I don't simulate the brass in my Godot gun effects at all. I just evaluate a casing's position from its age in the vertex shader. That's pretty much the stateless particles from Lutz Latta's "Building a Million Particle System" (GDC 2004). What I added is the bounces.
On a flat floor I can get the hit time straight from the quadratic. The shader loops over the bounces like this:
for (int k = 0; k < MX_BOUNCES; k++) { // 2
float h = max(p.y - gy, 0.0);
float t_hit = (v.y + sqrt(max(v.y * v.y + 2.0 * g * h, 0.0))) / g;
if (t_hit <= 0.0 || tt < t_hit) break;
p += v * t_hit;
p.y = gy;
v.y = -e * (v.y - g * t_hit); // restitution
v.x *= fr;
v.z *= fr; // friction
tt -= t_hit;
}
After the second bounce it slides with tau * (1 - exp(-t / tau)) and I tip it over onto its side. Ejecting one is a single write into two uniform arrays. Brass from three seconds ago costs what brass from this frame costs.
I also kept a GDScript copy of the formula so the game can ask where a casing is. At 10 sample times they agree within 5.4 mm, about a pixel! In the GIF the dotted line is the GDScript side and the casing is the shader. I made the casing bigger and turned restitution up to 0.5 for it, because at my default of 0.34 the second hop is about 2 px tall.
It only knows one floor height, though. A casing will go straight through a wall. Two bounces looked like enough to me, but I'm not sure a third would even read on screen?
