I need to reconstruct particle tracks starting from a generating disk and entering a detector. The geometry of the setup is shown in the schematic below.
Variables I know:
$D$: the distance of generating disk to detector center.
$\theta, \Phi$: azimuth and zenith angles for the orientation of the disk
$R$: on_disk radius. The distance of the particle starting point to the center of the disk
$\Theta$: on_disk azimuth angle
I am assuming that the track will have an equation $f(x(t),y(t),z(t)) = p_0 + ut$ where $p_0$ is the starting point position and $u$ the velocity times a vector normal to the disk. But I am having some trouble calculating the normal vector and the starting point. Any ideas?