Straight Skeletons and Mitered Offsets of Nonconvex Polytopes
- LecturerProf. Franz Aurehammer (Technische Universitaet Graz)
Host: Der-Tsai Lee - Time2016-01-04 (Mon.) 14:30 ~ 16:30
- LocationAuditorium 106 at IIS new Building
Abstract
A concise definition is given for mitered offset surfaces of nonconvex polytopes in 3-space. It implies the existence of 3D straight skeletons for general nonconvex polytopes. Some geometric and
topological features of such skeletons are presented, including a classification of their constructing events.
These results extend to the weighted setting, to a larger class of polytope decompositions, and to general dimensions. A novel layer partition for straight skeletons is also introduced, which leads
to the first nontrivial upper size bound for 3D straight skeletons.
Finally, we sketch some applications, to polygonal mesh offsetting, polytope flattening, and decomposing a polytope into a volume mesh with small cells.