How can I calculate the opacity of a crystal as function of its lattice orientation?

Question

I would like to plot the opacity of a crystal (when radiated by an ion beam) with $[100]$ orientation as a function of the tilt angle $\theta$ from $0^\circ$ to $90^\circ$. So far I've been doing it using Vesta, a program in which I can model the crystal structure in 3D. I insert the reference atomic radii for each atom, then rotate the whole thing for different angles and measure the free projected area for each angle using Photoshop.

Obviously that's very tedious, so I do it only in steps of $5^\circ$ or even $10^\circ$. I would like to find a more systematic way (or a program that can simulate the channeling for me?), since I now have to do it for different crystal structures and for another degree of freedom (azimuthal angle) as well.

Thank you very much in advance for your suggestions.

Julien.

Edit: I've attached a picture to make sure I expressed myself correctly. The top picture shows a [100] plane of gallium oxide (the black lines show the unit cell). The bottom picture shows the same rotated by about $27.4^\circ$ "sideways" ([101]). The calculations I describe above relate to the free area/area of projected unit cell for each orientation.