Flat Statistics Project Definition ( v1x01 )

Public Project Description - none yet available

Overview

This project will provide portable software tools that enable a remote researcher to compute statistics of geometric objects that are defined on topologically spherical flat maps.

Restrictions, Exclusions, Limitations

People Affected

Version

Requirements

• Java 1.5 is used to implement the tools produced by this project.

Requirements Change Procedure

• Changes to be mutually agreed upon by CS and programmer.
• Changes and their date will be entered in a 'requirements change' list.

Requirements Changes

Products

This project will result in the following products:

• Applications
• Documentation
  • Various TWiki web pages including

Approach

discarded approach 1

(reasons why it was abandoned)

discarded approach 2

(reasons why it was abandoned)

Notes

This application will compute statistics of certain geometric objects: points and sampled contours. The topology of the domain is spherical, which gives periodicity in each dimension. When comparing points, the statistics will be computed with representations of the points from the periodic extension of the domain which minimize the distance between the points.

For example, consider a domain D = [0,1]x[0,1] with d = (x,y) being an element of D. We can glue the boundaries together, such that (0,y) ~ (1,y) and (x,0) ~ (x,1). We can take a point (x,y) for any real x and y to be from the period extension of D. Hence, (n + x, m + y) ~ (x,y) for all integers m,n. If we have two points a = (0.1,0.1) and b = (0.9,0.9), the average without the periodicity is (0.5,0.5). If we take into account the periodicity, we can find representation from the equivalence classes of these points which minimize the distance between them. Since (0.9,0.9) ~ (-0.1,-0.1), b ~ (-0.1,-0.1). This minimizes the distance between the points, so we can average the points to find (0,0).

RACI Chart

R - Responsible person
A - Actions taken (Authorizes something, provides support, et. cetera)
C - Communicates or consults with this person
I - Inform this person

Lessons Learned

• lesson 1
• lesson 2