/*{
  "DESCRIPTION": "Orbital: a glowing surface shaped by real spherical harmonics, like an electron probability cloud. Its petal-lobes morph between harmonic modes and thin neon nodal lines trace every place the wavefunction changes sign (the + and - lobes glow in two colours). Morph and spin are integer-harmonic so it loops seamlessly over 16s. Real-time raymarch.",
  "CREDIT": "glslop agent (Claude)",
  "CATEGORIES": ["spherical-harmonics", "orbital", "neon", "raymarch", "organic"],
  "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": "amp",   "TYPE": "float", "DEFAULT": 0.5,  "MIN": 0.2, "MAX": 0.85 },
    { "NAME": "zoom",  "TYPE": "float", "DEFAULT": 1.0,  "MIN": 0.6, "MAX": 1.8 }
  ]
}*/

#define PI  3.14159265359
#define TAU 6.28318530718

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)));
}

// signed real-spherical-harmonic field on a unit direction; morphs+spins with th
float harm(vec3 n, float th){
  float ct  = clamp(n.z, -1.0, 1.0);          // cos(theta)
  float st  = sqrt(max(1.0 - ct * ct, 0.0));  // sin(theta)
  float phi = atan(n.y, n.x);
  float wA = cos(th), wB = sin(th);
  float p4  = pow(st, 4.0) * cos(4.0 * phi + th);     // 4-petal mode
  float p6  = pow(st, 6.0) * cos(6.0 * phi - th);     // 6-petal mode
  float pol = (3.0 * ct * ct - 1.0);                  // axial d-mode
  return wA * p4 + wB * p6 + 0.35 * cos(2.0 * th) * pol;
}

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

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

  // camera
  vec3 ro = vec3(0.0, 0.0, 9.0 / 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 + 2.2 * ww);   // longer lens

  // tumble the whole field (full turn -> seamless)
  mat2 ry = rot(th);
  mat2 rx = rot(0.5 * sin(th));

  vec3 col = vec3(0.0);
  float t = 1.0;
  float hsurf = 0.0;
  bool hit = false;
  for (int i = 0; i < 130; i++){
    vec3 p = ro + rd * t;
    vec3 q = p;
    q.xz = ry * q.xz;
    q.yz = rx * q.yz;
    vec3 n = normalize(q);
    float h = harm(n, th);
    float R = (0.9) + amp * h;
    float d = (length(q) - R) * 0.5;
    if (d < 0.0006 * t){ hit = true; hsurf = h; break; }
    t += d * 0.7;
    if (t > 12.0) break;
  }

  if (hit){
    vec3 p = ro + rd * t;
    vec3 q = p; q.xz = ry * q.xz; q.yz = rx * q.yz;
    // 4-tap normal in the rotated frame
    vec2 e = vec2(1.0, -1.0) * 0.0015;
    #define MAPQ(P) ((length(P) - (0.9 + amp * harm(normalize(P), th))) * 0.5)
    vec3 nor = normalize(
        e.xyy * MAPQ(q + e.xyy) + e.yyx * MAPQ(q + e.yyx)
      + e.yxy * MAPQ(q + e.yxy) + e.xxx * MAPQ(q + e.xxx));
    vec3 vd = normalize(q - vec3(0.0));   // outward-ish
    float fres = pow(1.0 - abs(dot(nor, normalize(ro * 0.0 - rd))), 3.0);

    // two-colour lobes by sign of the wavefunction
    vec3 cPlus  = pal(hue + ph + 0.0);
    vec3 cMinus = pal(hue + ph + 0.42);
    vec3 lobe   = mix(cMinus, cPlus, smoothstep(-0.12, 0.12, hsurf));
    lobe = mix(vec3(dot(lobe, vec3(0.33))), lobe, 1.35);   // saturate -> jewel
    float diff  = 0.45 + 0.55 * max(dot(nor, normalize(vec3(0.5, 0.7, 0.6))), 0.0);

    // thin-film iridescence sheen over the body (energy, not plastic)
    vec3 irid = pal(hue + 0.5 + 1.8 * fres + 0.4 * nor.y);

    // neon nodal lines where the harmonic crosses zero
    float node = pow(0.020 / (abs(hsurf) + 0.020), 1.5);
    // lobe interiors glow brighter toward their peak (|wavefunction| large)
    float core = smoothstep(0.2, 1.1, abs(hsurf));

    col  = lobe * (0.22 + 0.30 * diff);                    // luminous body
    col += lobe * core * 1.3 * glow;                       // glowing lobe interiors
    col += irid * (0.35 + 0.8 * core) * 0.6 * glow;        // iridescent sheen
    col += vec3(1.0, 1.0, 1.0) * node * 1.9 * glow;        // white-hot nodal lines
    col += mix(lobe, irid, 0.5) * fres * 2.4 * glow;       // iridescent neon rim
    col *= exp(-0.18 * max(t - 8.0, 0.0));                 // depth fog (object ~8 away)
  }

  col = col / (1.0 + col);
  col = pow(col, vec3(0.82));
  col *= 1.0 - 0.16 * dot(uv, uv);

  gl_FragColor = vec4(col, 1.0);
}