To calculate the angles of the Delaunay triangles

ZhG
2014 8 28
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更新时间：2014 8 28
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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?

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Roger Stafford
Roger Stafford 2014-8-28
编辑：Roger Stafford 2014-8-28

2 个投票

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.

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Michael Haderlein
Michael Haderlein 2014-8-28

1 个投票

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.

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