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

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

Answer 1

[Ahmet Cecen]

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.