Intersecting and Trimming Parametric Meshes on Finite-element Shells

We present an algorithm for intersecting finite-element meshes defined on parametric surface patches. The intersection curves are modeled precisely and both meshes are adjusted to the newly formed borders, without unwanted reparametrizations. The algorithm is part of an interactive shell modeling program that has been used in the design of large offshore oil structures. To achieve good interactive response, we represent meshes with a topological data structure that stores its entities in spatial indexing trees instead of linear lists. These trees speed up the intersection computations required to determine points of the trimming curves; moreover, when combined with the topological information, they allow remeshing using only local queries.