02傾いた軸が円を描く歳差のコマ

<main class="stage">
<div class="bp is-demo" id="bpRoot">
  <canvas class="bp__canvas" id="bpCanvas" width="480" height="300"></canvas>
  <p class="bp__caption">軸の傾き角からサインとコサインで先端の位置を計算し、先端が床の上で小さな円を描くようにして、胴が回る間に軸そのものもゆっくり一周する。</p>
</div>
</main>

@use "../../../../site/static/demo-tokens" as *;
@include stage($stage-ink);

.bp {
  position: relative;
  width: min(92vw, calc(160vh - 12.8vw));
  aspect-ratio: 480 / 300;
  margin: 0 auto;
  border-radius: $r-card;
  overflow: hidden;
  box-shadow: $shadow-raised;
  background: $stage-ink;
}

.bp__canvas {
  display: block;
  width: 100%;
  height: 100%;
}

.bp__canvas:focus-visible {
  outline: 2px solid rgba(255, 255, 255, .85);
  outline-offset: -6px;
}

.bp__caption {
  position: absolute;
  left: $sp-3;
  bottom: $sp-3;
  max-width: 80%;
  margin: 0;
  padding: $sp-1 $sp-3;
  border-radius: $r-pill;
  background: rgba(255, 255, 255, .85);
  color: $subject-ink;
  font-weight: 500;
  font-size: 12px;
  line-height: 1.4;
  pointer-events: none;
}

@media (max-width: 340px) {
  .bp__caption { font-size: 10px; padding: $sp-1 $sp-2; }
}

@media (prefers-reduced-motion: reduce) {
  .bp { cursor: default; }
}

html, body {
  margin: 0;
  overflow: hidden;
}

.stage {
  box-sizing: border-box;
  min-height: 100vh;
  display: grid;
  place-items: center;
  margin: 0;
  background: #17141a;
  font-family: -apple-system, "Segoe UI", "Noto Sans KR", sans-serif;
  padding: clamp(8px, 4vw, 24px);
}

.bp {
  position: relative;
  width: min(92vw, 160vh - 12.8vw);
  aspect-ratio: 480/300;
  margin: 0 auto;
  border-radius: 16px;
  overflow: hidden;
  box-shadow: 0 14px 24px rgba(23, 20, 26, 0.32);
  background: #17141a;
}

.bp__canvas {
  display: block;
  width: 100%;
  height: 100%;
}

.bp__canvas:focus-visible {
  outline: 2px solid rgba(255, 255, 255, 0.85);
  outline-offset: -6px;
}

.bp__caption {
  position: absolute;
  left: 12px;
  bottom: 12px;
  max-width: 80%;
  margin: 0;
  padding: 4px 12px;
  border-radius: 999px;
  background: rgba(255, 255, 255, 0.85);
  color: #17141a;
  font-weight: 500;
  font-size: 12px;
  line-height: 1.4;
  pointer-events: none;
}

@media (max-width: 340px) {
  .bp__caption {
    font-size: 10px;
    padding: 4px 8px;
  }
}
@media (prefers-reduced-motion: reduce) {
  .bp {
    cursor: default;
  }
}

(function () {
  var root = document.getElementById('bpRoot');
  var canvas = document.getElementById('bpCanvas');
  var ctx = canvas.getContext('2d');
  var wrap = canvas.parentElement;
  var CALC_W = 320, CALC_H = 200;
  var FIXED_DT = 16;
  var dtS = FIXED_DT / 1000;
  var STRIPE_COUNT = 6;
  var STRIPE_FUSE_HZ = 14;
  var reduce = window.matchMedia('(prefers-reduced-motion: reduce)').matches;
  var demo = !reduce;
  if (!demo) root.classList.remove('is-demo');
  function stopDemo() { demo = false; root.classList.remove('is-demo'); }

  function seedRand(seed) {
    var s = seed >>> 0;
    return function () { s = (s * 1664525 + 1013904223) >>> 0; return s / 4294967296; };
  }
  var rand = seedRand(435002);
  function clamp(v, lo, hi) { return v < lo ? lo : (v > hi ? hi : v); }

  var PALS = [
    { a: '#ffb3c7', b: '#fff1c9', mid: '#ffd6c8', body: '#f29bb7' },
    { a: '#a8e6cf', b: '#e6fbf1', mid: '#c9f1e0', body: '#7fcfae' },
    { a: '#c9b8ff', b: '#f1ecff', mid: '#ddd2ff', body: '#a590ef' },
    { a: '#9fd8ff', b: '#e6f5ff', mid: '#c4e6ff', body: '#6fb7ec' }
  ];
  var cw = 480, ch = 300, sc = 1.5, elapsed = 0;
  var rafId = 0;
  var cleaners = [];

  function makeTop(x, y, palIndex, R, omega) {
    return { x: x, y: y, vx: 0, vy: 0, omega: omega, tilt: 0.08, az: rand() * 6.283, spin: rand() * 6.283,
      R: R, pal: PALS[palIndex % PALS.length], kick: 0, tipX: x, tipY: y };
  }

  var pulses = [];
  function addPulse(x, y, rgb) { pulses.push({ x: x, y: y, born: elapsed, rgb: rgb || '255,255,255' }); }
  function stepPulses() {
    var live = [];
    for (var i = 0; i < pulses.length; i += 1) if (elapsed - pulses[i].born < 520) live.push(pulses[i]);
    pulses = live;
  }
  function drawPulses() {
    for (var i = 0; i < pulses.length; i += 1) {
      var p = pulses[i], f = (elapsed - p.born) / 520;
      ctx.save();
      ctx.translate(p.x, p.y);
      ctx.scale(1, 0.38);
      ctx.beginPath();
      ctx.arc(0, 0, 12 + f * 62, 0, 6.2832);
      ctx.strokeStyle = 'rgba(' + p.rgb + ',' + (0.8 * (1 - f)) + ')';
      ctx.lineWidth = 3;
      ctx.stroke();
      ctx.restore();
    }
  }

  function pushTrail(arr, x, y, max) { arr.push({ x: x, y: y }); if (arr.length > max) arr.shift(); }
  function drawTrail(arr, rgb, w) {
    ctx.lineCap = 'round';
    for (var i = 1; i < arr.length; i += 1) {
      var f = i / arr.length;
      ctx.beginPath();
      ctx.moveTo(arr[i - 1].x, arr[i - 1].y);
      ctx.lineTo(arr[i].x, arr[i].y);
      ctx.strokeStyle = 'rgba(' + rgb + ',' + (0.62 * f) + ')';
      ctx.lineWidth = w * (0.35 + 0.65 * f);
      ctx.stroke();
    }
  }

  var glowX = 160, glowY = 150, glowS = 1;
  function drawArena() {
    ctx.setTransform(1, 0, 0, 1, 0, 0);
    ctx.fillStyle = '#1d1a2b';
    ctx.fillRect(0, 0, cw, ch);
    ctx.setTransform(sc, 0, 0, sc, 0, 0);
    var g = ctx.createRadialGradient(160, 118, 10, 160, 118, 200);
    g.addColorStop(0, '#463e68');
    g.addColorStop(1, '#2a2442');
    ctx.fillStyle = g;
    ctx.fillRect(0, 0, CALC_W, CALC_H);
    ctx.strokeStyle = 'rgba(255,255,255,0.09)';
    ctx.lineWidth = 1;
    for (var k = 1; k <= 4; k += 1) {
      ctx.beginPath();
      ctx.ellipse(160, 120, 44 * k, 21 * k, 0, 0, 6.2832);
      ctx.stroke();
    }
    // 원근 격자: 팽이 위치(glowX)에 가까울수록 밝게 비친다
    var gl = ctx.createRadialGradient(glowX, glowY, 6, glowX, glowY, 140);
    gl.addColorStop(0, 'rgba(255,255,255,' + (0.62 * glowS) + ')');
    gl.addColorStop(1, 'rgba(255,255,255,0.07)');
    ctx.strokeStyle = gl;
    ctx.lineWidth = 1;
    for (var gr = 0; gr < 10; gr += 1) {
      var gf = gr / 9;
      var gy = 72 + 128 * Math.pow(gf, 1.7);
      ctx.beginPath();
      ctx.moveTo(0, gy);
      ctx.lineTo(CALC_W, gy);
      ctx.stroke();
    }
    for (var gc = -9; gc <= 9; gc += 1) {
      ctx.beginPath();
      ctx.moveTo(160 + gc * 12, 72);
      ctx.lineTo(160 + gc * 52, CALC_H);
      ctx.stroke();
    }
    var pool = ctx.createRadialGradient(glowX, glowY + 4, 0, glowX, glowY + 4, 120);
    pool.addColorStop(0, 'rgba(255,238,252,' + (0.3 * glowS) + ')');
    pool.addColorStop(1, 'rgba(255,238,252,0)');
    ctx.fillStyle = pool;
    ctx.fillRect(0, 0, CALC_W, CALC_H);
  }

  function wedges(R, n, base, alpha, color) {
    ctx.fillStyle = color;
    ctx.globalAlpha = alpha;
    for (var i = 0; i < n; i += 1) {
      var a0 = base + i * 6.2832 / n;
      ctx.beginPath();
      ctx.moveTo(0, 0);
      ctx.arc(0, 0, R, a0, a0 + 3.1416 / n);
      ctx.closePath();
      ctx.fill();
    }
    ctx.globalAlpha = 1;
  }

  function drawTop(t) {
    var R = t.R, L = R * 1.25;
    // 바닥에 남는 회전 잔상 원판과 도는 점선 고리
    var gw = Math.abs(t.omega);
    ctx.save();
    ctx.translate(t.x, t.y + 3);
    ctx.scale(1, 0.3);
    wedges(R * 1.7, STRIPE_COUNT, t.spin * 0.8, 0.2 + 0.14 * clamp(gw / 30, 0, 1), t.pal.a);
    ctx.beginPath();
    ctx.arc(0, 0, R * 1.95, 0, 6.2832);
    ctx.setLineDash([R * 0.3, R * 0.2]);
    ctx.lineDashOffset = -t.spin * R * 0.6;
    ctx.strokeStyle = t.pal.a;
    ctx.globalAlpha = 0.6;
    ctx.lineWidth = 8;
    ctx.stroke();
    ctx.globalAlpha = 1;
    ctx.restore();
    glowX = t.x + (t.tipX - t.x) * 0.5;
    glowY = t.y;
    glowS = 0.55 + 0.45 * clamp(gw / 30, 0, 1);
    var s = Math.sin(t.tilt), c = Math.cos(t.tilt);
    var cx = t.x + Math.cos(t.az) * s * L * 1.15;
    var cy = t.y - c * L * 0.95 + Math.sin(t.az) * s * L * 0.35;
    ctx.save();
    ctx.translate(t.x + R * 0.28, t.y + 1);
    ctx.scale(1, 0.26);
    ctx.beginPath();
    ctx.arc(0, 0, R * (0.8 + 0.6 * s), 0, 6.2832);
    ctx.fillStyle = 'rgba(10,8,20,' + (0.4 - 0.12 * s) + ')';
    ctx.fill();
    ctx.restore();

    var dx = cx - t.x, dy = cy - t.y;
    var dist = Math.hypot(dx, dy) || 1;
    var phi = Math.atan2(dx, -dy);
    ctx.save();
    ctx.translate(cx, cy);
    ctx.rotate(phi);
    ctx.beginPath();
    ctx.moveTo(-R, 0); ctx.lineTo(0, dist); ctx.lineTo(R, 0); ctx.closePath();
    ctx.fillStyle = t.pal.body;
    ctx.fill();
    ctx.beginPath();
    ctx.moveTo(0, 0); ctx.lineTo(0, dist); ctx.lineTo(R, 0); ctx.closePath();
    ctx.fillStyle = 'rgba(30,16,60,0.24)';
    ctx.fill();

    var kv = 0.34 + 0.3 * s;
    ctx.save();
    ctx.scale(1, kv);
    ctx.beginPath();
    ctx.arc(0, 0, R, 0, 6.2832);
    ctx.fillStyle = t.pal.b;
    ctx.fill();
    var sgn = t.omega < 0 ? -1 : 1;
    var w = Math.abs(t.omega);
    wedges(R, STRIPE_COUNT, t.spin, 1, t.pal.a);
    if (w > 8) {
      for (var k = 1; k <= 3; k += 1) wedges(R, STRIPE_COUNT, t.spin - sgn * k * w * 0.012, 0.2 / k, t.pal.a);
    }
    var f = w * STRIPE_COUNT / 6.2832;
    var blur = clamp((f - STRIPE_FUSE_HZ) / 26, 0, 0.8);
    if (blur > 0) {
      ctx.globalAlpha = blur;
      ctx.beginPath();
      ctx.arc(0, 0, R, 0, 6.2832);
      ctx.fillStyle = t.pal.mid;
      ctx.fill();
      ctx.globalAlpha = 1;
    }
    ctx.beginPath();
    ctx.arc(0, 0, R, 0, 6.2832);
    ctx.strokeStyle = 'rgba(255,255,255,0.55)';
    ctx.lineWidth = 1 / kv;
    ctx.stroke();
    ctx.restore();

    ctx.beginPath();
    ctx.moveTo(0, 0); ctx.lineTo(0, -R * 0.62);
    ctx.strokeStyle = t.pal.body;
    ctx.lineWidth = R * 0.16;
    ctx.lineCap = 'round';
    ctx.stroke();
    ctx.beginPath();
    ctx.arc(0, -R * 0.66, R * 0.12, 0, 6.2832);
    ctx.fillStyle = '#ffffff';
    ctx.fill();
    ctx.restore();
    t.tipX = cx + Math.sin(phi) * R * 0.66;
    t.tipY = cy - Math.cos(phi) * R * 0.66;
  }

  function wallBounce(t, rest, margin) {
    var m = t.R + margin;
    if (t.x < m) { t.x = m; t.vx = Math.abs(t.vx) * rest; }
    if (t.x > CALC_W - m) { t.x = CALC_W - m; t.vx = -Math.abs(t.vx) * rest; }
    var top = t.R * 2.1, bottom = CALC_H - 8;
    if (t.y < top) { t.y = top; t.vy = Math.abs(t.vy) * rest; }
    if (t.y > bottom) { t.y = bottom; t.vy = -Math.abs(t.vy) * rest; }
  }

  function pairCollide(a, b, rest, spinMix, kickAmt) {
    var dx = b.x - a.x, dy = (b.y - a.y) * 1.6;
    var dist = Math.hypot(dx, dy);
    var minDist = (a.R + b.R) * 0.92;
    if (dist <= 0 || dist >= minDist) return false;
    var nx = dx / dist, ny = dy / dist;
    var overlap = (minDist - dist) * 0.5;
    a.x -= nx * overlap; a.y -= ny * overlap / 1.6;
    b.x += nx * overlap; b.y += ny * overlap / 1.6;
    var vn = (b.vx - a.vx) * nx + (b.vy - a.vy) * ny;
    if (vn >= 0) return false;
    var j = -(1 + rest) * vn / 2;
    a.vx -= j * nx; a.vy -= j * ny;
    b.vx += j * nx; b.vy += j * ny;
    var tr = (b.omega - a.omega) * spinMix;
    a.omega += tr; b.omega -= tr;
    a.vx += -ny * tr * 1.4; a.vy += nx * tr * 1.4;
    b.vx -= -ny * tr * 1.4; b.vy -= nx * tr * 1.4;
    a.kick = kickAmt; b.kick = kickAmt;
    addPulse((a.x + b.x) / 2, (a.y + b.y) / 2 + 6, '255,255,255');
    return true;
  }
  // 기법: 기울기 각도의 사인 값을 각속도로 나눠 세차 각속도를 구하고, 그 각도로 축 끝점을 원 위에 놓는다.
  // 세차 계수(PRECESSION_GAIN)가 기울기 크기를 정해 축 끝이 바닥 위에서 그리는 원의 크기가 달라진다.
  var PRECESSION_GAIN = 0.6;
  var TILT_PER_GAIN = 0.7;
  var PRECESSION_K = 200;
  var AXIS_DECAY = 0.14;
  var OMEGA_FULL = 34;
  var spinTop = makeTop(160, 160, 2, 54, OMEGA_FULL);
  var tipTrail = [];

  function precessAxis(t) {
    var rate = PRECESSION_K * Math.sin(t.tilt) / Math.max(t.omega, 8);
    t.az += rate * dtS;
  }

  function stepWorld() {
    spinTop.omega *= Math.exp(-AXIS_DECAY * dtS);
    spinTop.spin += spinTop.omega * dtS;
    var slow = 1 - clamp(spinTop.omega / OMEGA_FULL, 0, 1);
    spinTop.tilt = TILT_PER_GAIN * PRECESSION_GAIN * (1 + 0.5 * slow);
    precessAxis(spinTop);
    pushTrail(tipTrail, spinTop.tipX, spinTop.tipY, 110);
    if (spinTop.omega < 12) {
      spinTop.omega = OMEGA_FULL;
      addPulse(spinTop.x, spinTop.y + 4, '201,184,255');
    }
    stepPulses();
  }

  function drawWorld() {
    drawArena();
    drawPulses();
    ctx.save();
    ctx.translate(spinTop.x, spinTop.y + 3);
    ctx.scale(1, 0.32);
    ctx.beginPath();
    ctx.arc(0, 0, spinTop.R * 1.25 * Math.sin(spinTop.tilt) * 1.15 + 6, 0, 6.2832);
    ctx.strokeStyle = 'rgba(241,236,255,0.7)';
    ctx.lineWidth = 7;
    ctx.stroke();
    ctx.restore();
    drawTrail(tipTrail, '241,236,255', 6);
    drawTop(spinTop);
    ctx.beginPath();
    ctx.arc(spinTop.tipX, spinTop.tipY, 4, 0, 6.2832);
    ctx.fillStyle = '#ffffff';
    ctx.fill();
  }

  function fit() {
    var r = wrap.getBoundingClientRect();
    cw = Math.max(1, Math.round(r.width));
    ch = Math.max(1, Math.round(r.height));
    canvas.width = cw; canvas.height = ch;
    sc = cw / CALC_W;
    drawWorld();
  }

  var lastTs = null;
  var acc = 0;
  function tick(ts) {
    if (lastTs === null) lastTs = ts;
    var frameDt = Math.min(ts - lastTs, 48);
    lastTs = ts;
    acc += frameDt;
    while (acc >= FIXED_DT) { elapsed += FIXED_DT; stepWorld(); acc -= FIXED_DT; }
    drawWorld();
    rafId = requestAnimationFrame(tick);
  }
  for (var w0 = 0; w0 < 40; w0 += 1) { elapsed += FIXED_DT; stepWorld(); }
  fit();
  window.addEventListener('resize', fit);
  cleaners.push(function () { window.removeEventListener('resize', fit); });
  if (!reduce) rafId = requestAnimationFrame(tick);

  function destroy() {
    cancelAnimationFrame(rafId);
    for (var i = 0; i < cleaners.length; i += 1) cleaners[i]();
  }

})();

import { useEffect, useRef } from "react";
import styles from "./SpinTopScenePrecessionWobble.module.scss";

type Pal = { a: string; b: string; mid: string; body: string };
type Top = { x: number; y: number; vx: number; vy: number; omega: number; tilt: number; az: number; spin: number; R: number; pal: Pal; kick: number; tipX: number; tipY: number };
type Pulse = { x: number; y: number; born: number; rgb: string };
type Pt = { x: number; y: number };

export default function SpinTopScenePrecessionWobble() {
  const rootRef = useRef<HTMLDivElement | null>(null);
  const canvasRef = useRef<HTMLCanvasElement | null>(null);

  useEffect(() => {
    const rootEl = rootRef.current;
    const canvasEl = canvasRef.current;
    if (!rootEl || !canvasEl) return;
    const root: HTMLDivElement = rootEl;
    const canvas: HTMLCanvasElement = canvasEl;
    const ctx0 = canvas.getContext("2d");
    if (!ctx0) return;
    const ctx: CanvasRenderingContext2D = ctx0;
    const wrap: HTMLElement = canvas.parentElement ?? root;
    var CALC_W = 320, CALC_H = 200;
    var FIXED_DT = 16;
    var dtS = FIXED_DT / 1000;
    var STRIPE_COUNT = 6;
    var STRIPE_FUSE_HZ = 14;
    var reduce = window.matchMedia('(prefers-reduced-motion: reduce)').matches;
    var demo = !reduce;
    if (!demo) root.classList.remove('is-demo');
    function stopDemo() { demo = false; root.classList.remove('is-demo'); }

    function seedRand(seed: number) {
      var s = seed >>> 0;
      return function () { s = (s * 1664525 + 1013904223) >>> 0; return s / 4294967296; };
    }
    var rand = seedRand(435002);
    function clamp(v: number, lo: number, hi: number) { return v < lo ? lo : (v > hi ? hi : v); }

    var PALS = [
      { a: '#ffb3c7', b: '#fff1c9', mid: '#ffd6c8', body: '#f29bb7' },
      { a: '#a8e6cf', b: '#e6fbf1', mid: '#c9f1e0', body: '#7fcfae' },
      { a: '#c9b8ff', b: '#f1ecff', mid: '#ddd2ff', body: '#a590ef' },
      { a: '#9fd8ff', b: '#e6f5ff', mid: '#c4e6ff', body: '#6fb7ec' }
    ];
    var cw = 480, ch = 300, sc = 1.5, elapsed = 0;
    var rafId = 0;
    var cleaners: Array<() => void> = [];

    function makeTop(x: number, y: number, palIndex: number, R: number, omega: number): Top {
      return { x: x, y: y, vx: 0, vy: 0, omega: omega, tilt: 0.08, az: rand() * 6.283, spin: rand() * 6.283,
        R: R, pal: PALS[palIndex % PALS.length], kick: 0, tipX: x, tipY: y };
    }

    var pulses: Pulse[] = [];
    function addPulse(x: number, y: number, rgb?: string) { pulses.push({ x: x, y: y, born: elapsed, rgb: rgb || '255,255,255' }); }
    function stepPulses() {
      var live: Pulse[] = [];
      for (var i = 0; i < pulses.length; i += 1) if (elapsed - pulses[i].born < 520) live.push(pulses[i]);
      pulses = live;
    }
    function drawPulses() {
      for (var i = 0; i < pulses.length; i += 1) {
        var p = pulses[i], f = (elapsed - p.born) / 520;
        ctx.save();
        ctx.translate(p.x, p.y);
        ctx.scale(1, 0.38);
        ctx.beginPath();
        ctx.arc(0, 0, 12 + f * 62, 0, 6.2832);
        ctx.strokeStyle = 'rgba(' + p.rgb + ',' + (0.8 * (1 - f)) + ')';
        ctx.lineWidth = 3;
        ctx.stroke();
        ctx.restore();
      }
    }

    function pushTrail(arr: Pt[], x: number, y: number, max: number) { arr.push({ x: x, y: y }); if (arr.length > max) arr.shift(); }
    function drawTrail(arr: Pt[], rgb: string, w: number) {
      ctx.lineCap = 'round';
      for (var i = 1; i < arr.length; i += 1) {
        var f = i / arr.length;
        ctx.beginPath();
        ctx.moveTo(arr[i - 1].x, arr[i - 1].y);
        ctx.lineTo(arr[i].x, arr[i].y);
        ctx.strokeStyle = 'rgba(' + rgb + ',' + (0.62 * f) + ')';
        ctx.lineWidth = w * (0.35 + 0.65 * f);
        ctx.stroke();
      }
    }

    var glowX = 160, glowY = 150, glowS = 1;
    function drawArena() {
      ctx.setTransform(1, 0, 0, 1, 0, 0);
      ctx.fillStyle = '#1d1a2b';
      ctx.fillRect(0, 0, cw, ch);
      ctx.setTransform(sc, 0, 0, sc, 0, 0);
      var g = ctx.createRadialGradient(160, 118, 10, 160, 118, 200);
      g.addColorStop(0, '#463e68');
      g.addColorStop(1, '#2a2442');
      ctx.fillStyle = g;
      ctx.fillRect(0, 0, CALC_W, CALC_H);
      ctx.strokeStyle = 'rgba(255,255,255,0.09)';
      ctx.lineWidth = 1;
      for (var k = 1; k <= 4; k += 1) {
        ctx.beginPath();
        ctx.ellipse(160, 120, 44 * k, 21 * k, 0, 0, 6.2832);
        ctx.stroke();
      }
      // 원근 격자: 팽이 위치(glowX)에 가까울수록 밝게 비친다
      var gl = ctx.createRadialGradient(glowX, glowY, 6, glowX, glowY, 140);
      gl.addColorStop(0, 'rgba(255,255,255,' + (0.62 * glowS) + ')');
      gl.addColorStop(1, 'rgba(255,255,255,0.07)');
      ctx.strokeStyle = gl;
      ctx.lineWidth = 1;
      for (var gr = 0; gr < 10; gr += 1) {
        var gf = gr / 9;
        var gy = 72 + 128 * Math.pow(gf, 1.7);
        ctx.beginPath();
        ctx.moveTo(0, gy);
        ctx.lineTo(CALC_W, gy);
        ctx.stroke();
      }
      for (var gc = -9; gc <= 9; gc += 1) {
        ctx.beginPath();
        ctx.moveTo(160 + gc * 12, 72);
        ctx.lineTo(160 + gc * 52, CALC_H);
        ctx.stroke();
      }
      var pool = ctx.createRadialGradient(glowX, glowY + 4, 0, glowX, glowY + 4, 120);
      pool.addColorStop(0, 'rgba(255,238,252,' + (0.3 * glowS) + ')');
      pool.addColorStop(1, 'rgba(255,238,252,0)');
      ctx.fillStyle = pool;
      ctx.fillRect(0, 0, CALC_W, CALC_H);
    }

    function wedges(R: number, n: number, base: number, alpha: number, color: string) {
      ctx.fillStyle = color;
      ctx.globalAlpha = alpha;
      for (var i = 0; i < n; i += 1) {
        var a0 = base + i * 6.2832 / n;
        ctx.beginPath();
        ctx.moveTo(0, 0);
        ctx.arc(0, 0, R, a0, a0 + 3.1416 / n);
        ctx.closePath();
        ctx.fill();
      }
      ctx.globalAlpha = 1;
    }

    function drawTop(t: Top) {
      var R = t.R, L = R * 1.25;
      // 바닥에 남는 회전 잔상 원판과 도는 점선 고리
      var gw = Math.abs(t.omega);
      ctx.save();
      ctx.translate(t.x, t.y + 3);
      ctx.scale(1, 0.3);
      wedges(R * 1.7, STRIPE_COUNT, t.spin * 0.8, 0.2 + 0.14 * clamp(gw / 30, 0, 1), t.pal.a);
      ctx.beginPath();
      ctx.arc(0, 0, R * 1.95, 0, 6.2832);
      ctx.setLineDash([R * 0.3, R * 0.2]);
      ctx.lineDashOffset = -t.spin * R * 0.6;
      ctx.strokeStyle = t.pal.a;
      ctx.globalAlpha = 0.6;
      ctx.lineWidth = 8;
      ctx.stroke();
      ctx.globalAlpha = 1;
      ctx.restore();
      glowX = t.x + (t.tipX - t.x) * 0.5;
      glowY = t.y;
      glowS = 0.55 + 0.45 * clamp(gw / 30, 0, 1);
      var s = Math.sin(t.tilt), c = Math.cos(t.tilt);
      var cx = t.x + Math.cos(t.az) * s * L * 1.15;
      var cy = t.y - c * L * 0.95 + Math.sin(t.az) * s * L * 0.35;
      ctx.save();
      ctx.translate(t.x + R * 0.28, t.y + 1);
      ctx.scale(1, 0.26);
      ctx.beginPath();
      ctx.arc(0, 0, R * (0.8 + 0.6 * s), 0, 6.2832);
      ctx.fillStyle = 'rgba(10,8,20,' + (0.4 - 0.12 * s) + ')';
      ctx.fill();
      ctx.restore();

      var dx = cx - t.x, dy = cy - t.y;
      var dist = Math.hypot(dx, dy) || 1;
      var phi = Math.atan2(dx, -dy);
      ctx.save();
      ctx.translate(cx, cy);
      ctx.rotate(phi);
      ctx.beginPath();
      ctx.moveTo(-R, 0); ctx.lineTo(0, dist); ctx.lineTo(R, 0); ctx.closePath();
      ctx.fillStyle = t.pal.body;
      ctx.fill();
      ctx.beginPath();
      ctx.moveTo(0, 0); ctx.lineTo(0, dist); ctx.lineTo(R, 0); ctx.closePath();
      ctx.fillStyle = 'rgba(30,16,60,0.24)';
      ctx.fill();

      var kv = 0.34 + 0.3 * s;
      ctx.save();
      ctx.scale(1, kv);
      ctx.beginPath();
      ctx.arc(0, 0, R, 0, 6.2832);
      ctx.fillStyle = t.pal.b;
      ctx.fill();
      var sgn = t.omega < 0 ? -1 : 1;
      var w = Math.abs(t.omega);
      wedges(R, STRIPE_COUNT, t.spin, 1, t.pal.a);
      if (w > 8) {
        for (var k = 1; k <= 3; k += 1) wedges(R, STRIPE_COUNT, t.spin - sgn * k * w * 0.012, 0.2 / k, t.pal.a);
      }
      var f = w * STRIPE_COUNT / 6.2832;
      var blur = clamp((f - STRIPE_FUSE_HZ) / 26, 0, 0.8);
      if (blur > 0) {
        ctx.globalAlpha = blur;
        ctx.beginPath();
        ctx.arc(0, 0, R, 0, 6.2832);
        ctx.fillStyle = t.pal.mid;
        ctx.fill();
        ctx.globalAlpha = 1;
      }
      ctx.beginPath();
      ctx.arc(0, 0, R, 0, 6.2832);
      ctx.strokeStyle = 'rgba(255,255,255,0.55)';
      ctx.lineWidth = 1 / kv;
      ctx.stroke();
      ctx.restore();

      ctx.beginPath();
      ctx.moveTo(0, 0); ctx.lineTo(0, -R * 0.62);
      ctx.strokeStyle = t.pal.body;
      ctx.lineWidth = R * 0.16;
      ctx.lineCap = 'round';
      ctx.stroke();
      ctx.beginPath();
      ctx.arc(0, -R * 0.66, R * 0.12, 0, 6.2832);
      ctx.fillStyle = '#ffffff';
      ctx.fill();
      ctx.restore();
      t.tipX = cx + Math.sin(phi) * R * 0.66;
      t.tipY = cy - Math.cos(phi) * R * 0.66;
    }

    function wallBounce(t: Top, rest: number, margin: number) {
      var m = t.R + margin;
      if (t.x < m) { t.x = m; t.vx = Math.abs(t.vx) * rest; }
      if (t.x > CALC_W - m) { t.x = CALC_W - m; t.vx = -Math.abs(t.vx) * rest; }
      var top = t.R * 2.1, bottom = CALC_H - 8;
      if (t.y < top) { t.y = top; t.vy = Math.abs(t.vy) * rest; }
      if (t.y > bottom) { t.y = bottom; t.vy = -Math.abs(t.vy) * rest; }
    }

    function pairCollide(a: Top, b: Top, rest: number, spinMix: number, kickAmt: number) {
      var dx = b.x - a.x, dy = (b.y - a.y) * 1.6;
      var dist = Math.hypot(dx, dy);
      var minDist = (a.R + b.R) * 0.92;
      if (dist <= 0 || dist >= minDist) return false;
      var nx = dx / dist, ny = dy / dist;
      var overlap = (minDist - dist) * 0.5;
      a.x -= nx * overlap; a.y -= ny * overlap / 1.6;
      b.x += nx * overlap; b.y += ny * overlap / 1.6;
      var vn = (b.vx - a.vx) * nx + (b.vy - a.vy) * ny;
      if (vn >= 0) return false;
      var j = -(1 + rest) * vn / 2;
      a.vx -= j * nx; a.vy -= j * ny;
      b.vx += j * nx; b.vy += j * ny;
      var tr = (b.omega - a.omega) * spinMix;
      a.omega += tr; b.omega -= tr;
      a.vx += -ny * tr * 1.4; a.vy += nx * tr * 1.4;
      b.vx -= -ny * tr * 1.4; b.vy -= nx * tr * 1.4;
      a.kick = kickAmt; b.kick = kickAmt;
      addPulse((a.x + b.x) / 2, (a.y + b.y) / 2 + 6, '255,255,255');
      return true;
    }
    // 기법: 기울기 각도의 사인 값을 각속도로 나눠 세차 각속도를 구하고, 그 각도로 축 끝점을 원 위에 놓는다.
    // 세차 계수(PRECESSION_GAIN)가 기울기 크기를 정해 축 끝이 바닥 위에서 그리는 원의 크기가 달라진다.
    var PRECESSION_GAIN = 0.6;
    var TILT_PER_GAIN = 0.7;
    var PRECESSION_K = 200;
    var AXIS_DECAY = 0.14;
    var OMEGA_FULL = 34;
    var spinTop = makeTop(160, 160, 2, 54, OMEGA_FULL);
    var tipTrail: Pt[] = [];

    function precessAxis(t: Top) {
      var rate = PRECESSION_K * Math.sin(t.tilt) / Math.max(t.omega, 8);
      t.az += rate * dtS;
    }

    function stepWorld() {
      spinTop.omega *= Math.exp(-AXIS_DECAY * dtS);
      spinTop.spin += spinTop.omega * dtS;
      var slow = 1 - clamp(spinTop.omega / OMEGA_FULL, 0, 1);
      spinTop.tilt = TILT_PER_GAIN * PRECESSION_GAIN * (1 + 0.5 * slow);
      precessAxis(spinTop);
      pushTrail(tipTrail, spinTop.tipX, spinTop.tipY, 110);
      if (spinTop.omega < 12) {
        spinTop.omega = OMEGA_FULL;
        addPulse(spinTop.x, spinTop.y + 4, '201,184,255');
      }
      stepPulses();
    }

    function drawWorld() {
      drawArena();
      drawPulses();
      ctx.save();
      ctx.translate(spinTop.x, spinTop.y + 3);
      ctx.scale(1, 0.32);
      ctx.beginPath();
      ctx.arc(0, 0, spinTop.R * 1.25 * Math.sin(spinTop.tilt) * 1.15 + 6, 0, 6.2832);
      ctx.strokeStyle = 'rgba(241,236,255,0.7)';
      ctx.lineWidth = 7;
      ctx.stroke();
      ctx.restore();
      drawTrail(tipTrail, '241,236,255', 6);
      drawTop(spinTop);
      ctx.beginPath();
      ctx.arc(spinTop.tipX, spinTop.tipY, 4, 0, 6.2832);
      ctx.fillStyle = '#ffffff';
      ctx.fill();
    }

    function fit() {
      var r = wrap.getBoundingClientRect();
      cw = Math.max(1, Math.round(r.width));
      ch = Math.max(1, Math.round(r.height));
      canvas.width = cw; canvas.height = ch;
      sc = cw / CALC_W;
      drawWorld();
    }

    var lastTs: number | null = null;
    var acc = 0;
    function tick(ts: number) {
      if (lastTs === null) lastTs = ts;
      var frameDt = Math.min(ts - lastTs, 48);
      lastTs = ts;
      acc += frameDt;
      while (acc >= FIXED_DT) { elapsed += FIXED_DT; stepWorld(); acc -= FIXED_DT; }
      drawWorld();
      rafId = requestAnimationFrame(tick);
    }
    for (var w0 = 0; w0 < 40; w0 += 1) { elapsed += FIXED_DT; stepWorld(); }
    fit();
    window.addEventListener('resize', fit);
    cleaners.push(function () { window.removeEventListener('resize', fit); });
    if (!reduce) rafId = requestAnimationFrame(tick);

    function destroy() {
      cancelAnimationFrame(rafId);
      for (var i = 0; i < cleaners.length; i += 1) cleaners[i]();
    }

    return destroy;
  }, []);

  return (
    <main className={styles.stage}>
      <div className={`${styles.bp} is-demo`} ref={rootRef}>
        <canvas className={styles.bp__canvas} ref={canvasRef} width={480} height={300} />
        <p className={styles.bp__caption}>팽이 축의 기울기 각도에 따라 위쪽 끝점이 바닥 위에서 작은 원을 그리도록 위치를 사인·코사인으로 계산해, 몸통이 돌면서 축 자체도 천천히 한 바퀴씩 돈다.</p>
      </div>
    </main>
  );
}