Probing Convex polygons with half-planes
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In this article, the authors developed techniques based on X-ray probing to determine convex n-gons in 7n + 7 half-plane probes and proved linear lower bounds for determination and verification.About:
This article is published in Journal of Algorithms.The article was published on 1991-09-01 and is currently open access. It has received 26 citations till now. The article focuses on the topics: Convex polygon & Polygon covering.read more
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Journal ArticleDOI
On the Area of Overlap of Translated Polygons
TL;DR: A number of mathematical results regarding the area-of-overlap function of PandQ, which has a number of applications in areas such as motion planning and object recognition, are presented.
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Problems in geometric probing
TL;DR: This work reviews results in geometric probing and gives a collection of open problems for a variety of probing models and objects.
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Interactive reconstruction via geometric probing
TL;DR: Geometric probing as mentioned in this paper considers problems of determining a geometric structure or some aspect of that structure from the results of a mathematical or physical measuring device, a probe, by using the results from all previous measurements to determine the orientation of the next probe so it provides the maximum amount of information about the structure.
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Local tests for consistency of support hyperplane data
TL;DR: The results serve to generalize existing planar conditions to arbitrary dimensions by providing a generalization of the notion of nearest neighbor for plane vectors which utilizes a simple positive cone condition on the respective support sample normals.
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Techniques for exploring the suboptimal set
Joëlle Skaf,Stephen Boyd +1 more
TL;DR: Some basic techniques for quantitatively characterizing $\mathcal{X}_{\epsilon}$, for a given value of ε, when the original problem is convex, by solving a modest number of related convex optimization problems.
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Book
Image reconstruction from projections : the fundamentals of computerized tomography
TL;DR: The fundamentals of computerized tomography computer ebook, image reconstruction from projections, and the fundamentals ofComputerized Tomography computer epub are revealed.
Book
Shape From Probing
Richard Cole,Chee Yap +1 more
TL;DR: It is shown that 3n probes are sufficient, but 3n − 1 are necessary, to determine the shape and position of any n-gon, under a mild assumption.
Proceedings ArticleDOI
Probing convex polytopes
TL;DR: In this paper, the authors investigate the complexity of determining the shape and presentation of convex polytopes in multi-dimensional Euclidean space using a variety of probe models.