Fun_With_Math/experiments/basic/fourier.html at main · SimiaCryptus/Fun_With_Math · GitHub

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<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8" />
  <meta name="viewport" content="width=device-width, initial-scale=1.0" />
  <meta name="description" content="Visualize Fourier series approximations with interactive spinning circles." />
  <title>Fourier Series – Fun With Math</title>
  <link rel="stylesheet" href="../../css/style.css" />
  <style>
    canvas { display: block; background: #0d1117; }
    .canvas-wrapper { position: relative; }
    #waveCanvas {
      border-top: 1px solid var(--border);
      background: #0a0e14;
    }
    .col2 { display: flex; flex-direction: column; gap: 1.5rem; }
  </style>
</head>
<body>

<nav>
  <a class="brand" href="../../index.html">∑ Fun With Math</a>
  <a href="../../index.html">← All Experiments</a>
</nav>

<div class="page-header">
  <h1>Fourier Series Visualizer</h1>
  <p>Sum of rotating circles that together draw any periodic waveform.</p>
</div>

<div class="experiment-layout">
  <div class="col2">
    <div class="canvas-wrapper">
      <canvas id="circleCanvas"></canvas>
    </div>
    <div class="canvas-wrapper">
      <canvas id="waveCanvas"></canvas>
    </div>
  </div>

  <aside class="controls">
    <h3>Controls</h3>

    <label>
      Harmonics: <span id="termLabel">7</span>
      <input type="range" id="termRange" min="1" max="41" step="2" value="7" />
    </label>

    <label>
      Speed: <span id="speedLabel">1.0×</span>
      <input type="range" id="speedRange" min="0.1" max="4" step="0.1" value="1" />
    </label>

    <label>
      Waveform
      <select id="waveform">
        <option value="square">Square Wave</option>
        <option value="sawtooth">Sawtooth Wave</option>
        <option value="triangle">Triangle Wave</option>
      </select>
    </label>

    <div style="display:flex;gap:.5rem;flex-wrap:wrap">
      <button class="btn btn-primary"   id="toggleBtn">⏸ Pause</button>
      <button class="btn btn-secondary" id="clearBtn">Clear Trail</button>
    </div>

    <div class="info-box">
      <h4>Square Wave</h4>
      <p>
        <code>f(t) = (4/π) Σ sin((2k-1)t) / (2k-1)</code>
        for k = 1, 2, 3, …<br />
        Only odd harmonics contribute.
      </p>
    </div>

    <div class="info-box">
      <h4>What you're seeing</h4>
      Each circle spins at a harmonic frequency. Their combined tip traces the
      target wave on the right. Add more harmonics for a sharper approximation.
    </div>
  </aside>
</div>

<footer>
  <p><a href="../../index.html">← Back to all experiments</a></p>
</footer>

<script>
(function () {
  const cCanvas = document.getElementById('circleCanvas');
  const wCanvas = document.getElementById('waveCanvas');
  const cCtx    = cCanvas.getContext('2d');
  const wCtx    = wCanvas.getContext('2d');
  const wrap    = cCanvas.parentElement;

  const termRange  = document.getElementById('termRange');
  const termLabel  = document.getElementById('termLabel');
  const speedRange = document.getElementById('speedRange');
  const speedLabel = document.getElementById('speedLabel');
  const waveSelect = document.getElementById('waveform');
  const toggleBtn  = document.getElementById('toggleBtn');
  const clearBtn   = document.getElementById('clearBtn');

  let paused = false;
  let t = 0;
  let wavePoints = [];

  // ── Fourier coefficients ─────────────────────────────────
  function getTerms(type, N) {
    // Returns array of { freq, amp, phase }
    const terms = [];
    for (let k = 1; k <= N; k++) {
      switch (type) {
        case 'square':
          if (k % 2 !== 0) terms.push({ freq: k, amp: (4 / Math.PI) / k, phase: 0 });
          break;
        case 'sawtooth':
          terms.push({ freq: k, amp: (2 / Math.PI) * (k % 2 === 0 ? -1 : 1) / k, phase: 0 });
          break;
        case 'triangle':
          if (k % 2 !== 0) {
            const sign = Math.floor((k - 1) / 2) % 2 === 0 ? 1 : -1;
            terms.push({ freq: k, amp: sign * (8 / (Math.PI * Math.PI)) / (k * k), phase: 0 });
          }
          break;
      }
    }
    return terms;
  }

  // ── Canvas sizing ────────────────────────────────────────
  function resize() {
    const w = wrap.clientWidth;
    cCanvas.width  = w;
    cCanvas.height = Math.round(w * 0.65);
    wCanvas.width  = w;
    wCanvas.height = Math.round(w * 0.3);
    wavePoints = [];
  }

  // ── Draw frame ───────────────────────────────────────────
  function draw() {
    const N       = parseInt(termRange.value);
    const type    = waveSelect.value;
    const terms   = getTerms(type, 50).slice(0, N); // up to N terms
    const W  = cCanvas.width,  H  = cCanvas.height;
    const wW = wCanvas.width,  wH = wCanvas.height;

    // Background
    cCtx.fillStyle = '#0d1117';
    cCtx.fillRect(0, 0, W, H);

    // Center for circle diagram
    let cx = W * 0.35;
    let cy = H * 0.5;
    const scale = Math.min(H, W * 0.6) * 0.38;

    cCtx.save();
    // Draw circles and arms
    let x = cx, y = cy;
    for (const { freq, amp } of terms) {
      const r   = amp * scale;
      const ang = freq * t;
      const nx  = x + r * Math.cos(ang);
      const ny  = y + r * Math.sin(ang);

      // Circle
      cCtx.beginPath();
      cCtx.arc(x, y, Math.abs(r), 0, Math.PI * 2);
      cCtx.strokeStyle = 'rgba(88,166,255,.15)';
      cCtx.lineWidth = 1;
      cCtx.stroke();

      // Arm
      cCtx.beginPath();
      cCtx.moveTo(x, y);
      cCtx.lineTo(nx, ny);
      cCtx.strokeStyle = 'rgba(88,166,255,.6)';
      cCtx.lineWidth = 1.5;
      cCtx.stroke();

      x = nx; y = ny;
    }

    // Tip dot
    cCtx.beginPath();
    cCtx.arc(x, y, 4, 0, Math.PI * 2);
    cCtx.fillStyle = '#bc8cff';
    cCtx.fill();

    cCtx.restore();

    // ── Waveform canvas ──────────────────────────────────
    const wMidY = wH / 2;
    const relY  = (y - cy) / scale; // tip position normalized to circle radius

    wavePoints.unshift({ relY });
    if (wavePoints.length > wW) wavePoints.length = wW;

    wCtx.fillStyle = '#0a0e14';
    wCtx.fillRect(0, 0, wW, wH);

    wCtx.beginPath();
    wCtx.strokeStyle = 'rgba(188,140,255,.9)';
    wCtx.lineWidth   = 2;
    for (let i = 0; i < wavePoints.length; i++) {
      const py = wMidY + wavePoints[i].relY * (wH * 0.45);
      if (i === 0) wCtx.moveTo(0, py);
      else          wCtx.lineTo(i, py);
    }
    wCtx.stroke();

    // Zero line
    wCtx.beginPath();
    wCtx.strokeStyle = 'rgba(255,255,255,.08)';
    wCtx.lineWidth   = 1;
    wCtx.moveTo(0, wMidY); wCtx.lineTo(wW, wMidY);
    wCtx.stroke();

    // Connector
    cCtx.save();
    cCtx.beginPath();
    cCtx.setLineDash([4, 4]);
    cCtx.moveTo(x, y);
    cCtx.lineTo(W, y);
    cCtx.strokeStyle = 'rgba(188,140,255,.3)';
    cCtx.lineWidth = 1;
    cCtx.stroke();
    cCtx.restore();

    // Advance time
    if (!paused) t += 0.02 * parseFloat(speedRange.value);
  }

  function loop() {
    draw();
    requestAnimationFrame(loop);
  }

  // ── Controls ─────────────────────────────────────────────
  termRange.addEventListener('input', () => {
    termLabel.textContent = termRange.value;
    wavePoints = [];
  });
  speedRange.addEventListener('input', () => {
    speedLabel.textContent = parseFloat(speedRange.value).toFixed(1) + '×';
  });
  waveSelect.addEventListener('change', () => { wavePoints = []; t = 0; });
  toggleBtn.addEventListener('click', () => {
    paused = !paused;
    toggleBtn.textContent = paused ? '▶ Resume' : '⏸ Pause';
  });
  clearBtn.addEventListener('click', () => { wavePoints = []; });

  // ── Init ─────────────────────────────────────────────────
  new ResizeObserver(resize).observe(wrap);
  resize();
  loop();
})();
</script>
</body>
</html>