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</head>
<body>

<header>
  <div class="header-titles">
    <h1>GLM · <em>3D Distributions</em></h1>
    <p class="sub">Generalisierte Lineare Modelle · 3D-Posterior-Landschaft · Interaktiv · Drehen · Zoom</p>
    <p class="author">© Dr. Rainer Düsing · Interactive Tools by Claude</p>
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</header>

<div id="shell">

<div class="controls-bar">
  <div class="tab-group">
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    <button class="tab" onclick="setModel('poisson', this)">Poisson</button>
    <button class="tab" onclick="setModel('negbinom', this)">Neg. Binomial</button>
    <button class="tab" onclick="setModel('gamma', this)">Gamma</button>
    <button class="tab" onclick="setModel('binomial', this)">Binomial</button>
    <button class="tab" onclick="setModel('logistic', this)">Logistisch</button>
  </div>

  <div class="sep"></div>

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    <span class="param-val" id="sigmaval">0.8</span>
  </div>
  <div class="param-group" id="shape-group" style="display:none">
    <div class="sep"></div>
    <label>κ (Shape)</label>
    <input type="range" id="shape" min="0.5" max="8.0" step="0.25" value="2.0" oninput="updateParams()">
    <span class="param-val" id="shapeval">2.0</span>
  </div>
  <div class="param-group" id="ntrials-group" style="display:none">
    <div class="sep"></div>
    <label>n (Trials)</label>
    <input type="range" id="ntrials" min="1" max="20" step="1" value="10" oninput="updateParams()">
    <span class="param-val" id="ntrialsval">10</span>
  </div>
  <div class="param-group" id="nbr-group" style="display:none">
    <div class="sep"></div>
    <label>r (Dispersion)</label>
    <input type="range" id="nbr" min="0.25" max="10" step="0.25" value="2" oninput="updateParams()">
    <span class="param-val" id="nbrval">2.00</span>
  </div>

  <div class="sep"></div>
  <button class="btn-toggle" id="btn-data" onclick="toggleData()">
    <span class="dot"></span> Datenpunkte
  </button>
  <div class="param-group" id="nsamples-group" style="display:none">
    <label>N</label>
    <input type="range" id="nsamples" min="10" max="200" step="10" value="30" oninput="updateParams()">
    <span class="param-val" id="nsamplesval">30</span>
  </div>
</div>

<div class="viz-grid">
  <div class="panel" id="panel1">
    <div class="panel-label"><span>01</span> Balken-Histogramm</div>
    <div class="infobox" id="infobox1"></div>
    <div class="legend" id="legend1"></div>
    <div class="hint">🖱 Drehen / Zoom</div>
  </div>
  <div class="panel" id="panel2">
    <div class="panel-label"><span>02</span> Kurven / Flächen</div>
    <div class="infobox" id="infobox2"></div>
    <div class="legend" id="legend2"></div>
    <div class="hint">🖱 Drehen / Zoom</div>
  </div>
</div>

</div><!-- /shell -->

<script>
// ─── Math helpers ────────────────────────────────────────────────────────────
function poissonPMF(k, lambda) {
  if (lambda <= 0) return k === 0 ? 1 : 0;
  let logP = k * Math.log(lambda) - lambda;
  for (let i = 2; i <= k; i++) logP -= Math.log(i);
  return Math.exp(logP);
}

// Negative Binomial PMF: NB(r, p) parametrised by mean μ
// p_success = r/(r+μ), so Var(Y) = μ + μ²/r  (→ Poisson as r→∞)
function negbinomPMF(k, mu, r) {
  if (mu <= 0 || r <= 0) return k === 0 ? 1 : 0;
  // log P(Y=k) = lgamma(k+r) - lgamma(r) - lgamma(k+1)
  //              + r*log(r/(r+mu)) + k*log(mu/(r+mu))
  const pS = r / (r + mu);
  const logP = logGammaFn(k + r) - logGammaFn(r) - logGammaFn(k + 1)
             + r * Math.log(pS) + k * Math.log(1 - pS);
  return Math.exp(logP);
}
function normalPDF(x, mu, sigma) {
  return Math.exp(-0.5 * ((x - mu) / sigma) ** 2) / (sigma * Math.sqrt(2 * Math.PI));
}
function logisticP(eta) { return 1 / (1 + Math.exp(-eta)); }

// Binomial PMF: B(n, p) — n trials, success prob p
function binomialPMF(k, n, p) {
  if (k < 0 || k > n) return 0;
  // log C(n,k) + k*log(p) + (n-k)*log(1-p)
  let logC = 0;
  for (let i = 0; i < k; i++) logC += Math.log(n - i) - Math.log(i + 1);
  const lp = p > 0 ? Math.log(p) : -Infinity;
  const l1p = (1 - p) > 0 ? Math.log(1 - p) : -Infinity;
  return Math.exp(logC + k * lp + (n - k) * l1p);
}

// Gamma PDF: shape=k, scale=mu/k  → mean=mu, var=mu²/k
function gammaPDF(x, mu, kShape) {
  if (x <= 0 || mu <= 0 || kShape <= 0) return 0;
  const scale = mu / kShape;
  // Use log-space for numerical stability
  return Math.exp((kShape - 1) * Math.log(x) - x / scale - kShape * Math.log(scale) - _logGammaCache(kShape));
}
// Cache log-gamma result — kShape only changes on slider release, not per-point
let _lgCache = { z: -1, val: 0 };
function _logGammaCache(z) {
  if (z === _lgCache.z) return _lgCache.val;
  _lgCache = { z, val: logGammaFn(z) };
  return _lgCache.val;
}
// Lanczos approximation for log-gamma
function logGammaFn(z) {
  const g = 7;
  const c = [0.99999999999980993,676.5203681218851,-1259.1392167224028,
    771.32342877765313,-176.61502916214059,12.507343278686905,
    -0.13857109526572012,9.9843695780195716e-6,1.5056327351493116e-7];
  if (z < 0.5) return Math.log(Math.PI / Math.sin(Math.PI * z)) - logGammaFn(1 - z);
  z -= 1;
  let x = c[0];
  for (let i = 1; i < g + 2; i++) x += c[i] / (z + i);
  const t = z + g + 0.5;
  return 0.5 * Math.log(2 * Math.PI) + (z + 0.5) * Math.log(t) - t + Math.log(x);
}

// ─── Coordinate convention ───────────────────────────────────────────────────
// X-axis (Three X) = Prädiktor x
// Z-axis (Three Z) = Outcome y/k  (negative Z = higher outcome values)
// Y-axis (Three Y) = Probability / density  (up)
//
// Regression curve μ(x) lives on the FLOOR (Y=0) at position (x, 0, -mu*zScale)
// Distributions rise upward (Y > 0) from that floor point.

// ─── State ────────────────────────────────────────────────────────────────────
let model = 'normal';
let beta0 = 0.5, beta1 = 0.4, sigma = 0.8, kShape = 2.0, nTrials = 10, nSamples = 30, nbR = 2.0;
let showData = false;
let renderers = [], scenes = [], cameras = [];

// Per-model settings — each model remembers its own β₀, β₁ and extras independently
const modelSettings = {
  normal:    { beta0: 0.5,  beta1: 0.4,  sigma: 0.8 },
  poisson:   { beta0: 0.5,  beta1: 0.4  },
  negbinom:  { beta0: 0.5,  beta1: 0.4,  nbR: 2.0 },
  gamma:     { beta0: 0.5,  beta1: 0.4,  kShape: 2.0 },
  binomial:  { beta0: 0.0,  beta1: 0.8,  nTrials: 10 },
  logistic:  { beta0: 0.0,  beta1: 0.8  },
};

// ─── Model info definitions ───────────────────────────────────────────────────
const MODEL_INFO = {
  normal: {
    name: 'Normal (OLS)',
    family: 'Gaussisch',
    link: 'Identität',
    linkFn: 'μ = η',
    varFn: 'Var(Y) = σ²',
    eta: 'η = β₀ + β₁x',
    note: 'Konstante Varianz. Residuen ∼ N(0, σ²).',
  },
  poisson: {
    name: 'Poisson',
    family: 'Poisson',
    link: 'Log',
    linkFn: 'μ = exp(η)',
    varFn: 'Var(Y) = μ',
    eta: 'η = β₀ + β₁x',
    note: 'Für Zähldaten (≥ 0). Varianz wächst mit μ.',
  },
  negbinom: {
    name: 'Neg. Binomial',
    family: 'Neg. Binomial',
    link: 'Log',
    linkFn: 'μ = exp(η)',
    varFn: 'Var(Y) = μ + μ²/r',
    eta: 'η = β₀ + β₁x',
    note: 'Überdispergierte Zähldaten. r → ∞ = Poisson. Kleines r = starke Überdispersion.',
  },
  gamma: {
    name: 'Gamma',
    family: 'Gamma',
    link: 'Log',
    linkFn: 'μ = exp(η)',
    varFn: 'Var(Y) = μ²/κ',
    eta: 'η = β₀ + β₁x',
    note: 'Positive stetige Werte. Rel. Varianz konstant.',
  },
  binomial: {
    name: 'Binomial',
    family: 'Binomial',
    link: 'Logit',
    linkFn: 'p = 1/(1+e⁻ᶯ)',
    varFn: 'Var(Y) = np(1−p)',
    eta: 'η = β₀ + β₁x',
    note: 'Outcome = k/n ∈ [0,1]. k Erfolge aus n Versuchen.',
  },
  logistic: {
    name: 'Logistisch',
    family: 'Binomial (n=1)',
    link: 'Logit',
    linkFn: 'p = 1/(1+e⁻ᶯ)',
    varFn: 'Var(Y) = p(1−p)',
    eta: 'η = β₀ + β₁x',
    note: 'Binär: Y ∈ {0,1}. Spezialfall Binomial.',
  },
};

// ─── Simulated data points ────────────────────────────────────────────────────
// Fixed seed-like RNG so points don't jump on every rebuild
function seededRand(seed) {
  let s = seed;
  return () => { s = (s * 16807 + 0) % 2147483647; return (s - 1) / 2147483646; };
}

function generateDataPoints() {
  const rng = seededRand(42);
  const randn = () => {
    const u = rng(), v = rng();
    return Math.sqrt(-2 * Math.log(u + 1e-10)) * Math.cos(2 * Math.PI * v);
  };
  const points = [];
  for (let i = 0; i < nSamples; i++) {
    const xJitter = (rng() * 6) - 3;   // uniform in [-3, 3]
    const mu = getMuAt(xJitter);
    let y;
    if (model === 'normal') {
      y = mu + randn() * sigma;
    } else if (model === 'poisson') {
      y = Math.max(0, Math.round(mu + randn() * Math.sqrt(mu)));
    } else if (model === 'negbinom') {
      // Approximate: NB via Gamma-Poisson mixture
      const nbVar = mu + mu * mu / nbR;
      y = Math.max(0, Math.round(mu + randn() * Math.sqrt(nbVar)));
    } else if (model === 'gamma') {
      const sd = mu / Math.sqrt(kShape);
      y = Math.max(0.01, mu + randn() * sd);
    } else if (model === 'binomial') {
      if (nTrials === 1) {
        y = rng() < mu ? 1 : 0;
      } else {
        let successes = 0;
        for (let t = 0; t < nTrials; t++) if (rng() < mu) successes++;
        y = successes / nTrials;  // proportion k/n ∈ [0,1]
      }
    } else if (model === 'logistic') {
      y = rng() < mu ? 1 : 0;
    }
    points.push({ x: xJitter, y });
  }
  return points;
}

// getMu at any x (not just grid) — used for data generation
function getMuAt(x) {
  const eta = beta0 + beta1 * x;
  if (model === 'poisson' || model === 'gamma' || model === 'negbinom') return Math.exp(eta);
  if (model === 'normal')   return eta;
  if (model === 'binomial') return logisticP(eta);
  if (model === 'logistic') return logisticP(eta);
  return eta;
}

// ─── Setup Three.js for both panels ──────────────────────────────────────────
function makeRenderer(panelId) {
  const panel = document.getElementById(panelId);
  const w = panel.clientWidth, h = panel.clientHeight;
  const renderer = new THREE.WebGLRenderer({ antialias: true, alpha: true });
  renderer.setSize(w, h);
  renderer.setPixelRatio(window.devicePixelRatio);
  renderer.setClearColor(0x0d0f14, 1);
  panel.appendChild(renderer.domElement);
  return renderer;
}

function makeCamera(w, h) {
  const cam = new THREE.PerspectiveCamera(45, w / h, 0.01, 1000);
  cam.position.set(6, 5, 8);
  cam.lookAt(0, 0, 0);
  return cam;
}

// ─── Orbit Controls ───────────────────────────────────────────────────────────
function addOrbitControls(camera, domEl) {
  let isDragging = false, isRightDrag = false;
  let lastX = 0, lastY = 0;
  let theta = 0.55, phi = 0.85, radius = 13;
  let targetX = 0, targetY = 1;

  function updateCam() {
    camera.position.x = targetX + radius * Math.sin(phi) * Math.sin(theta);
    camera.position.y = targetY + radius * Math.cos(phi);
    camera.position.z = radius * Math.sin(phi) * Math.cos(theta);
    camera.lookAt(targetX, targetY, 0);
  }
  updateCam();

  domEl.addEventListener('mousedown', e => {
    isDragging = true;
    isRightDrag = e.button === 2;
    lastX = e.clientX; lastY = e.clientY;
    e.preventDefault();
  });
  domEl.addEventListener('contextmenu', e => e.preventDefault());
  window.addEventListener('mouseup', () => isDragging = false);
  window.addEventListener('mousemove', e => {
    if (!isDragging) return;
    const dx = e.clientX - lastX, dy = e.clientY - lastY;
    lastX = e.clientX; lastY = e.clientY;
    if (!isRightDrag) {
      theta -= dx * 0.01;
      phi = Math.max(0.1, Math.min(Math.PI - 0.1, phi + dy * 0.01));
    } else {
      targetX -= dx * 0.02;
      targetY += dy * 0.02;
    }
    updateCam();
  });
  domEl.addEventListener('wheel', e => {
    radius = Math.max(3, Math.min(30, radius + e.deltaY * 0.02));
    updateCam();
    e.preventDefault();
  }, { passive: false });
}

// ─── Colors ───────────────────────────────────────────────────────────────────
// 9 perceptually distinct colors — one per x-value (−3 to +3, step 0.75)
// Chosen to avoid similar hues and remain readable on both dark and light bg
const BAR_COLORS_HEX = [
  '#e05252', // x=−3.00  red
  '#e8853a', // x=−2.25  orange
  '#d4c23a', // x=−1.50  yellow
  '#52b04a', // x=−0.75  green
  '#3fc4c4', // x= 0.00  teal
  '#4a90d9', // x=+0.75  blue
  '#7b5ea7', // x=+1.50  purple
  '#c45696', // x=+2.25  pink-magenta
  '#a0785a', // x=+3.00  brown
];

function hexToInt(h) { return parseInt(h.replace('#',''), 16); }

const COLORS = {
  bars:    BAR_COLORS_HEX.map(hexToInt),
  grid:    0x1f2433,
  axis:    0x4b5563,
  mu_line: 0xf06292,
  mu_dot:  0xf06292,
};

let isLightMode = localStorage.getItem('btl-theme') === 'light';

function getThemeColors() {
  return isLightMode
    ? { grid: 0xd1d5db, axis: 0x9ca3af, mu_line: 0xe11d48, mu_dot: 0xe11d48, rendererBg: 0xf0f2f8 }
    : { grid: 0x1f2433, axis: 0x4b5563, mu_line: 0xf06292, mu_dot: 0xf06292, rendererBg: 0x0d0f14 };
}

// ─── Scales ───────────────────────────────────────────────────────────────────
const zScaleDefault  = 0.42;
const zScaleLogistic = 3.0;
const zScaleBinomial = 0.38;
const pScale = 4.5;

function outcomeToZ(k) {
  if (model === 'logistic' || model === 'binomial') return -k * zScaleLogistic;
  return -k * zScaleDefault;
}
function probToY(p) { return p * pScale; }
function isContinuous() { return model === 'normal' || model === 'gamma'; }
function isBinary()     { return model === 'logistic'; }
function isDiscrete()   { return model === 'poisson' || model === 'negbinom' || model === 'binomial'; }

// ─── Dispose helper — frees GPU memory before removing objects ────────────────
function disposeObject(obj) {
  if (obj.geometry) obj.geometry.dispose();
  if (obj.material) {
    if (Array.isArray(obj.material)) obj.material.forEach(m => m.dispose());
    else obj.material.dispose();
  }
}

function clearScene(scene) {
  // Walk backwards so splice doesn't skip items
  for (let i = scene.children.length - 1; i >= 0; i--) {
    const obj = scene.children[i];
    disposeObject(obj);
    scene.remove(obj);
  }
}

// ─── Debounced rebuild — prevents thrashing GPU on rapid slider moves ─────────
let _rebuildTimer = null;
function scheduleRebuild() {
  if (_rebuildTimer) clearTimeout(_rebuildTimer);
  _rebuildTimer = setTimeout(() => {
    _rebuildTimer = null;
    buildBars(scenes[0]);
    buildCurves(scenes[1]);
  }, 40); // ~25fps max rebuild rate, feels instant but won't pile up
}

function addGrid(scene) {
  const tc = getThemeColors();
  const isCompact = model === 'logistic' || model === 'binomial';
  const zMax  = isCompact ? 3.5 : 7;
  const zStep = isCompact ? 0.5 : 1;

  const axMat = new THREE.LineBasicMaterial({ color: tc.axis });
  addLine(scene, [-5,0,0], [5,0,0], axMat);
  addLine(scene, [0,0,0],  [0,5,0], axMat);
  addLine(scene, [0,0,0],  [0,0,-zMax], axMat);

  const gridMat = new THREE.LineBasicMaterial({ color: tc.grid, transparent: true, opacity: 0.6 });
  for (let ix = -5; ix <= 5; ix++) addLine(scene, [ix,0,0], [ix,0,-zMax], gridMat);
  for (let iz = 0; iz >= -zMax; iz -= zStep) addLine(scene, [-5,0,iz], [5,0,iz], gridMat);
}

function addLine(scene, a, b, mat) {
  const geo = new THREE.BufferGeometry().setFromPoints([new THREE.Vector3(...a), new THREE.Vector3(...b)]);
  scene.add(new THREE.Line(geo, mat));
}

// Axis labels via sprites
function makeTextSprite(text, colorDark, colorLight) {
  const color = isLightMode ? (colorLight || '#374151') : (colorDark || '#9ca3af');
  const c = document.createElement('canvas'); c.width = 320; c.height = 72;
  const ctx = c.getContext('2d');
  ctx.fillStyle = color;
  ctx.font = 'bold 38px monospace';
  ctx.textAlign = 'center'; ctx.textBaseline = 'middle';
  ctx.fillText(text, 160, 36);
  const tex = new THREE.CanvasTexture(c);
  const mat = new THREE.SpriteMaterial({ map: tex, transparent: true });
  const sprite = new THREE.Sprite(mat);
  sprite.scale.set(2.0, 0.45, 1);
  return sprite;
}

// ─── Model computations ───────────────────────────────────────────────────────
function getXValues() {
  const xs = [];
  for (let x = -3; x <= 3; x += 0.75) xs.push(+x.toFixed(2));
  return xs;
}

// Returns μ in outcome-space (used for placing regression curve on floor)
function getMu(x) {
  const eta = beta0 + beta1 * x;
  if (model === 'poisson' || model === 'gamma' || model === 'negbinom') return Math.exp(eta);
  if (model === 'normal')   return eta;
  if (model === 'binomial') return logisticP(eta);  // p = success probability
  if (model === 'logistic') return logisticP(eta);
  return eta;
}

// Returns distribution points {k, p} for the distribution at predictor value x
function getDistPoints(x) {
  const mu = getMu(x);
  const pts = [];
  if (model === 'poisson') {
    const kmax = Math.max(14, Math.ceil(mu * 2.5 + 6));
    for (let k = 0; k <= kmax; k++) pts.push({ k, p: poissonPMF(k, mu) });
  } else if (model === 'negbinom') {
    // NB is more spread out — extend range by variance contribution μ²/r
    const nbVar = mu + mu * mu / nbR;
    const kmax = Math.max(20, Math.ceil(mu + 4 * Math.sqrt(nbVar) + 4));
    for (let k = 0; k <= kmax; k++) {
      const p = negbinomPMF(k, mu, nbR);
      if (p > 0) pts.push({ k, p });
    }
  } else if (model === 'normal') {
    for (let k = mu - 3.5 * sigma; k <= mu + 3.5 * sigma; k += sigma * 0.12)
      pts.push({ k, p: normalPDF(k, mu, sigma) * sigma * 0.12 });
  } else if (model === 'gamma') {
    const sd = mu / Math.sqrt(kShape);
    const kMax = mu + 4 * sd;
    const N = 36;
    const step = kMax / N;
    for (let i = 1; i <= N; i++)
      pts.push({ k: i * step, p: gammaPDF(i * step, mu, kShape) * step });
  } else if (model === 'binomial') {
    if (nTrials === 1) {
      // n=1 is identical to logistic: only k/n = 0 or 1
      pts.push({ k: 0, p: 1 - mu });
      pts.push({ k: 1, p: mu });
    } else {
      // Outcome is proportion k/n ∈ [0,1] — each bar at k/n position
      for (let k = 0; k <= nTrials; k++)
        pts.push({ k: k / nTrials, p: binomialPMF(k, nTrials, mu) });
    }
  } else if (model === 'logistic') {
    pts.push({ k: 0, p: 1 - mu });
    pts.push({ k: 1, p: mu });
  }
  return pts;
}

// ─── Data points overlay ──────────────────────────────────────────────────────
function addDataPoints(scene) {
  if (!showData) return;
  const pts = generateDataPoints();
  const geo = new THREE.SphereGeometry(0.055, 6, 6);   // small
  const mat = new THREE.MeshBasicMaterial({ color: 0xffffff, transparent: true, opacity: 0.90 });
  pts.forEach(({ x, y }) => {
    const mesh = new THREE.Mesh(geo, mat);
    mesh.position.set(x, 0.02, outcomeToZ(y));
    scene.add(mesh);
  });
}

// Helper: z label position depends on model
function zLabelZ() {
  return (model === 'logistic' || model === 'binomial') ? -4.0 : -7.8;
}
// The key insight: μ(x) is drawn on the FLOOR (Y=0) as a curve in the X-Z plane.
// For each predictor x, μ(x) tells us the expected outcome → that's the Z position.
// The distributions then rise UPWARD (Y) from each (x, 0, outcomeToZ(k)) point.

function addRegressionFloorCurve(scene) {
  const tc = getThemeColors();
  const pts = [];
  for (let x = -3; x <= 3.01; x += 0.08) {
    const mu = getMu(x);
    pts.push(new THREE.Vector3(x, 0.01, outcomeToZ(mu)));
  }
  const geo = new THREE.BufferGeometry().setFromPoints(pts);
  scene.add(new THREE.Line(geo, new THREE.LineBasicMaterial({ color: tc.mu_line, linewidth: 3 })));

  getXValues().forEach(x => {
    const mu = getMu(x);
    const dot = new THREE.Mesh(
      new THREE.SphereGeometry(0.09, 10, 10),
      new THREE.MeshBasicMaterial({ color: tc.mu_dot })
    );
    dot.position.set(x, 0.01, outcomeToZ(mu));
    scene.add(dot);
  });
}

// ─── Version 1: Bar Histograms ────────────────────────────────────────────────
function buildBars(scene) {
  clearScene(scene);
  addGrid(scene);
  addRegressionFloorCurve(scene);
  addDataPoints(scene);

  const xs = getXValues();

  xs.forEach((x, xi) => {
    const pts = getDistPoints(x);
    const color = COLORS.bars[xi % COLORS.bars.length];

    // For continuous distributions (normal, gamma): use narrow bars as histogram approx
    // For discrete (poisson, negbinom) and binary (logistic): use wider bars
    const barWActual = isContinuous() ? 0.08 : 0.16;

    pts.forEach(({ k, p }) => {
      const h = probToY(p);
      if (h < 0.008) return;
      const zPos = outcomeToZ(k);

      const geo = new THREE.BoxGeometry(barWActual, h, barWActual * 0.85);
      const mat = new THREE.MeshPhongMaterial({
        color,
        transparent: true,
        opacity: isContinuous() ? 0.65 : 0.78,
        shininess: 50,
      });
      const mesh = new THREE.Mesh(geo, mat);
      mesh.position.set(x, h / 2, zPos);
      scene.add(mesh);

      // Subtle wireframe edges
      const wf = new THREE.LineSegments(
        new THREE.EdgesGeometry(geo),
        new THREE.LineBasicMaterial({ color: 0xffffff, transparent: true, opacity: 0.10 })
      );
      wf.position.copy(mesh.position);
      scene.add(wf);
    });
  });

  // Lights
  scene.add(new THREE.AmbientLight(0xffffff, 0.55));
  const dir = new THREE.DirectionalLight(0xffffff, 0.9);
  dir.position.set(4, 9, 4); scene.add(dir);
  const dir2 = new THREE.DirectionalLight(0x4fc3f7, 0.25);
  dir2.position.set(-4, 3, -4); scene.add(dir2);

  // Axis labels
  const lx = makeTextSprite('x (Prädiktor)', '#4fc3f7', '#0284c7');
  lx.position.set(5.8, 0.1, 0); scene.add(lx);
  const ly = makeTextSprite('P(Y=k)', '#aaaaaa', '#6b7280');
  ly.position.set(-0.5, 4.8, 0); scene.add(ly);
  const lz = makeTextSprite('k (Outcome)', '#81c784', '#16a34a');
  lz.position.set(0, 0.1, zLabelZ()); scene.add(lz);

  updateInfobox(1);
  updateLegend(1, xs);
}

// ─── Version 2: Curve Surfaces ────────────────────────────────────────────────
function buildCurves(scene) {
  clearScene(scene);
  addGrid(scene);
  addRegressionFloorCurve(scene);
  addDataPoints(scene);

  const xs = getXValues();

  xs.forEach((x, xi) => {
    const pts = getDistPoints(x);
    const color = new THREE.Color(COLORS.bars[xi % COLORS.bars.length]);

    if (isContinuous()) {
      const validPts = pts.filter(({ p }) => p > 0.002);
      if (validPts.length < 2) return;
      const curvePts = [
        new THREE.Vector3(x, 0, outcomeToZ(validPts[0].k)),
        ...validPts.map(({ k, p }) => new THREE.Vector3(x, probToY(p), outcomeToZ(k))),
        new THREE.Vector3(x, 0, outcomeToZ(validPts[validPts.length - 1].k)),
      ];
      const lGeo = new THREE.BufferGeometry().setFromPoints(curvePts);
      scene.add(new THREE.Line(lGeo, new THREE.LineBasicMaterial({ color, linewidth: 2 })));
      const shapeVerts = [];
      shapeVerts.push(new THREE.Vector3(x, 0, outcomeToZ(validPts[0].k)));
      validPts.forEach(({ k, p }) => shapeVerts.push(new THREE.Vector3(x, probToY(p), outcomeToZ(k))));
      shapeVerts.push(new THREE.Vector3(x, 0, outcomeToZ(validPts[validPts.length - 1].k)));
      const positions = [];
      for (let i = 1; i < shapeVerts.length - 1; i++) {
        positions.push(...shapeVerts[0].toArray(), ...shapeVerts[i].toArray(), ...shapeVerts[i + 1].toArray());
      }
      const fillGeo = new THREE.BufferGeometry();
      fillGeo.setAttribute('position', new THREE.Float32BufferAttribute(positions, 3));
      fillGeo.computeVertexNormals();
      scene.add(new THREE.Mesh(fillGeo, new THREE.MeshBasicMaterial({ color, transparent: true, opacity: 0.35, side: THREE.DoubleSide })));