Details:
Title  On the isotopic meshing of an algebraic implicit surface  Author(s)  Daouda Niang Diatta, Bernard Mourrain, Olivier Ruatta  Type  Article in Journal  Abstract  We present a new and complete algorithm for computing the topology of an algebraic surface S given by a square free 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 Diatta et al. (2008), on the topology of nonreduced algebraic space curves, and apply it to the polar curve or apparent contour of the surface S . We exploit a simple algebraic criterion to certify the pseudogenericity 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 twodimensional 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 O_B ( d^21 τ ) for the complexity of the computation of the topology of an implicit algebraic surface defined by integer coefficient polynomial of degree d and coefficient size τ . Examples illustrate the implementation in Mathemagix of this first complete code for certified topology of algebraic surfaces.  Keywords  Real algebraic surafces, Topology, Resultants, Triangulation, Singularities  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717111001453 
Language  English  Journal  Journal of Symbolic Computation  Volume  47  Number  8  Pages  903  925  Year  2012  Edition  0  Translation 
No  Refereed 
No 
