Isogeometric segmentation: Construction of cutting surfaces. (September 2017) - Haberleitner, Michael; Jüttler, Bert
Abstract: The objective of Isogeometric Segmentation is to generate a decomposition of a solid, given in boundary representation, into a collection of a relatively small number of base solids, which can easily be subdivided into topological hexahedra. This can be achieved by repeatedly splitting the solid. In each splitting step, one chooses a cutting loop, which is a cycle of curves around the boundary of the solid, and constructs a cutting surface that splits the solid into two simpler ones. When only hexahedra or pre-defined base solids are left this process terminates. The construction of the cutting surface must ensure that two essential properties are fulfilled: the boundary curves of the surface interpolate the previously constructed cutting loop and the surface neither intersects itself nor the boundary of the solid. A novel method for generating the cutting surface is presented in this paper. The method combines two steps: First we generate an implicit guiding surface, which is subsequently approximated by a trimmed spline surface in the second step. Highlights: Cutting surface splits solid into two smaller ones. Construction uses an implicit guiding surface to avoid collisions. Trimmed NURBS representation of the cutting surface.