How can I convert a 2D particle ring (Saturn-like) into a true 3D particle system?

I’m building a real-time particle system (WebGL/Canvas-based), currently rendering different formations like swarms, explosions, and a Saturn-like ring.

Right now, my “Saturn” effect is essentially a 2D circular particle distribution with a tilted illusion, but it’s not truly 3D.

I want to:

Convert this into a true 3D particle ring

Allow camera rotation / perspective

Maintain performance with thousands of particles

Current approach:

Particles positioned using polar coordinates:

x = r * cos(theta)

y = r * sin(theta)

Rotation is faked using transforms

What I’m looking for:

How to distribute particles in a 3D ring (torus-like or disk-like structure)?

Should I move to WebGL shaders (GLSL) for this?

Best way to handle depth, perspective, and camera movement

Any lightweight approach to simulate orbital motion in 3D

Constraints:

Real-time performance is critical

Running in browser (WebGL preferred, but open to libraries like Three.js)

Any guidance, math references, or examples would be really helpful.