Rotational Polygon Containment and Minimum Enclosure

An algorithm and a robust floating point implementation is given for rotational polygon containment: given polygons P1,P2,P3,...,Pk and a container polygon C, find rotations and translations for the k polygons that place them into the container without overlapping. A version of the algorithm and implementation also solves rotational minimum enclosure: given a class C of container polygons, find a container C ∈ C of minimum area for which containment has a solution. The minimum enclosure is approximate: it bounds the minimum area between (1 − ε)A and A. Experiments indicate that finding the minimum enclosure is practical for k = 2,3 but not larger unless optimality is sacrificed or angles ranges are limited (although these solutions can still be useful). Important applications for these algorithm to industrial problems are discussed. The paper also gives practical algorithms and numerical techniques for robustly calculating polygon set intersection, Minkowski sum, and range i...

• Type: Conference
• Year: 1998
• Where: COMPGEOM
• Authors: Victor Milenkovic
• Keywords: COMPGEOM 1998, Container Polygons, Discrete Geometry, Minimum Enclosure, Polygon