How to Calculate the Radii of Curvature for a 3D Flexible Chain?

[chandan]

Dear all,

I was wondering how the radii of curvature can be calculated of a flexible chain (polymer chain). I have the x,y and z values of the polymer chain. For a 2D chain, I can calculate the curvature radii (http://www.intmath.com/applications-differentiation/8-radius-curvature.php). I am unable to extend it to 3D. Any help or guidance is appreciated.

 

[SteamKing]

It's not clear what you mean when you want to extend radius of curvature to 3D.

 

[micromass]

http://en.wikipedia.org/wiki/Curvature#Curvature_of_space_curves

 

[chandan]

Thanks for response SteamKing and micromass. Sorry for the unclear post.
Let me pose the problem in a little different manner.

Suppose, I have 6 points. Its coordinates x, y, and z are known. Say, (x1,y1,z1), (x2,y2,z2), …, (x6,y6,z6).
The aim is to compute its curvature.

One possible way, I can think is to consider the 3 points, and draw a circle that closely passes through these points. And then draw a circle for the next 3 set of points.

Now, these 3 points are lying in a plane. And I have x, y and z coordinates of these points. I do not know how to obtain a circle from these points. The circle also lies in the same plane.
Any suggestion on these would be very helpful.

If anyone can share other ways to compute the curvature, it would be fruitful.

Chandan