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Curvature calculations on triangular 3D surface

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05 Aug 2009 (Updated )

Calculate principal curvatures on a triangular mesh in 3D.

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Description

Function to calculate the principal curvatures on a triangular mesh. Approximations of curvature are based on local (N=1) neighborhood elements and vertices.

Note: Directions of curvatures aren't calculated appropriately. Will post an updated version once this is implemented.

Note that calculations at vertices with few adjacent triangles, and hence few adjacent vertices, are expanded to a greater neighborhood.

Reference:
1) Chen and Schmitt (1992) Intrinsic surface properties from surface triangulation
2) Dong et al. (2005) Curvature estimation on triangular mesh, JZUS

This code makes use of routines: buildInverseTriangualtion.m & removeDO.m
initially written by: David Gringas. He is gratefully acknowledged

MATLAB release MATLAB 7.7 (R2008b)
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Comments and Ratings (3)
07 Mar 2012 yvus

Hi,

I am very happy to find for the first time curvature estimation works on triangular meshes on matlab. Therefore I am very interested in the corrected version of the file.

Let me know when you have such a version, or, do you know an other file doing the same job than yours without this little bug?

Cheers
Yvus

28 Jan 2010 J. Ole Kaven

Hi Matt
k1 is the maximum principal curvature. See Chen & Schmidt equation (6).
Link to paper (requires authorization):
http://www.springerlink.com/content/y57127165032r535/

28 Jan 2010 Matt

Works well, however, I routinely get a "divide by zero" warning at line 65, even when using a hyperbolic paraboloid:
[x,y]=meshgrid(-3:.25:3,-3:.25:3);
tri=delaunay(x,y);
z=0.25*x.^2-0.25*y.^2;

Also, is please be more specific in defining output of which is minimum/maximum curvature, k1 or k2. Thanks!

Updates
06 Aug 2009

Directions of curvatures aren't calculated appropriately. Will post an updated version once this is implemented.

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