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# Circle Regression Analysis

IP.com Disclosure Number: IPCOM000076334D
Original Publication Date: 1972-Feb-01
Included in the Prior Art Database: 2005-Feb-24
Document File: 2 page(s) / 31K

IBM

## Related People

Lewis, SH: AUTHOR

## Abstract

This program calculates the "best fit" center and radius for a set of data points which describe a circular curvature. The data points are read in as pairs of X and Y coordinates, each describing some position on the curve. These coordinates are counted and checked to see if there are at least three points. If not, the program is terminated and a message is outputted informing the operator that there is insufficient data to determine a unique center and radius. For three or more data points the program continues.

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Circle Regression Analysis

This program calculates the "best fit" center and radius for a set of data points which describe a circular curvature. The data points are read in as pairs of X and Y coordinates, each describing some position on the curve. These coordinates are counted and checked to see if there are at least three points. If not, the program is terminated and a message is outputted informing the operator that there is insufficient data to determine a unique center and radius. For three or more data points the program continues.

For each coordinate a Zi = Xi/2/ + Yi/2/. The equation Z = AX + BY + C is solved using any multiple regression analysis subroutine and the constants A and B are determined.

Solving XC = A/2 and YC = B/2 yield the "best fit" center of the data points. The radius is determined by finding the average radius. This is accomplished by solving

(Image Omitted)

where M is the number of data points, (Xi, Yi) are the coordinates of the data points, and (XC, YC) is the coordinate of the center previously calculated.

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