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## EQSP: Recursive Zonal Sphere Partitioning Toolbox

version 1.0.0.0 (108 KB) by Penguian

### Penguian (view profile)

A suite of Matlab functions intended for use in exploring equal area sphere partitioning.

Updated 15 Dec 2006

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

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.

Peter Paul

### Peter Paul (view profile)

I'm OK with the not-working installation routine. But could you please replace the NARGCHK usages by their modern equivalents? All these warnings are annoying.

Zahra

### Zahra (view profile)

The install function does not work anymore in 2014b version, with the following error. Does anyone know how to fix this?

>> install_eq_toolbox
Error using fileparts
Too many output arguments.

Error in install_eq_toolbox (line 89)
[command_dir name ext ver] = fileparts(mfilename('fullpath'));

Steffen

### Steffen (view profile)

Great submission. However I wonder why I get region coordinates with values larger than 2*pi? Any explanation for this?

Nick

### Nick (view profile)

To be more concrete, take the earth with high density at the north pole and decreasing density as you go south in latitude

Nick

### Nick (view profile)

This is great! Can the method be extended to spheres with variable density to partition into equal mass?

Nick

Georg Wiora

Excellent work!

Anton Semechko

### Anton Semechko (view profile)

This submission is awesome!!! You should apply more tags to it. Anyone interested in spherical parameterization and mesh resampling will most likely find this very useful. Thank you very much!

 15 Dec 2006 1.0.0.0 Fix summary. Fix spacing in description. Add URLs.
##### MATLAB Release Compatibility
Created with R14
Compatible with any release
##### Platform Compatibility
Windows macOS Linux
##### Acknowledgements

Inspired by: Toolbox Installer 2.2