Curvature calculations on triangular 3D surface

Calculate principal curvatures on a triangular mesh in 3D.

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)

[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!

[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/