Input Light Position with Arcball

Question

I am trying to implement a functionality in OpenGL using GLUI such that the "Arcball" control is used to input the position of the light. I'm not sure how to go about this as the rotation matrix given by the arcball is of 4x4 dimensions, while the light position is an 1-D array of 3 coordinates.

Answer 1

Rotationg a light around the scene makes only sense for directional lights (i.e. positions at infinity). So you're not rotating a point, but a direction, just like a normal. Easy enough: Let the unrotated light have the direction (0,0,1,0). Then to rotate this around the scene you multiply it by the transpose-inverse of the given matrix. But since you know, that this matrix does contain only a rotation, this is a special case where the transpose-inverse is the same as the original matrix.

So you just multiply your initial light direction (0,0,1,0) with the matrix.

We can simplify this even further. If you look at the multiplication, you see, that it essentially just extracts the (weighted) column(s) of the matrix for which the original light position vector is nonzero. So, if we really start with a light direction of (0,0,1,0), you just take the 3rd column from the arcball rotation matrix.