javascript - Problems With Vector Reflection with Particle Collisions -

i wondering whether made math mistake in particle collision simulation found here.

the particles don't seem separate during collision resolution. here code snippet function separates particles , changes velocities:

//particle 1 var pi = particles[i]; //particle 2 var pj = particles[j];  //particle 1 particle 2 var pimpj = pi.mesh.position.clone().sub(pj.mesh.position);  //particle 2 particle 1 var pjmpi = pj.mesh.position.clone().sub(pi.mesh.position);  //if colliding (radius 20) if(pimpj.length() < 20 && pimpj.length() != 0)  {       //reflect velocity off of 1->2     pi.velocity = pi.velocity.reflect(pimpj.clone().normalize()).multiplyscalar(restitution);     //reflect velocity off of 2->1      pj.velocity = pj.velocity.reflect(pjmpi.clone().normalize()).multiplyscalar(restitution);      //move particle 1 appropiate location based off of distance in between     var pip = pi.velocity.clone().normalize().multiplyscalar(20-pimpj.length());     //move particle 2      var pjp = pj.velocity.clone().normalize().multiplyscalar(20-pimpj.length());     pi.mesh.position.add(pip);     pj.mesh.position.add(pjp); } 

i have tried reversing pimpj pjmpi while changing pi.velocity, no effect.

note: using three.js

firstly, particle collisions seem looking elastic collisions, there maths covering calculation of velocities after collision.

the collision simplest in centre of momentum frame, if first calculate frame v = (m₁v₁ + m₂v₂)/(m₁+m₂), can subtract both particles, simple symmetric collision , add frame velocity on afterwards.

from there, calculate velocities using formulae in 2 & 3d section of page.

specific points on code:

1. pimpj = -pjmpi, don't need both
2. a collision occurs when paths between last frame , frame got close; if check distance @ each frame have problems particles fly through each other @ high speed, , have keep shifting positions because overlapping when detect collision.
3. ideally calculate positions on impact , use redirect them.
4. for speed, calculate pimpj.clone().normalize() once, , store - you're not changing direction unit vector later, don't need keep recalculating it, or calculating pjmpi-derived equivalents (see #1)