An optimal algorithm for finding minimal enclosing triangles
Journal of Algorithms
Simultaneous containment of several polygons
SCG '87 Proceedings of the third annual symposium on Computational geometry
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Translational polygon containment and minimal enclosure using linear programming based restriction
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Determining the minimum-area encasing rectangle for an arbitrary closed curve
Communications of the ACM
Cutting a Country for Smallest Square Fit
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
A simple method for fitting of bounding rectangle to closed regions
Pattern Recognition
Bundling three convex polygons to minimize area or perimeter
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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We consider the problem of packing several convex polygons into minimum size rectangles. For this purpose the polygons may be moved either by translations only, or by combinations of translations and rotations. We investigate both cases, that the polygons may overlap when being packed or that they must be disjoint. The size of a rectangle to be minimized can either be its area or its perimeter. In the case of overlapping packing very efficient algorithms whose runtime is close to linear or 0(n log n) can be found even for an arbitrary number of polygons. Disjoint optimal packing is known to be NP-hard for arbitrary numbers of polygons. Here, efficient algorithms are given for disjoint packing of two polygons with a runtime close to linear for tanslations and 0(03) for geneal isometries.