Abstract EN:

Surface/surface intersection is a fundamental geometric operation in solid modelling, computer aided design,. . . . For general parametric surface intersections, the most commonly used methods include Tracing and Subdivision. However, one shortcoming of all these methods is the inability to compute accurately and reliably tangential surface intersections. Two surfaces patches intersect each other generally at a set of points, form open curves or closed loops. While open curves are easily located by following the boundary curves of the two patches, close loops and singularities pose a robustness challenge since such points or loops can be easily missed by any subdivision or tracing intersection algorithms, especially when the intersecting patches are tangent or nearly parallel (Pseudo-tangent). In this thesis an algorithm is described that solves the Pseudo-Tangential surface intersection problem, the method developed consists on approaching the surface intersections problem as a meshing problem, in the sense that we are given not only two parametric surface patches, but also mesh on them. Both the parameterization and the meshes must be taken into account when computing the intersection. In other word we must compute intersection that lie on both surfaces and on both meshes. The balance between robustness and efficiency of the algorithm is controlled by a set of tolerances. A suite of examples concludes this thesis. The algorithms has been implemented in the Open Cascade kernel 3D and has proved to be reliable, efficient and accurate.