Journal ArticleDOI
Algorithms for Reporting and Counting Geometric Intersections
TLDR
Algorithms that count the number of pairwise intersections among a set of N objects in the plane and algorithms that report all such intersections are given.Abstract:
An interesting class of "geometric intersection problems" calls for dealing with the pairwise intersections among a set of N objects in the plane, These problems arise in many applications such as printed circuit design, architectural data bases, and computer graphics. Shamos and Hoey have described a number of algorithms for detecting whether any two objects in a planar set intersect. In this paper we extend their work by giving algorithms that count the number of such intersections and algorithms that report all such intersections.read more
Citations
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Spatial Planning: A Configuration Space Approach
TL;DR: In this article, the authors propose an approach based on characterizing the position and orientation of an object as a single point in a configuration space, in which each coordinate represents a degree of freedom in the position or orientation of the object.
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Spatial planning: a configuration space approach
TL;DR: Algorithms for computing constraints on the position of an object due to the presence of ther objects, which arises in applications that require choosing how to arrange or how to move objects without collisions are presented.
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The Algorithm Design Manual
TL;DR: This newly expanded and updated second edition of the best-selling classic continues to take the "mystery" out of designing algorithms, and analyzing their efficacy and efficiency.
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Davenport-Schinzel sequences and their geometric applications
Micha Sharir,Pankaj K. Agarwal +1 more
TL;DR: A close to linear bound on the maximum length of Davenport--Schinzel sequences enable us to derive sharp bounds on the combinatorial structure underlying various geometric problems, which in turn yields efficient algorithms for these problems.
Journal ArticleDOI
Relative neighborhood graphs and their relatives
TL;DR: Property, bounds on the size, algorithms, and variants of the neighborhood graphs are discussed and numerous applications including computational morphology, spatial analysis, pattern classification, and databases for computer vision are described.
References
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Proceedings ArticleDOI
Geometric intersection problems
Michael Ian Shamos,Dan Hoey +1 more
TL;DR: An O(N log N) algorithm is given to determine whether any two intersect and use it to detect whether two simple plane polygons intersect and to show that the Simplex method is not optimal.
Journal ArticleDOI
The complexity of finding fixed-radius near neighbors☆
Proceedings ArticleDOI
Fast algorithms for LSI artwork analysis
TL;DR: A novel IC mask analysis algorithm is described which does not restrict the representation of artwork, permits a wide range of functions, avoids pathologies, and achieves good runtime and tolerable main memory demands, even for LSI applications.