/*{
  "DESCRIPTION": "A trefoil knot rendered as volumetric plasma, with a second wire snaking around it. The main cord is the exact zero-set of cos(3*phi - 2*a) on a torus, so the knot's three crossings are real geometry - the ray marcher resolves the over/under occlusion where the cord passes through itself. The cord is a hollow braided sleeve (two counter-wound filament families beating into moire, the guilloche trick in 3D) around an incandescent core, and a thin satellite strand spirals along its whole length, orbiting the cord as it travels. Integrated as glow x transmittance; hue runs along the knot, decoupled from density, so it stays a vivid 2-tone. HDR march, bloom and tone-map in a second pass. Seamless 12s loop.",
  "CREDIT": "glslop agent",
  "CATEGORIES": ["volumetric", "raymarch", "knot", "trefoil", "plasma", "loop"],
  "INPUTS": [
    { "NAME": "cordRadius", "TYPE": "float", "DEFAULT": 0.145, "MIN": 0.07, "MAX": 0.28 },
    { "NAME": "density",    "TYPE": "float", "DEFAULT": 1.0,   "MIN": 0.3,  "MAX": 2.2 },
    { "NAME": "filaments",  "TYPE": "float", "DEFAULT": 1.0,   "MIN": 0.0,  "MAX": 2.0 },
    { "NAME": "molten",     "TYPE": "float", "DEFAULT": 0.35,  "MIN": 0.0,  "MAX": 1.6 },
    { "NAME": "satTurns",   "TYPE": "long",  "DEFAULT": 5,     "MIN": 0,    "MAX": 60 },
    { "NAME": "satOrbit",   "TYPE": "float", "DEFAULT": 1.55,  "MIN": 0.8,  "MAX": 3.0 },
    { "NAME": "satWeight",  "TYPE": "float", "DEFAULT": 1.0,   "MIN": 0.0,  "MAX": 2.5 },
    { "NAME": "satColor",   "TYPE": "color", "DEFAULT": [1.0, 0.66, 0.18, 1.0] },
    { "NAME": "hueTravel",  "TYPE": "float", "DEFAULT": 1.0,   "MIN": 0.0,  "MAX": 3.0 },
    { "NAME": "bloom",      "TYPE": "float", "DEFAULT": 1.0,   "MIN": 0.0,  "MAX": 2.5 },
    { "NAME": "exposure",   "TYPE": "float", "DEFAULT": 1.0,   "MIN": 0.4,  "MAX": 2.5 },
    { "NAME": "speed",      "TYPE": "float", "DEFAULT": 1.0,   "MIN": 0.0,  "MAX": 3.0 }
  ],
  "PASSES": [
    { "TARGET": "scene", "FLOAT": true },
    { }
  ]
}*/

#define TAU 6.28318530718
#define STEPS 112
const float PERIOD = 12.0;

const float RING = 1.00;   // torus centre-circle radius
const float ROFF = 0.40;   // how far the cord sits from that circle

// NB: mat2 is COLUMN-major, so this constructor rotates by -a. Signs below assume that.
mat2 rot(float a){ float c = cos(a), s = sin(a); return mat2(c, -s, s, c); }

// shortest signed distance between two angles (keeps everything single-valued)
float wrapAng(float x){ return atan(sin(x), cos(x)); }

float wobble(vec3 p, float th){
  vec3 q = p + vec3(cos(th), sin(th), cos(th)) * 0.30;
  float f  = sin(q.x * 3.1) * sin(q.y * 3.7) * sin(q.z * 2.9);
  f += 0.5 * sin(q.x * 6.7 + q.z * 2.1) * sin(q.y * 7.3);
  return f * 0.667;
}

// Trefoil density field.
//   a = angle around the ring, phi = angle around the tube.
//   The (3,2) torus knot is the set where cos(3*phi - 2*a) is maximal; the SIGNED angular
//   error to it, scaled by ROFF, gives a usable distance to the cord.
// Outputs: arc  = continuous coordinate along the cord (drives hue)
//          core = incandescent filament down the cord's axis
//          sat  = the satellite wire spiralling around the cord
float knot(vec3 p, float th, out float arc, out float core, out float sat){
  float a   = atan(p.z, p.x);
  vec2  cs  = vec2(length(p.xz) - RING, p.y);
  float rad = length(cs);
  float phi = atan(cs.y, cs.x);

  float serr = wrapAng(3.0 * phi - 2.0 * a) / 3.0;

  // local frame on the cord: distance from its axis, and psi = angle AROUND the cord
  vec2  local = vec2(rad - ROFF, ROFF * serr);
  float dist  = length(local);
  float psi   = atan(local.y, local.x);

  float w = wobble(p * 2.4, th);
  float r = cordRadius * (1.0 + 0.18 * w);

  // HOLLOW sleeve, not a solid tube: density lives in a thin shell so the far wall
  // shows through the near wall — that overlap is what makes the moire.
  float shell = smoothstep(r, r * 0.72, dist) * smoothstep(r * 0.30, r * 0.60, dist);

  // TWO counter-wound filament families braided over the sleeve; where they cross they
  // beat against each other into large-scale moire (the guilloche trick, in 3D).
  float f1 = 0.5 + 0.5 * sin( 7.0 * psi + 21.0 * a + w * 1.1);
  float f2 = 0.5 + 0.5 * sin(-7.0 * psi + 26.0 * a - w * 1.1);
  float lace = pow(f1, 14.0) + pow(f2, 14.0);
  lace += 1.4 * pow(f1, 14.0) * pow(f2, 14.0);         // bright nodes at the crossings

  // rhythm: bright passages travelling the cord so it breathes instead of being
  // uniformly busy (integer harmonic of a -> loop-safe)
  float rhythm = 0.55 + 0.45 * sin(2.0 * a - th);

  arc = (2.0 * a + 3.0 * phi) / TAU;                   // continuous coord along the cord

  // incandescent filament down the cord's axis: hot core inside coloured gas
  core = smoothstep(r * 0.22, r * 0.01, dist) * rhythm;

  // SATELLITE: a thin wire orbiting the cord at radius satOrbit*r, advancing satTurns
  // times along the knot and drifting one whole turn per loop (both integer -> loop-safe).
  float orbitR = r * satOrbit;
  float dpsi   = wrapAng(psi - (float(satTurns) * a + th));
  float dsat   = length(vec2(dist - orbitR, orbitR * dpsi));
  sat = smoothstep(r * 0.21, r * 0.015, dsat);
  sat *= 0.75 + 0.25 * sin(9.0 * a - 2.0 * th);        // it glows unevenly as it travels

  return shell * mix(0.45, lace, filaments * 0.85) * rhythm;
}

vec3 pal(float t){
  return mix(vec3(0.00, 0.45, 0.90), vec3(1.00, 0.10, 0.38), 0.5 + 0.5 * cos(TAU * t));
}

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

  if (PASSINDEX == 0){
    vec2 uv = (gl_FragCoord.xy - 0.5 * RENDERSIZE.xy) / RENDERSIZE.y;

    vec3 ro = vec3(0.0, 4.60, 4.60);          // camera OUTSIDE the volume
    vec3 rd = normalize(vec3(uv, -1.95));
    rd.yz = rot(0.785) * rd.yz;               // aim down at the knot
    ro.xz = rot(th) * ro.xz;                  // one full turn per loop
    rd.xz = rot(th) * rd.xz;

    float dt = 0.030;
    float t  = 4.9;
    vec3  col   = vec3(0.0);
    float trans = 1.0;

    for (int i = 0; i < STEPS; i++){
      vec3 p = ro + rd * t;
      float arc, core, sat;
      float sheath = knot(p, th, arc, core, sat) * density;
      float d = sheath + core * density * 0.55 + sat * satWeight * density * 0.85;

      if (d > 0.002){
        float hueArg = (atan(p.z, p.x) / TAU) * hueTravel + 0.06 * arc + ph;
        vec3 emit = pal(hueArg);
        emit += vec3(1.0, 0.84, 0.56) * core * 4.0;                     // incandescent core
        emit += vec3(1.0, 0.42, 0.10) * pow(sheath, 2.0) * molten * 3.0; // molten hot spots
        emit += satColor.rgb * sat * satWeight * 2.4;                    // satellite wire

        col   += emit * d * trans * dt * 15.0 * exp(-0.26 * (t - 4.9));
        trans *= exp(-d * dt * 24.0);
        if (trans < 0.01) break;
      }
      t += dt;
      if (t > 8.4) break;
    }

    col += vec3(0.030, 0.018, 0.060) * exp(-length(uv) * 3.2);
    gl_FragColor = vec4(max(col, 0.0), 1.0);

  } else {
    vec2 uv = isf_FragNormCoord;
    vec3 c  = IMG_THIS_PIXEL(scene).rgb;

    vec3 glow = vec3(0.0);
    for (int i = 0; i < 16; i++){
      float a = TAU * (float(i) + 0.5) / 16.0;
      vec2 dir = vec2(cos(a), sin(a));
      glow += max(IMG_NORM_PIXEL(scene, uv + dir * 0.013).rgb - 0.55, 0.0);
      glow += max(IMG_NORM_PIXEL(scene, uv + dir * 0.034).rgb - 0.55, 0.0) * 0.55;
    }
    glow /= 24.8;

    vec3 col = c + glow * bloom * 1.5;
    col *= exposure * 1.25;
    col = 1.0 - exp(-col);                    // soft knee at DISPLAY only
    col = pow(max(col, 0.0), vec3(0.92));
    gl_FragColor = vec4(col, 1.0);
  }
}