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Contribution à la conception, la mise en oeuvre et l'amélioration des algorithmes de calcul des intersections de carreaux NURBS

Abstract : Solid objects shape modelling is a basic sight of CAD. The shape of a solid is usually defined by assembling several surfaces (Boundary representation). Many mathematic surface models, suitables for CAD/CAM have been built. This paper deals with NURBS (Non Uniform Rational B-spline) surfaces ; they generalize the Bézier Patches and provide an exact representation of quadric surfaces. Building objects by assembling several patches leads the solid modeler to be able to trim the surface patches and, hence, to be able to compute intersections between surfaces. In this report we study the different ways to solve the problem parametric surface-parametric surface intersection. The standard methods are recalled. We mean : the well known divide and conquer method which reduces the general problem to the case of flat surfaces intersection ; Farouki's method which deals with the case of parametric surface implicit surface intersection ; the tracing algorithm which computes a sequence of close-set points along the intersection curve. The three approaches are interesting, they suit to differents sights of the same problem. Some solutions which try to combine the different advantages, are developped. A new simplifying NURBS patches algorithm which generalizes the first standard method is designed ; its associates recursive subdivision and degree decrease. The resultant's theory provides a complete solution of the problem degree 2 rational curve-bicadric rational patche intersection. It can be efficiently applied to the computation of intersection curves. At last an algorithm based on the tracing curves scheme is implemented. In this algorithm, the being built curve is parameterized by the arc length. This allows one to get, for each point, geometric informations which are used to accurate the curve behaviour. They contribute to improve the performance of the algorithm. Uniting these three operations leads to a general algorithm. The main difficulties of builiding intersection curves, detection of closed curves and dealing with singularities are discussed and partially solved in some cases
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Dominique Michel. Contribution à la conception, la mise en oeuvre et l'amélioration des algorithmes de calcul des intersections de carreaux NURBS. Sciences de l'ingénieur [physics]. Université Paul Verlaine - Metz, 1992. Français. ⟨NNT : 1992METZ011S⟩. ⟨tel-01775969⟩



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