# An Efficient Search Algorithm for Minimum Covering Polygons on the Sphere

@article{Wang2013AnES, title={An Efficient Search Algorithm for Minimum Covering Polygons on the Sphere}, author={Ning Wang}, journal={SIAM J. Sci. Comput.}, year={2013}, volume={35} }

One of the computationally intensive tasks in the numerical simulation of dynamic systems discretized on an unstructured grid over the sphere is to find a number of spherical minimum covering polygons of given locations, whose vertices are chosen from the grid points. Algorithms have been proposed attempting to perform this task efficiently. However, these algorithms only reduce the linear search time for each polygon vertex candidate by a constant factor, and their polygon search algorithms…

## Figures and Tables from this paper

## One Citation

### A Vertically Flow-Following Icosahedral Grid Model for Medium-Range and Seasonal Prediction. Part I: Model Description

- Environmental Science
- 2015

AbstractA hydrostatic global weather prediction model based on an icosahedral horizontal grid and a hybrid terrain-following/isentropic vertical coordinate is described. The model is an extension to…

## References

SHOWING 1-10 OF 25 REFERENCES

### Geometric Properties of the Icosahedral-Hexagonal Grid on the Two-Sphere

- Computer ScienceSIAM J. Sci. Comput.
- 2011

This paper presents an analytical analysis of several geometric properties of the icosahedral grids based on two basic constructions: recursive and nonrecursive construction and points out that these geometric properties can be improved with modified construction procedures.

### Optimal Expected-Time Algorithms for Closest Point Problems

- Computer ScienceTOMS
- 1980

Algorithms for solving a number of closest-point problems in k- space, including nearest neighbor searching, finding all nearest neighbors, and computing planar minimum spanning trees can be implemented to solve practical problems very efficiently.

### Near Neighbor Search in Large Metric Spaces

- Computer ScienceVLDB
- 1995

A data structure to solve the problem of finding approximate matches in a large database called a GNAT { Geometric Near-neighbor Access Tree} is introduced based on the philosophy that the data structure should act as a hierarchical geometrical model of the data as opposed to a simple decomposition of theData that does not use its intrinsic geometry.

### Geometric Range Searching and Its Relatives

- Computer Science
- 2007

This volume provides an excellent opportunity to recapitulate the current status of geometric range searching and to summarize the recent progress in this area.

### Icosahedral Discretization of the Two-Sphere

- Computer Science
- 1985

An almost uniform triangulation of the two-sphere, derived from the icosahedron, is presented, and a procedure for discretization of a partial differential equation using this triangular grid is described.

### Ray shooting and parametric search

- Computer ScienceSTOC '92
- 1992

Efficient algorithms for the ray shooting problem are presented, and the parametric search technique is reduced to the segment emptiness problem.

### The Operational Global Icosahedral-Hexagonal Gridpoint Model GME: Description and High-Resolution Tests

- Environmental Science
- 2002

The German Weather Service (Deutscher Wetterdienst) has recently developed a new operational global numerical weather prediction model, named GME, based on an almost uniform icosahedral‐hexagonal grid and the formulation of the discrete operators for this grid is described and evaluations that demonstrate their second-order accuracy are provided.

### A Finite-Volume Icosahedral Shallow-Water Model on a Local Coordinate

- Physics
- 2009

Abstract An icosahedral-hexagonal shallow-water model (SWM) on the sphere is formulated on a local Cartesian coordinate based on the general stereographic projection plane. It is discretized with the…

### A Randomized Algorithm for Closest-Point Queries

- Computer ScienceSIAM J. Comput.
- 1988

This result approaches the $\Omega (n^{\lceil {{d / 2}} \rceil } )$ worst-case time required for any algorithm that constructs the Voronoi...

### An Algorithm for Finding Best Matches in Logarithmic Expected Time

- Computer ScienceTOMS
- 1977

An algorithm and data structure are presented for searching a file containing N records, each described by k real valued keys, for the m closest matches or nearest neighbors to a given query record.…