Polygonal Boundary Evaluation of Minkowski Sums and Swept Volumes

13 years 6 months ago
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...
Marcel Campen, Leif Kobbelt
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2010
Where CGF
Authors Marcel Campen, Leif Kobbelt
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