External polygon containment problems

AbstractGiven a convex polygonal object P with k vertices and an environment consisting of polygonal obstacles with a total of n corners, we seek a placement for the largest copy of P that does not intersect any of the obstacles, allowing translation, rotation and scaling. We employ the parametric search technique of Megiddo (1983), and the fixed size polygon placement algorithms developed by Leven and Sharir (1987), to obtain an algorithm that runs in time O(k2nλ6(kn)log3(kn)loglog(kn)). We also present several other efficient algorithms for restricted variants of the extremal polygon containment problem, using the same ideas. These variants include: placement of the largest homothetic copies of one or two convex polygons in another convex polygon and placement of the largest similar copy of a triangle in a convex polygon

An Evaluation of Potential Compute Platforms for Picosatellites

What compute platform should picosatellites use? CubeSats, classified as nanosatellites, are transitioning from microcontrollers that cannot run modern operating systems and modern programming environments to Linux-capable compute platforms. As electronics continue to shrink, picosatellite missions are likely to become more common, perhaps using the PocketQube standard. This paper characterizes the requirements that compute platforms for picosatellites should satisfy and analyzes in detail 4 potential platforms. We show that suitable hardware does exist, but that it is not yet supported well enough to allow small teams to use it in satellites or other specialized sensor nodes