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Patch Curvature

4.2 | 10 ratings Rate this file 24 Downloads (last 30 days) File Size: 314 KB File ID: #32573 Version: 1.2
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Patch Curvature


Dirk-Jan Kroon (view profile)


18 Aug 2011 (Updated )

Principal, Gaussian and Mean Curvature of triangulated mesh

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  This function calculates the principal curvature directions and values
  of a triangulated mesh.
  The function first rotates the data so the normal of the current
  vertex becomes [-1 0 0], so we can describe the data by XY instead of
  Secondly it fits a least-squares quadratic patch to the local
  neighborhood of a vertex "f(x,y) = ax^2 + by^2 + cxy + dx + ey + f".
  Then the eigenvectors and eigenvalues of the hessian are used to
  calculate the principal, mean and gaussian curvature.
    FV : A triangulated mesh (see Patch)
    usethird : Use third order neighbour vertices for the curvature
               fit, making it smoother but less local. true/ false (default)
    Cmean : Mean Curvature
    Cgaussian : Gaussian Curvature
    Dir1 : XYZ Direction of first Principal component
    Dir2 : XYZ Direction of second Principal component
    Lambda1 : value of first Principal component
    Lambda2 : value of second Principal component

MATLAB release MATLAB 7.12 (R2011a)
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Comments and Ratings (13)
23 Aug 2016 KK

KK (view profile)

When I try to run the file on my data, I get the error:
Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.
> In VectorRotationMatrix (line 7)

Any comments??

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30 Jun 2016 G. Sken

G. Sken (view profile)

By shifting around a sphere we obtain different curvatures. thus the curvature seems to depend on the position of the centre (?)
[xx,yy,zz] = meshgrid(1:side,1:side,1:side);
c=[h_side h_side h_side]; % centre
rr = sqrt( (xx-c(1)).^2 + (yy-c(2)).^2 + (zz-c(3)).^2 );
FV= isosurface(rr,radius);

10 Mar 2016 XiaoGang

30 Oct 2015 Stefano Cauzzi

Great tool, however I keep on getting the following warning:
Warning: Rank deficient
Did anyone experience the same problem? Did you find a solution?

04 Feb 2015 Helia

Helia (view profile)

why shifting the cylinder changes the curvature values? Is there an error in calculation?
I used the cylinder provided with this code but shifted the vertices keeping the same scaling. I obtained a different curvature values. Sounds strange to me.

11 Dec 2014 Marta

Marta (view profile)


26 Oct 2014 Leo

Leo (view profile)

Dear author, Thank you for this work.

However, I have a problem about this code. I am not quite understand the meanning of:
k = rand(1,3)
in the VectorRotationMatrix.
It will be very kind of you, if you can give me some hint.
Thanks again.

15 Jan 2014 Binhang

This version seems much better!

15 Jan 2014 Dirk-Jan Kroon

Dirk-Jan Kroon (view profile)

* Binhang
Thank you, there was a bug which I solved by removing abs from the eigenvalues. This version will probably be online in one or two days.

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13 Jan 2014 Binhang

Dear author, I have a question for the result.

Have you ever test your code for the torus? Did you notice that all the values for gauss and mean curvature are positive?

Well, I think this is incorrect.

06 Apr 2013 baziham


Dear Mr.Kroon ,
Is it possible that you include how to calculate squared mean curvature over the mesh .

Comment only
10 Jan 2012 Jonathan Sullivan

Great submission. Very help. Nice examples provided too!

15 Jan 2014 1.2

Fixed eigenvector calculation, sign of eigenvalues and sorting of eigenvectors

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