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

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NIKHIL PATIL
NIKHIL PATIL 2016-5-18
编辑： Ahmet Cecen 2016-5-18
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

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回答（1 个）

Ahmet Cecen
Ahmet Cecen 2016-5-18
编辑：Ahmet Cecen 2016-5-18
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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