# EQSP 1.0

OS : Windows / Linux / Mac OS / BSD / Solaris

Script Licensing : Freeware

Created : Aug 21, 2007

Downloads : 4

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## The Recursive Zonal Equal Area (EQ) Sphere ...

The Recursive Zonal Equal Area (EQ) Sphere partition Toolbox is a suite of Matlab functions. These functions are intended for use in exploring different aspects of EQ sphere partitioning.

- Find properties of EQ partitions

- Find properties of EQ point sets

- Produce illustrations

- Test the toolbox

- Perform some utility function

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).

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.

**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

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).

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.

**EQSP 1.0 scripting tags:**points, eqsp mathematics, center, matlab mathematics, defined, regions, matlab eqsp, partition, spherical.

**What is new in EQSP 1.0 software script?**- Unable to find EQSP 1.0 news.

**What is improvements are expecting?**Newly-made EQSP 1.1 will be downloaded from here. You may download directly. Please write the reviews of the EQSP. License limitations are unspecified.