I'm having some issues with particles rendering. 

The renderer I'm using GLGraphics and the calls I make are basic:

1. beginShape(POINTS);
2. for(Particle p: particles) vertex(p.x,p.y,p.z);
3. endShape();

The issue I'm having is hardware related: When the camera

gets close enough to particles on some computers the vertex() calls get rendered as circles (newer/better graphic cards)

while on other computers(older ones or with integrated/less powerful graphic cards) they get rendered as squares.

Is there any way to get past that issue ? I was thinking of drawing ellipses instead of vertices, but I've got a few thousand particles animating in a busy scene and on cheap video cards framerate goes down to 12 fps and I fear adding more vertices per particle won't help. 

I don't have a lot of experience with OpenGL, but is there any other hack that could work in this situation ?

Thanks,

George