To calculate the angles of the Delaunay triangles

I am trying to calculate the 3 angles of each triangle generated by Delaunay triangulation. For example, I have already obtained the area and the perimeter of each triangle. But I also wanna calculate the angles of each triangle. Anyone help?

Answer 1

[Roger Stafford]

If P1, P2, and P3 are coordinates of the three vertices of a triangle, and A is its area, its angle at P1 can be calculated as:

 a1 = atan2(2*A,dot(P2-P1,P3-P1)); % <-- Corrected

and similarly for the other two angles.

[Roger Stafford]

I corrected the formula.

Answer 2

[Michael Haderlein]

I like that question. I'm curious if there's a faster solution (maybe even a built-in function I don't know), but my code looks like this:

x=rand(5);
y=rand(5);
TRI=delaunay(x,y);
X=x(TRI);
Y=y(TRI);
a=zeros(size(X));
for cnt=1:3
a(:,cnt)=abs(diff(angle(bsxfun(@minus,X(:,[1:cnt-1 cnt+1:end]),X(:,cnt))+1i*bsxfun(@minus,Y(:,[1:cnt-1 cnt+1:end]),Y(:,cnt))),[],2));
end

This should work but please check for testcases if it's really the case.

[ZhG]

This is not necessary to deal with divide operation. Thumb up.

Answer 3

[ZhG]

Thank you guys.