How to compute the inverse orthogonal projection of a point in the viewing plane onto a plane in the scene?
<p>Suppose I have a viewing plane <code>vn</code>, with an orientation <code>q1</code> and a plane in the scene <code>un</code> with an orientation <code>q2</code>.</p>

<p><code>q1</code> and <code>q2</code> are quaternions.</p>

<p>How would I find the unknown point <code>ux, uy, uz</code> such that <code>proj_u_plane_vn</code> is equal to a known point <code>vx, vy, 0</code>?</p>

<p>Would the problem be simpler by finding the relative orientation <code>q2-q1</code>?</p>

<p>Right now I'm trying to do it with i, j and k values, but it seems like overkill and I'm not seeing the answer pop out without doing inverse trig, not that I would mind that, but I'm looking for a more elegant solution.</p>

<p>Thanks in advance. :)</p>