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Article Dans Une Revue Journal of Symbolic Computation Année : 2012

On the isotopic meshing of an algebraic implicit surface

Daouda Niang Diatta
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DMI
Bernard Mourrain
Olivier Ruatta
DMI

Résumé

We present a new and complete algorithm for computing the topology of an algebraic surface given by a squarefree polynomial in Q[X, Y, Z]. Our algorithm involves only subresultant computations and entirely relies on rational manipulation, which makes it direct to implement. We extend the work in [15], on the topology of non-reduced algebraic space curves, and apply it to the polar curve or apparent contour of the surface S. We exploit simple algebraic criterion to certify the pseudo-genericity and genericity position of the surface. This gives us rational parametrizations of the components of the polar curve, which are used to lift the topology of the projection of the polar curve. We deduce the connection of the two-dimensional components above the cell defined by the projection of the polar curve. A complexity analysis of the algorithm is provided leading to a bound in OB (d15 τ ) for the complexity of the computation of the topology of an implicit algebraic surface defined by integer coefficients polynomial of degree d and coefficients size τ . Examples illustrate the implementation in Mathemagix of this first complete code for certified topology of algebraic surfaces.
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Dates et versions

hal-00421214 , version 1 (05-11-2009)

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Daouda Niang Diatta, Bernard Mourrain, Olivier Ruatta. On the isotopic meshing of an algebraic implicit surface. Journal of Symbolic Computation, 2012, 47 (8), pp.903-925. ⟨10.1016/j.jsc.2011.09.010⟩. ⟨hal-00421214⟩
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