Mean Curvature (Fast code)

Calculate the Mean curvature of a given surface (x,y,z) using vectorized form.

Description

This function is a modified form of original code (see below). I vectorized the code to make the code time efficient.

The function calculates the mean curvature of the input structured matrix data. The input are the coordinate matrices of x,y & z (as generated by meshgrid or similar functions).

The outputs are a matrix containing the mean curvature at each point and a scalar giving the surface average mean curvature (SAMC).

Mistake found by Anthony Beaucamp. Thanks for letting me know! File has been updated.

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
Mean Curvature

• MATLAB release: MATLAB 7.0.4 (R14SP2)
• Other requirements: na

[M. Tetouan]

Computing the mean curvature of an implicit surface is very simple and straightforward. The challenging problem is how to efficiently compute the curvatures of a 3D triangle mesh. The most common representation of a 3D surface in computer graphics is the triangle mesh which consists of a set of vertices (geometry) and a set of faces (connectivety).

[John D'Errico]

That this function does not work on a triangulation does not make it worth deletion. It merely makes it of less value to at least one user than it might be otherwise.

I do have two issues though. First is the claim in the description that it works on a "point cloud". The phrase point cloud suggests an unstructured set of points. This code requires a structured array of data, as meshgrid might have generated. My second comment is a related one - There is very little information supplied in the help to this function, only one vague line. I'd have preferred a much better description of what the inputs must be. Ordinarily I'd have given this file a rating of 2 due to these flaws, but since its already gotten a rating of 1, I chose to round up.

[Pratik Kamdar]

Thnx for the comments John. I will update the file description. Presently, I am having trouble logging into my account.

[John D'Errico]

Cleaned up the help and description. I also compared this code to its predecessor - on a 100x100 grid, I saw a 40x speedup.
(This review may appear twice.)

[Anthony Beaucamp]

That's a big improvement from the original code, but you made a mistake: It's not (2.*(E.*G)-F.^2) but 2.*((E.*G)-F.^2). Anyway, I am working on an extended version that calculates everything: Principal Curvatures, Directions, Mean and Gaussian. I will post it as soon as it's ready.

[Pratik Kamdar]

File updated to remove error found by Anthony Beaucamp. Thanks for letting me know! Dont know how I missed that! Btw, the original file also has the same error.

[Claude Gouedard]

It seems I recognize my own code (!) I sent you because I told you that yours was not in the Matlab spirit ...
I don't see any citation ...no thanks ...

[Claude Gouedard]

I apologize !
I didn't send my code to you ...
It was to Ahmed Elnagar about "Gaussian Curvature " http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=5229&objectType=file

However ...
this code, yours, sounds a lot like mine. Perhaps there is only one way to program fine ....

[Pratik Kamdar]

@Claude Gouedard:

I acknowledged the original author in my post. I dont think I am responsible for any missing citations on the part of the original author.
(This review might appear twice).

[mehdi ravanbakhsh]

Hi pratik,
Can you please let me know how I can use your code to calculate the curvature of a 2-D curve?
Thanks,Mehdi