Conversion CSG-BRep de scènes définies par des quadriques. (Boundary evaluation of scenes defined by quadrics)

The objective of this thesis is to investigate the problem of boundary evaluation, which transforms the CSG model of a scene to its BRep corresponding model, for scenes defined by quadrics. This algorithm consists of four steps : (i) the parameterization of every intersection curve between quadrics ; (ii) the calculation of the intersection points between such curves and the quadrics ; (iii) the determination, among the resulting arcs of curves, of those that limit a face of the BRep model ; (iv) the identification of the arcs that delimit a single face, and their assembling into chains of arcs ; some faces might contain « holes », and thus may be limited by several chains of arcs. The first two steps were solved using two algorithms from the litterature. The two remaining steps were solved by introducing new algorithms : VE (Visible Edges) and CA (Chains Assembling) respectively. Our algorithm of boundary evaluation is robust in the sense that all degenerate configurations are considered in the paradigm of exact geometric computing. It solves entirely the problem for scenes defined by quadrics. Its time-complexity is O(n) in the worst case, where n is the number of quadrics. A partial implementation was developed and preliminary experimental results were obtained.