The Department of Applied Mathematics weekly seminar is given by scholars and researchers working in applied mathematics, broadly interpreted.
Title: N-dimensional solid modeling without topology
Abstract: Modern design and manufacturing of everything from toys to commercial airliners depends on solid modeling. Boolean operations on solid models are essential for their construction and deployment. The boundary representations of solids used by nearly all solid modeling systems rely on topological information to stitch together the numerically challenging surface intersections inherent in Boolean operations. This reliance on topology adds complexity to Boolean operations, leads to inevitable inconsistencies between geometry and topology, limits surface variation, and does not scale well beyond three dimensions. This talk presents a simple new approach to Boolean operations on solids that does not rely on topology. The algorithm supports arbitrary manifolds with unit normals in any dimension. Examples developed using the “BSpy” open source B-Spline Python package will be demonstrated.