blackhole.vert

// Played with vector fields at https://anvaka.github.io/fieldplay

float phi(float x) {
  return 1./(1.+exp(-x));
}

vec2 get_velocity(vec2 p) {
  vec2 v = vec2(0., 0.);
  float pi = 3.14159;
  float alpha = pi/2.*phi(length(p)-2.*pi)+pi/2.;
  if (length(p)<pi) {
    alpha = pi/2.*phi(1.6*(pi/2.-length(p)))+pi/2.;
  }
  else {
    alpha = pi/2.*phi(length(p)-2.*pi)+pi/2.;
    alpha = - alpha;
  }
  v.x = cos(alpha)*p.x+sin(alpha)*p.y;
  v.y = -sin(alpha)*p.x+cos(alpha)*p.y;
  if (length(p)<pi) {
    vec2 u = vec2(0., 0.);
    u.x = v.x/length(v);
  	u.y = v.y/length(v);
    return u*pi;
  }
  else {
    return v;
  }
}