection de quadriques : II. Classification des faisceaux Résumé : Alors que la partie I [2] de cet article s’est principalement focalisée sur les paires de quadriques dont l’intersection est une quartique lisse, nous nous concentrons maintenant sur les intersections singulières. Pour parvenir à l’obtention de paramétrages optimaux ou quasi-optimaux dans tous les cas, nous découplons la détermination du type réel de l’intersection du paramétrage proprement dit. Dans cette seconde partie de notre article, nous présentons la première classification des faisceaux de quadriques basée sur le type de l’intersection réelle et nous montrons comment cette classification peut être utilisée pour calculer efficacement le type réel de l’intersection. Les algorithmes quasi-optimaux de paramétrage dans tous les cas sont présentés dans la partie III [3]. Mots-clés : Intersection de surfaces, quadriques, faisceaux de quadriques, classification, paramétrisation. Near-Optimal Parameterization of the Intersection of Quadrics: II. A Classification of Pencils 3
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ورودعنوان ژورنال:
- J. Symb. Comput.
دوره 43 شماره
صفحات -
تاریخ انتشار 2008