See also http://eqsp.sourceforge.net/ and Paul Leopardi, "A partition of the unit sphere into regions of equal area and small diameter",
https://etna.mcs.kent.edu/vol.25.2006/pp309-327.dir/pp309-327.html
Electronic Transactions on Numerical Analysis, Volume 25, 2006, pp. 309-327.
Preprint: Applied Maths Report AMR05/18, May 2005, Updated June 2006.
http://www.maths.unsw.edu.au/applied/files/2005/amr05_18.pdf
FAQ - from the README
What is the Recursive Zonal Equal Area (EQ) Sphere Partitioning Toolbox?
The Recursive Zonal Equal Area (EQ) Sphere Partitioning Toolbox is a suite of Matlab functions. These functions are intended for use in exploring different aspects of EQ sphere partitioning.
The functions are grouped into the following groups of tasks:
Create EQ partitions
Find properties of EQ partitions
Find properties of EQ point sets
Produce illustrations
Test the toolbox
Perform some utility function
What is an EQ partition?
An EQ partition is a partition of S^dim [the unit sphere in the dim+1 Euclidean space R^(dim+1)] into a finite number of regions of equal area. The area of each region is defined using the Lebesgue measure inherited from R^(dim+1).
The diameter of a region is the sup of the Euclidean distance between any two points of the region. The regions of an EQ partition have been proven to have small diameter, in the sense that there exists a constant C(dim) such that the maximum diameter of the regions of an N region EQ partition of S^dim is bounded above by C(dim)*N^(-1/dim).
What is an EQ point set?
An EQ point set is the set of center points of the regions of an EQ partition. Each region is defined as a product of intervals in spherical polar coordinates. The center point of a region is defined via the center points of each interval, with the exception of spherical caps and their descendants, where the center point is defined using the center of the spherical cap.
Which versions of Matlab can I use?
This toolbox has been tested with Matlab versions 6.5 and 7.0.1 on Linux, and 6.5.1 on Windows.
How do I install the Recursive Zonal Equal Area Sphere Partitioning Toolbox?
This toolbox is organized into a number of directories. To use it effectively, these directories need to be on your Matlab path every time you start Matlab. You will therefore need to install the toolbox before using it.
To do this,
Unzip the file eqsp-x.y.zip into the directory where you want the toolbox to reside. This will create the subdirectory eq_sphere_partitions.
Run Matlab, change directory to eq_sphere_partitions and then run install_eq_toolbox.
For more information, see INSTALL.txt. |
