Rotational polygon containment and minimum enclosure

Research output: Chapter in Book/Report/Conference proceedingConference contribution

20 Citations (Scopus)

Abstract

An algorithm and 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. Minimum enclosure algorithms are given for the following classes: 1) rectangles of fixed width, 2) scaled copies of a fixed convex polygon, 3) arbitrary rectangles. Containment and minimum enclosure are NP-hard (even in the purely translational case). The minimum enclosure is approximate: it bounds the minimum area between (1 - ε)A and A. Experiments are done to determine the largest practical value of k for both containment and minimum enclosure. 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 intersection: the intersection of a polygon with itself as it rotates through a range of angles.

Original language English (US) Proceedings of the Annual Symposium on Computational Geometry ACM 1-8 8 Published - 1998 Proceedings of the 1998 14th Annual Symposium on Computational Geometry - Minneapolis, MN, USADuration: Jun 7 1998 → Jun 10 1998

Other

Other Proceedings of the 1998 14th Annual Symposium on Computational Geometry Minneapolis, MN, USA 6/7/98 → 6/10/98

Fingerprint

Enclosure
Enclosures
Polygon
Containers
Container
Intersection
Rectangle
Minkowski Sum
Convex polygon
Numerical Techniques
Range of data
Overlapping
NP-complete problem
Angle
Arbitrary
Experiments
Experiment

ASJC Scopus subject areas

• Chemical Health and Safety
• Software
• Safety, Risk, Reliability and Quality
• Geometry and Topology

Cite this

Milenkovic, V. (1998). Rotational polygon containment and minimum enclosure. In Proceedings of the Annual Symposium on Computational Geometry (pp. 1-8). ACM.
Proceedings of the Annual Symposium on Computational Geometry. ACM, 1998. p. 1-8.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Milenkovic, V 1998, Rotational polygon containment and minimum enclosure. in Proceedings of the Annual Symposium on Computational Geometry. ACM, pp. 1-8, Proceedings of the 1998 14th Annual Symposium on Computational Geometry, Minneapolis, MN, USA, 6/7/98.
Milenkovic V. Rotational polygon containment and minimum enclosure. In Proceedings of the Annual Symposium on Computational Geometry. ACM. 1998. p. 1-8
Milenkovic, Victor. / Rotational polygon containment and minimum enclosure. Proceedings of the Annual Symposium on Computational Geometry. ACM, 1998. pp. 1-8
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