A Robust Algorithm to Determine Surface/Surface Intersection in Both Parametric Spaces

Abstract

An algorithm providing the intersection curves in the parametric space of both involved surfaces is presented allowing the correct union of trimmed patch surfaces to represent complex models and the generation of finite element meshes. The algorithm has four steps. On the first one, a subdivision method is used to obtain an adaptive quadtree structure of surface regions where potentially intersection curves segments can be contained. On the second one, each element of this quadtree structure is approximated by triangles; the intersection segments of triangle pairs are determined as an initial approximation of intersection curves in 3D space. On the third step, a refinement process and parametric mapping of coordinates provides the intersection points on the parametric and real spaces. In the last step, the intersection segments are reordered to obtain intersection curves in parametric form. Several examples are included to check the robustness and efficiency of the algorithm.