What is the mathematical proof for the formula to find angle between 3 points in an image?

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Hi everyone,
I'm trying to find angle between 3 points (say a, b, & c with b at the canter) in an image. I've used this formula for calculating the angle
angle_in_radian = atan2(norm(cross(n1,n2)),dot(n1,n2))
where n1 is the vector formed using points a & b while n2 is the vector formed using points c & b
The above formula corresponds to atan2(Y,X) in matlab i.e. norm(cross(n1,n2)) gives us Y and dot(n1,n2) gives us X
The formula works correct. I need the mathematical derivation of this formula. I searched about the vectors, the cross and dot products but didn't found expected result.
Please help me, i need to add this point in my thesis.
Thanks in advance

Answers (1)

Ahmet Cecen
Ahmet Cecen on 18 May 2016
Edited: Ahmet Cecen on 18 May 2016
https://en.wikipedia.org/wiki/Scalar_projection
https://en.wikipedia.org/wiki/Cross_product
Get the expression for sine and cosine there. Divide sine by cosine and you will get the expression you are looking for.

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