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Given a line defined as two points in screen coordinate space (which themselves are two 2D vector positions) how would I calculate a 2D Vector perpendicular in the "up" direction for determining a normal force?

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The normal is not consistently defined if what you have is just a pair of (A,B) points. But you can choose one in your 2D plane, e.g. the one pointing at the left w.r.t to your BA vector. – teodron Aug 30 '12 at 11:11
@Casey, check this link for a solution: gamedev.net/topic/367293-finding-the-normal-to-a-2d-line – boobami Aug 30 '12 at 11:15

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If you have a vector v = A - B (the direction is from B to A), then you need to find a vector u so that dot(u,v) = 0.

If v=(x,y), there's no unique solution for this problem, but let's choose the normal pointing to the left side of the v vector. This one is u=(-y,x) and it is attained by rotating v by 90 degrees. Using complex numbers: v = x + i y and a rotation of 90 degrees means multiplying v by i. Hence u= vi = i x - y or in cartesian coordinates: u=(-y,x).

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