Polygonal Boundary Evaluation of Minkowski Sums and Swept Volumes

We present a novel technique for the efficient boundary evaluation of sweep operations applied to objects in polygonal boundary representation. These sweep operations include Minkowski addition, offsetting, and sweeping along a discrete rigid motion trajectory. Many previous methods focus on the construction of a polygonal superset (containing self-intersections and spurious internal geometry) of the boundary of the volumes which are swept. Only few are able to determine a clean representation of the actual boundary, most of them in a discrete volumetric setting. We unify such superset constructions into a succinct common formulation and present a technique for the robust extraction of a polygonal mesh representing the outer boundary, i.e. it makes no general position assumptions and always yields a manifold, watertight mesh. It is exact for Minkowski sums and approximates swept volumes polygonally. By using plane-based geometry in conjunction with hierarchical arrangement computation...

• Type: Journal
• Year: 2010
• Where: CGF
• Authors: Marcel Campen, Leif Kobbelt
• Keywords: CGF 2010, Efficient Boundary Evaluation, Polygonal Boundary Representation, Sweep Operations