Find maximum angle in a triangle mesh, using matlab

Alec Jacobson

February 08, 2010

weblog/

If a,b,c are the lengths of the side of a triangle then the maximum angle of the triangle is the angle opposite the largest side, call that one c. A formula for this angle is then 
     / a2 + b2 - c2 \
cos-1| ------------ |
     \    2*a*b    /
So then if you have a variable edge_norms which is an n by 3 matrix of the lengths of edges in your mesh, a way to find the maximum angle of each face is to issue: 
acos(((sum(edge_norms'.^2)-2*max(edge_norms').^2)) ...
  ./(2*prod(edge_norms')./max(edge_norms')))
I like to make mine in degrees by adding 
(...)./(2*pi).*360
And then you can find the maximum angle over all by issuing 
max(...)
Surely this can be optimized, but I think matlab does a fair job on its own at that already.