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How to calculate the angle between two lines from the same origin?

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Please I need help on this, I have extracted severla minutia points from this fingerprint image and I have been able to calculate the angle of each minutia according to the ridge direction, which i have dipslayed in green small arrows, and i want to take one of the minutia as a reference point and calculate the distance and angle each other minutia forms with the reference minutia, that is the angles in orange color, please help me on this. thanks
  8 Comments
Fego Etese
Fego Etese on 9 Jun 2020
Edited: Fego Etese on 9 Jun 2020
Thanks Adam, please I also want to ask, I used gradient direction estimation woth block processing to get the angle of the reference minutia, from a gray scale image, that is to get the angle of the ridges, does this method calculate the angle to the x-axis?
Also i want to find the angle of the white valley in a bifurcation, that is the white space in between the two ridges of a bifurcation, please how can i go about it? I saw on that paper that i need to calculate the angle of the bifurcation on the negative image of the fingeprint but i don't know how it'll work since I calculated it on a gray image not a binary image

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Accepted Answer

KSSV
KSSV on 9 Jun 2020
O = [0. 0.] ; % origin
% Two points
A = rand(1,2) ;
B = rand(1,2) ;
u = O-A ;
v = O-B ;
CosTheta = (dot(u,v) / (norm(u)*norm(v)));
  8 Comments
Fego Etese
Fego Etese on 9 Jun 2020
So i should like draw a line for the origin minutiae and use an arbitrary maginitude and the coordinates at the end of the line?
KSSV
KSSV on 9 Jun 2020
It need not to be origin....any three non colliniear points.

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More Answers (1)

David Hill
David Hill on 9 Jun 2020
Seems like just a math problem. If you have two vectors A and B, then angle between them is:
angle = acos(dot(A,B)/norm(A)/norm(B));
  4 Comments
Fego Etese
Fego Etese on 9 Jun 2020
Edited: Fego Etese on 9 Jun 2020
Please look at the example i gave on KSSV's answer, it highlights what I'm facing better, the minutiae O has no magnitude but has an angle from the gradient calculation and i want to find the angle minutia A is making with miunutiae O
David Hill
David Hill on 9 Jun 2020
You need four pixel points, to generate the three vectors from the origin. It does not matter what the magnitudes are since they get divided out to compute the angle.

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