Rotational polygon containment and minimum enclosure

An algorithm and implementation is given for rotats’onal poly~gon wntainment: given polygons A, Pz, P3,. . . , A and a container polygon C, find rotation8 and translations for the k polygons that place them into the container without overlapping. A version of the algorithm and implementation also oolves rotational minimum enclosure: given a class C of container polygons, find a container C E C of minimum area for which containment has a solution. Minimum enclosure algorithm8 are given for the following classes: 1) rcctanglco of fixed width, 2) scaled copies of a fixed convex polygon, 3) arbitrary rectangles. Containment and minimum cnclosuro arc NP-hard (even in the purely translational ca~o). The minimum enclosure is approximate: it bounds the the minimum area between (1 e)A and A. Experiments arc done. to determine the largest practical value of 1; for both containment and minimum enclosure. Important applicntions for these algorithm to industrial problems are dincunsed. The paper also give8 practical algorithms and numoricnl techniques for robustly calculating polygon set intcracction, Minkowski sum, and range intersection: the intcrscction of a polygon with itself as it rotates through a range of angles.

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