The Origin Forum
File Exchange
Try Origin for Free
The Origin Forum
Home | Profile | Register | Active Topics | Members | Search | FAQ | Send File to Tech support
Username:
 Password:
Save Password
Forgot your Password? | Admin Options

 All Forums
 Origin Forum
 Origin Forum
 radius of curvature		  New Topic  Reply to Topic
 Printer Friendly
Author Previous Topic Topic Next Topic Lock Topic Edit Topic Delete Topic New Topic Reply to Topic

19102208

Germany
Posts
Posted - 01/20/2014 :  04:42:21 AM  Show Profile  Edit Topic  Reply with Quote  View user's IP address  Delete Topic
Origin Ver. 8

Can I calculate the radius of curvature for data points?
Thanks for help.

Hideo Fujii

USA
1582 Posts
Posted - 01/20/2014 :  3:30:59 PM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
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
Go to Top of Page

zahraa

USA
52 Posts
Posted - 01/20/2014 :  4:19:02 PM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
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
Edited by - zahraa on 01/20/2014 5:59:16 PM
Go to Top of Page
  Previous Topic Topic Next Topic Lock Topic Edit Topic Delete Topic New Topic Reply to Topic
 New Topic  Reply to Topic
 Printer Friendly
Jump To:
The Origin Forum © 2020 Originlab Corporation Go To Top Of Page
Snitz Forums 2000