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 How to fit a circle beneath a curve

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afry Posted - 02/26/2014 : 06:40:06 AM
Origin Ver. and Service Release (Select Help-->About Origin): 9
Operating System:Win7
Hello,

I would like to know how to fit a circle beneath a curve like in the example below.It's for characterizing the roundness of the curve.





Thanks in advance
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zahraa Posted - 02/26/2014 : 12:40:00 PM
Dear Afry,

One way to do this would be to use the built in Circle function present under Analysis: Fitting: Non Linear Implicit Curve Fit in Origin 9.1. However you would need to adjust the function to make it lie just under your curve. Also you would need to specify tangent points.

I am assuming that you want to find the radius of curvature of your curve. I used this source:
http://www.intmath.com/applications-differentiation/8-radius-curvature.php
and it might be easier for you to use this formula:


to find the radius of curvature at the maximum x value of your curve.
(You can go to Analysis: Mathematics: Differentiate for single and double differentiation).
If you wish to represent this visually, you could then create a circle object with the radius you found in your calculation. This is not the most optimum solution but it is one way of doing this.


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