# Geometric intersection problems

@article{Shamos1976GeometricIP, title={Geometric intersection problems}, author={Michael Ian Shamos and Dan Hoey}, journal={17th Annual Symposium on Foundations of Computer Science (sfcs 1976)}, year={1976}, pages={208-215} }

We develop optimal algorithms for forming the intersection of geometric objects in the plane and apply them to such diverse problems as linear programming, hidden-line elimination, and wire layout. Given N line segments in the plane, finding all intersecting pairs requires O(N2) time. We give an O(N log N) algorithm to determine whether any two intersect and use it to detect whether two simple plane polygons intersect. We employ an O(N log N) algorithm for finding the common intersection of N…

## 451 Citations

An optimal time and minimal space algorithm for rectangle intersection problems

- Mathematics, Computer ScienceInternational Journal of Computer & Information Sciences
- 2004

It is demonstrated that classical divide-and-conquer technique and conventional data structures such as linked lists are sufficient to achieve a time bound ofO(n logn) +s, and a space bound of Θ(n), both of which are optimal.

Plane-sweep algorithms for intersecting geometric figures

- Mathematics, Computer ScienceCACM
- 1982

Algorithms in computational geometry are of increasing importance in computer-aided design, for example, in the layout of integrated circuits. The efficient computation of the intersection of several…

An efficient algorithm for planar subdivision intersection problems

- Computer Science
- 1994

A generalization of Mairson's algorithm to solve the planar subdivision intersection problem is proposed and an implementation of the algorithm is presented and the empirical results are analyzed.

Algorithms for Reporting and Counting Geometric Intersections

- Computer ScienceIEEE Transactions on Computers
- 1979

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.

A Plane-Sweep Algorithm for Finding a Closest Pair Among Convex Planar Objects

- Mathematics, Computer ScienceSTACS
- 1992

A plane-sweep algorithm which finds a closest pair with respect to any LP -metric, 1≤p≤∞, for planar configurations consisting of n (possibly intersecting) compact convex objects such as line segments, circular discs and convex polygons is presented.

Set theoretic operations on polygons using the scan-grid approach

- Mathematics
- 1986

This paper describes an algorithm to compute the union, intersection and difference of two polygons using a scan-grid approach. Basically, in this method, the screen is divided into cells and the…

An optimal algorithm for intersecting three-dimensional convex polyhedra

- Mathematics, Computer Science30th Annual Symposium on Foundations of Computer Science
- 1989

A linear algorithm for intersecting two convex polyhedra in 3-space is described and a number of optimal algorithms for other problems are obtained directly from this result.

38 Geometric Intersection

- 1997

Detecting whether two geometric objects intersect and computing the region of intersection are fundamental problems in computational geometry. Geometric intersection problems arise naturally in a…

Linear Approximation of Simple Objects

- Mathematics, Computer ScienceSTACS
- 1992

Algorithms to solve the weighted minmax approximation and the weightedminsum approximation problems to solve a set of m convex polygons in the plane with a total number of n vertices are presented.

New Intersection Algorithm of Convex Polygons Based on Voronoi Diagrams

- Mathematics, Computer Science2006 3rd International Symposium on Voronoi Diagrams in Science and Engineering
- 2006

A new fast and easy to implement tracing algorithm is presented for querying the intersection points of two convex polygons and can be used to query one intersection point of a convex polygon and a general polygon in a special virtual indoor scene to detect collision.

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