/*{
  "DESCRIPTION": "Hopf Bloom: a real-time render of the Hopf fibration. Every point on a hidden 2-sphere becomes a great circle on the 3-sphere; stereographically projected into space they form a nest of glowing, mutually-linked neon rings. Light flows along the fibers (the Hopf flow) and the camera orbits once, so it loops seamlessly over 16s.",
  "CREDIT": "glslop agent (Claude)",
  "CATEGORIES": ["hopf", "fibration", "topology", "neon", "4D"],
  "INPUTS": [
    { "NAME": "speed", "TYPE": "float", "DEFAULT": 1.0,  "MIN": 0.0,  "MAX": 3.0 },
    { "NAME": "glow",  "TYPE": "float", "DEFAULT": 1.0,  "MIN": 0.3,  "MAX": 3.0 },
    { "NAME": "hue",   "TYPE": "float", "DEFAULT": 0.0,  "MIN": 0.0,  "MAX": 1.0 },
    { "NAME": "tube",  "TYPE": "float", "DEFAULT": 0.06, "MIN": 0.02, "MAX": 0.14 },
    { "NAME": "zoom",  "TYPE": "float", "DEFAULT": 1.0,  "MIN": 0.5,  "MAX": 2.0 }
  ]
}*/

#define PI  3.14159265359
#define TAU 6.28318530718
#define N   24

const float PERIOD = 16.0;

mat2 rot(float a){ float c = cos(a), s = sin(a); return mat2(c, -s, s, c); }

vec3 pal(float t){
  return 0.5 + 0.5 * cos(TAU * (t + vec3(0.0, 0.33, 0.66)));
}

// a point on the fiber of base (theta,phi0) at fiber-parameter psi, projected to R^3
vec3 fiberPoint(float theta, float phi0, float psi){
  float ct2 = cos(theta * 0.5), st2 = sin(theta * 0.5);
  float x = ct2 * cos(psi);
  float y = ct2 * sin(psi);
  float z = st2 * cos(psi + phi0);
  float w = st2 * sin(psi + phi0);
  return vec3(x, y, z) / (1.0 - w * 0.999);   // stereographic from the w=1 pole
}

void main(){
  vec2 uv = (gl_FragCoord.xy - 0.5 * RENDERSIZE.xy) / RENDERSIZE.y;

  float ph = fract(TIME * speed / PERIOD);
  float th = TAU * ph;

  // ---- precompute the N projected fiber circles (center / normal / radius) ----
  vec3  cen[N];
  vec3  nrm[N];
  float rad[N];
  float fhue[N];
  for (int k = 0; k < N; k++){
    int   lat = k / 8;
    float fi  = float(k - lat * 8);
    float theta = mix(0.85, 2.25, float(lat) / 2.0);
    float phi0  = fi * (TAU / 8.0) + float(lat) * 0.4;

    // sample 3 points along the fiber (offset by the Hopf flow th) -> circle through 3 pts
    vec3 p0 = fiberPoint(theta, phi0, th + 0.0);
    vec3 p1 = fiberPoint(theta, phi0, th + TAU / 3.0);
    vec3 p2 = fiberPoint(theta, phi0, th + 2.0 * TAU / 3.0);

    vec3 ab = p1 - p0, ac = p2 - p0;
    vec3 abXac = cross(ab, ac);
    float den = 2.0 * dot(abXac, abXac);
    vec3 toC = (cross(abXac, ab) * dot(ac, ac) + cross(ac, abXac) * dot(ab, ab)) / max(den, 1e-6);
    cen[k]  = p0 + toC;
    rad[k]  = length(toC);
    nrm[k]  = normalize(abXac);
    fhue[k] = float(lat) * 0.18 + fi * 0.012;
  }

  // ---- camera: orbits the cluster once per loop (seamless) ----
  float orbit = th;
  vec3 ro = vec3(sin(orbit), 0.35, cos(orbit)) * (4.6 / zoom);
  vec3 ta = vec3(0.0);
  vec3 ww = normalize(ta - ro);
  vec3 uu = normalize(cross(vec3(0.0, 1.0, 0.0), ww));
  vec3 vv = cross(ww, uu);
  vec3 rd = normalize(uv.x * uu + uv.y * vv + 1.5 * ww);

  // ---- glow accumulation through a bounded region ----
  float w0 = tube * tube;
  vec3 col = vec3(0.0);
  float t = 2.0;
  for (int s = 0; s < 70; s++){
    vec3 p = ro + rd * t;
    float dmin = 1e9;
    for (int k = 0; k < N; k++){
      vec3 q = p - cen[k];
      float h = dot(q, nrm[k]);
      vec3 proj = q - h * nrm[k];
      float d = length(vec2(length(proj) - rad[k], h));
      dmin = min(dmin, d);
      float g = w0 / (d * d + w0);
      g = g * g;                                  // square -> thin bright cores, no haze
      col += pal(hue + ph + fhue[k]) * g * 0.13;
    }
    // adaptive-ish stepping: move by the nearest ring distance (clamped)
    t += clamp(dmin * 0.8, 0.035, 0.4);
    if (t > 9.0) break;
  }

  col *= glow;
  // white-hot cores where rings overlap / are dense
  col += vec3(0.85, 0.92, 1.0) * pow(max(max(col.r, col.g), col.b) * 0.4, 3.0);

  col = col / (1.0 + col);
  col = pow(col, vec3(0.82));
  col *= 1.0 - 0.18 * dot(uv, uv);   // vignette

  gl_FragColor = vec4(col, 1.0);
}