| T O P I C R E V I E W |
| 19102208 |
Posted - 01/20/2014 : 04:42:21 AM
Origin Ver. 8
Can I calculate the radius of curvature for data points?
Thanks for help.
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| 2 L A T E S T R E P L I E S (Newest First) |
| zahraa |
Posted - 01/20/2014 : 4:19:02 PM
Hi,
I am not sure if you want one value for a radius of curvature for your plotted data or values for the ROC for each data point. To get the radius of curvature for your entire curve there is a feature in Origin 9.1 that allows you to do an implicit circle fit on your data and the fit report shows the radius value for the curve (see image below):
For the curvature of every point the simplified equation for ROC is :
For a data set with X and Y (2D plot), you can use the Analysis: Mathematics: Differentiate option to get the first and second derivatives in two columns. Then use the Set column Values option in a fifth column to input the above equation. This will give the value for radius of curvature for each point on your curve. This can be done with any equation, not necessarily the one above.
(Equation found from:
http://www.intmath.com/applications-differentiation/8-radius-curvature.php
http://mathworld.wolfram.com/RadiusofCurvature.html)
If this is not the answer you are looking for please send your data to: tech@originlab.com and we will take a closer look at it.
Originlab Technical Representative |
| Hideo Fujii |
Posted - 01/20/2014 : 3:30:59 PM
Hi 19102208,
The curvature can be obtained by:
f"/(1+f'^2)^1.5
So, you can first calculate the 1st order and 2nd order derivatives, then use Set Column Values tool to calculate the above formula, e.g., if your XY data is stored in columns A and B, first get the derivatives in column C and D, then run the Set Column Values tool with the formula:col(D)/(1+col(C)^2)^1.5) Radius is simply the reciprocal of the curvature, but if you are considering to plot the values, you might want to stay as with curvature because radius often diverges when curvature is close to 0.
Also, you can calculate the radius geometrically from the neighboring 3 points, but it may lead more errors. See the screenshot (I take the absolute values, but it is up to you):
--Hideo Fujii
OriginLab |
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