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Patch Curvature

version (314 KB) by Dirk-Jan Kroon
Principal, Gaussian and Mean Curvature of triangulated mesh


Updated 15 Jan 2014

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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

Cite As

Dirk-Jan Kroon (2021). Patch Curvature (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (17)

Pieter Livens

For those using this code and noticing small errors in the principle values, the 'eig2' function compares the principle values based on the absolute value, which is incorrect.
If you simply remove both 'abs' functions in the if loop on line 156, the direction of the principle curvatures will be correct. Everything else works perfectly, many thanks for sharing this code.

Dongjin Han

Great work! Thank you

Martin Kefer

Seems to only work on closed patches, if there are open spots, missing faces, Cmean is complex

Nairouz Mohamed


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??

Gianni Schena

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);


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?


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.




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.


This version seems much better!

Dirk-Jan Kroon

* 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.


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.



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

Jonathan Sullivan

Great submission. Very help. Nice examples provided too!

MATLAB Release Compatibility
Created with R2011a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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