Journal ArticleDOI
Algorithms for bichromatic line-segment problems and polyhedral terrains
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A variety of problems on the interaction between two sets of line segments in two and three dimensions are considered, including counting the number of intersecting pairs between m blue segments andn red segments in the plane.Abstract:
We consider a variety of problems on the interaction between two sets of line segments in two and three dimensions. These problems range from counting the number of intersecting pairs between m blue segments andn red segments in the plane (assuming that two line segments are disjoint if they have the same color) to finding the smallest vertical distance between two nonintersecting polyhedral terrains in three-dimensional space. We solve these problems efficiently by using a variant of the segment tree. For the three-dimensional problems we also apply a variety of recent combinatorial and algorithmic techniques involving arrangements of lines in three-dimensional space, as developed in a companion paper.read more
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Journal ArticleDOI
Efficient algorithms for geometric optimization
Pankaj K. Agarwal,Micha Sharir +1 more
TL;DR: A wide range of applications of parametric searching and other techniques to numerous problems in geometric optimization, including facility location, proximity problems, statistical estimators and metrology, placement and intersection of polygons and polyhedra, and ray shooting and other query-type problems.
Journal ArticleDOI
Measuring and comparing brain cortical surface area and other areal quantities.
Anderson M. Winkler,Mert R. Sabuncu,Mert R. Sabuncu,B.T. Thomas Yeo,Bruce Fischl,Bruce Fischl,Douglas N. Greve,Peter Kochunov,Peter Kochunov,Thomas E. Nichols,Thomas E. Nichols,John Blangero,David C. Glahn +12 more
TL;DR: It is demonstrated that direct measurement and comparison of the surface area of the cerebral cortex at a fine scale is possible using mass conservative interpolation methods.
Book
Partitioning Arrangements of Lines: II. Applications
TL;DR: An algorithm that preprocesses a set ofn points in the plane, into a data structure of sizeO(m) forn logn≤m≤n2, so that the number of points ofS lying inside a query triangle can be computed inO((n/√m) log3/2n) time.
Journal ArticleDOI
Diameter, width, closest line pair, and parametric searching
TL;DR: Megiddo's parametric searching technique is applied to several geometric optimization problems and significantly improved solutions for them are derived.
References
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Computational geometry. an introduction
TL;DR: This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry.
Book
Computational Geometry: An Introduction
TL;DR: In this article, the authors present a coherent treatment of computational geometry in the plane, at the graduate textbook level, and point out the way to the solution of the more challenging problems in dimensions higher than two.
Journal ArticleDOI
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
TL;DR: This paper describes a general-purpose programming technique, called Simulation of Simplicity, that can be used to cope with degenerate input data for geometric algorithms and it is believed that this technique will become a standard tool in writing geometric software.
Journal ArticleDOI
Optimal point location in a monotone subdivision
TL;DR: A substantial refinement of the technique of Lee and Preparata for locating a point in $\mathcal{S}$ based on separating chains is exhibited, which can be implemented in a simple and practical way, and is extensible to subdivisions with edges more general than straight-line segments.
Posted Content
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
TL;DR: A general purpose programming technique, called the Simulation of Simplicity, which can be used to cope with degenerate input data for geometric algorithms, and it is believed that this technique will become a standard tool in writing geometric software.