Treatment of particle boundary collision

Deal with collisions for individual particles ：

First , To determine whether particles penetrate the boundary , If it penetrates , It's a collision . This is achieved by collision detection algorithm . This algorithm is very complex , Especially when multiple objects and complex surfaces are involved . Let's not discuss , Just discuss the simplest case .

Suppose we have detected a collision , And we know the normal direction of the wall N. Also know the current particle speed and position .

that

1. Judge $v\cdot N<0?$ The former means that the speed should continue to move in the direction of penetrating the boundary . If not , It means that the particles have moved in the direction of leaving the solid , It is likely that it has been handled at the last moment , But the particles that haven't left yet .
2. According to the normal direction of the wall N, Disassemble the speed into normal and tangential . Then multiply the normal by the normal attenuation coefficient and reverse , Multiply the tangent by the tangent attenuation coefficient . However, it should be noted that the tangential attenuation coefficient is calculated according to Coulomb's law of friction . The calculated value is related to the ratio of normal velocity to tangential velocity .
3. Recombine normal and tangential velocities . Then move the particles .

Reference resources ：games103 Hua Min Wang

import taichi as ti
import random

x = random.randint(0, 9)
y = random.randint(-3, 3)

velocities = ti.Vector([x, y, 0])
print(velocities)

n_dir = ti.Vector([0, 1, 0]).normalized()


vn = velocities.dot(n_dir) * n_dir
vt = velocities - vn
vt_norm = vt.norm()
vn_norm = vn.norm()
print(f"vn_norm:{
      vn_norm}; vt_norm:{
      vt_norm}")


if(velocities.dot(n_dir) < 0 and vt_norm != 0):
    mu_N = 1
    mu_T = 1
    vn_new = -mu_N * vn
    a = ti.max((1 - mu_T * (1 + mu_N) * vn.norm() / vt_norm ), 0)
    print(1 - mu_T * (1 + mu_N) * vn.norm() / vt_norm )
    print(f"a={
      a}")
    vt_new = a * vt

    v_new = vn_new + vt_new

    print(v_new)