Converting 2D viewport translation to 3D rotation

Question

I am trying to rotate a 3D Cylinder with reference to a 2D viewport. With the radius of the cylinder and the 2D translation known, how can i find out the angle it turns?

Answer 1

Let's assume the cylinder rotates from A to B. Further, let's assume that A is θ degrees counterclockwise and B is θ degrees clockwise from the horizontal. Thus, the angle between A and B is 2θ .

The y coordinate of A is given by r*sin(θ) , that of B is simply -r*sin(θ) .

Thus, 2*r*sin(θ) = D (the pan distance)

Solve for θ :

θ = asin(D/(2*r))

(where asin is the arc sine function)

Another (possibly more robust) method would be to compute the perpendicular and base of the triangle and then do an atan2(perp,base) .

The perpendicular is simply D/2 , while the base is sqrt(R*R - D*D/4) .