math - How to find the orientation of three points in a two dimensional space given coordinates of those points? -

actually found formula, dont know how works.

let p,q , r 3 points,

k=(q.y - p.y)*(r.x - q.x)-(q.x - p.x) * (r.y - q.y);  if(k==0): colinear if(k>0) : clockwise if(k<0) : counter clockwise 

i pleased if explains how works.

this formula used calculate cross product of vectors q-p , q-r. can see in geometric meaning section cross product value c = x b = |a|*|b|*sin(theta), theta angle between these vectors (point-to-point directions). sin(theta) = 0 parallel vectors, positive when theta < 180, negative otherwise.

example:

clockwise triplet abc: cross product of ab , ac vectors >0

anticlockwise triplet acd: cross product of ac , ad negative.