The ultimate planar convex hull algorithm
SIAM Journal on Computing
Extremal polygon containment problems
Computational Geometry: Theory and Applications
Computing the smallest k-enclosing circle and related problems
Computational Geometry: Theory and Applications
The robot localization problem
WAFR Proceedings of the workshop on Algorithmic foundations of robotics
An optimal algorithm for finding segments intersections
Proceedings of the eleventh annual symposium on Computational geometry
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Translating a convex polygon to contain a maximum number of points
Computational Geometry: Theory and Applications
Offset-polygon annulus placement problems
WADS '97 Selected papers presented at the international workshop on Algorithms and data structure
Efficient approximation and optimization algorithms for computational metrology
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Optimal placement of convex polygons to maximize point containment
Computational Geometry: Theory and Applications
Tentative Prune-And-Search For Computing Fixed-Points With Applications To Geometric Computation
Fundamenta Informaticae
Planar expropriation problem with non-rigid rectangular facilities
Computers and Operations Research
Offset polygon and annulus placement problems
Computational Geometry: Theory and Applications
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We consider problems in which we try to cover a given set of points (or a maximum number of them) with a given polygon. To solve these problems we use a new type of diagram that captures point-containment information for scalable, rotated, and/or translated versions of convex polygons. For a given polygon P and a contact point q in a point set S, the diagram parameterizes possible translations, rotations, and scales of P in order to represent containment regions for every other point v@?S. We present geometric and combinatorial properties of this diagram, and describe how it can be computed and used in the solution of several geometric matching problems. The latter have direct applications to object recognition and tolerancing problems in manufacturing.