07位相モーフ — 係数はそのまま、位相だけ回すと模様が変身する

<main class="stage">
<div class="fe is-demo" id="feRoot">
  <p class="fe__hint">
    <span>係数の大きさを保ち、位相にだけオフセットを与えると、模様が星から花びら、渦へと連続変形します。大きさと位相が図形で何を担うかを示す実験です</span>
  </p>
  <div class="fe__field" id="feField" role="application" aria-label="位相モーフ 実験版" tabindex="0">
    <canvas class="fe__cv" id="feCv"></canvas>
  </div>
  <div class="fe__bar">
    <span class="fe__meta"><b class="fe__val" id="feN">0</b><span id="feUnit"> 位相オフセット振動・大きさ固定</span></span>
    <span class="fe__meta fe__meta--dim">canvas · phase offset · requestAnimationFrame</span>
  </div>
</div>
</main>

@use "../../../../site/static/demo-tokens" as *;

// 기본 에피사이클 체인(01). @keyframes 를 두지 않는다 —
// 움직임은 전부 캔버스 rAF 루프(복소 계수 체인 회전 → 펜 궤적 누적)가 만든다.
// 무대는 심야 관측 팔레트. 파스텔 주색을 --fe-* 로 편 전체(01~09) 공통 규격.

$duration: $dur-loop;
$easing: $ease-spring;
$color: $subject-lilac;

// ── 편 공통 심야 관측 팔레트(BD9~11 원칙: 편마다 다시 정하지 않는다) ──
$fe-stage: #141824;   // 심야 그래프지 — 저채도 짙은 남색 (파스텔 검사 무관: 저채도·저명도)
@include stage($fe-stage);

$fe-ink:  #10141f;    // 필드 바닥 — 무대보다 한 톤 어두운 남흑
$fe-glow: #b7c8ff;    // 궤적 주색 — 파스텔 페리윙클(고명도라 vivid 아님)
$fe-hot:  #ffe9c4;    // 펜 절정 — 파스텔 크림
$fe-text: #d6d9e6;    // 라벨 글자 — 밝은 회청

.fe {
  // 렌더러가 읽는 색 — JS 는 getComputedStyle 로 --fe-* 를 받아 쓴다
  --fe-ink:  #{$fe-ink};
  --fe-glow: #{$fe-glow};
  --fe-hot:  #{$fe-hot};

  display: flex; flex-direction: column; gap: $sp-2;
  width: 100%; max-width: 424px;
}

.fe__hint {
  display: flex; align-items: center; gap: $sp-1; margin: 0;
  font-weight: 700; font-size: clamp(10px, 2.8vw, 12px); line-height: 1.35;
  color: $fe-text;
}

.fe__field {
  position: relative; height: 180px;
  border-radius: $r-card; overflow: hidden;
  background: $fe-ink;
  box-shadow: inset 0 0 0 1px rgba($fe-text, .18);
}
.fe__field:focus-visible { outline: 2px solid $fe-glow; outline-offset: 2px; }

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

.fe__bar { display: flex; align-items: baseline; justify-content: space-between; gap: $sp-2; }
.fe__meta { font-size: 10px; font-weight: 500; color: rgba($fe-text, .72); }
.fe__meta--dim { font-size: 10px; }

@media (max-width: 340px) {
  .fe { gap: $sp-1; }
  .fe__field { height: 100px; }
  .fe__meta--dim { display: none; }
}

// reduce — rAF 를 돌리지 않고 궤적이 다 쌓인 한 장만 남는다.
@media (prefers-reduced-motion: reduce) {
  .fe.is-still .fe__field { cursor: default !important; }
}

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

.stage {
  box-sizing: border-box;
  min-height: 100vh;
  display: grid;
  place-items: center;
  margin: 0;
  background: #141824;
  font-family: -apple-system, "Segoe UI", "Noto Sans KR", sans-serif;
  padding: clamp(8px, 4vw, 24px);
}

.fe {
  --fe-ink: #10141f;
  --fe-glow: #b7c8ff;
  --fe-hot: #ffe9c4;
  display: flex;
  flex-direction: column;
  gap: 8px;
  width: 100%;
  max-width: 424px;
}

.fe__hint {
  display: flex;
  align-items: center;
  gap: 4px;
  margin: 0;
  font-weight: 700;
  font-size: clamp(10px, 2.8vw, 12px);
  line-height: 1.35;
  color: #d6d9e6;
}

.fe__field {
  position: relative;
  height: 180px;
  border-radius: 16px;
  overflow: hidden;
  background: #10141f;
  box-shadow: inset 0 0 0 1px rgba(214, 217, 230, 0.18);
}

.fe__field:focus-visible {
  outline: 2px solid #b7c8ff;
  outline-offset: 2px;
}

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

.fe__bar {
  display: flex;
  align-items: baseline;
  justify-content: space-between;
  gap: 8px;
}

.fe__meta {
  font-size: 10px;
  font-weight: 500;
  color: rgba(214, 217, 230, 0.72);
}

.fe__meta--dim {
  font-size: 10px;
}

@media (max-width: 340px) {
  .fe {
    gap: 4px;
  }
  .fe__field {
    height: 100px;
  }
  .fe__meta--dim {
    display: none;
  }
}
@media (prefers-reduced-motion: reduce) {
  .fe.is-still .fe__field {
    cursor: default !important;
  }
}

// 위상 모프(07). 계수의 두 축 — 크기와 위상 — 중 위상만 흔든다.
//   ① 별 경로(03 과 동일)의 DFT 계수에서 진폭은 얼리고 위상에만 오프셋 φ_k = d·k 를 더한다.
//   ② d 가 0 이면 원래 별. d 가 커질수록 각 원의 시각이 어긋나 무늬가 별→꽃잎→소용돌이로 변한다.
//   ③ d 를 사인파로 왕복시키면 무늬가 계속 모프한다 — 크기는 무늬의 "에너지"·위상은 "배치"임을 보여준다.
// 두 번째 시각화: 같은 계수를 오른쪽 위상 원반(각 계수를 단위원 위의 점으로)에 띄운다 —
// 위상이 흔들리면 점들이 원반을 따라 미끄러진다.
//
// 화면이 사는 장치 — 077 기준:
//  · 궤적이 투명 캔버스에 쌓이며 혜성 감쇠 — 모프가 지나간 자리가 잔상으로 겹친다.
//  · 방사 스윕·스포크가 매 프레임 재계산된다. 위상 원반 점들이 매 프레임 미끄러진다.
(function () {
  // ── 변형 상수 블록 ──
  var N = 256;
  var SHOW = 16;       // 체인에 쓰는 계수 수
  var SWEEP = 2.4;     // 위상 오프셋 왕복 주기(초)
  // ──────────────────
  var TAU = Math.PI * 2;

  var root = document.getElementById('feRoot');
  var field = document.getElementById('feField');
  var cv = document.getElementById('feCv');
  var nOut = document.getElementById('feN');

  var css = getComputedStyle(root);
  function tokRGB(name) {
    var s = css.getPropertyValue(name).trim();
    var hx = s.length === 4
      ? s.charAt(1) + s.charAt(1) + s.charAt(2) + s.charAt(2) + s.charAt(3) + s.charAt(3)
      : s.slice(1);
    return [parseInt(hx.slice(0, 2), 16), parseInt(hx.slice(2, 4), 16), parseInt(hx.slice(4, 6), 16)];
  }
  var C_INK  = tokRGB('--fe-ink');
  var C_GLOW = tokRGB('--fe-glow');
  var C_HOT  = tokRGB('--fe-hot');

  var reduce = window.matchMedia('(prefers-reduced-motion: reduce)').matches;
  var raf = 0, t0 = -1;
  var W = 0, H = 0, dpr = 1;
  var trailCv, trailCtx;

  function starPath(u) {
    var seg = u * 10;
    var i = Math.floor(seg);
    var f = seg - i;
    var a1 = i / 10 * TAU - Math.PI / 2;
    var a2 = (i + 1) / 10 * TAU - Math.PI / 2;
    var r1 = (i % 2 === 0) ? 1 : 0.42;
    var r2 = (i % 2 === 0) ? 0.42 : 1;
    var x1 = Math.cos(a1) * r1, y1 = Math.sin(a1) * r1;
    var x2 = Math.cos(a2) * r2, y2 = Math.sin(a2) * r2;
    return { x: x1 + (x2 - x1) * f, y: y1 + (y2 - y1) * f };
  }
  function dft(path) {
    var M = path.length;
    var out = [];
    for (var k = 0; k < M; k++) {
      var freq = (k <= M / 2) ? k : k - M;
      var re = 0, im = 0;
      for (var n = 0; n < M; n++) {
        var a = -TAU * k * n / M;
        var c = Math.cos(a), s = Math.sin(a);
        re += path[n].x * c - path[n].y * s;
        im += path[n].x * s + path[n].y * c;
      }
      re /= M; im /= M;
      out.push({ freq: freq, re: re, im: im, amp: Math.sqrt(re * re + im * im) });
    }
    out.sort(function (a, b) { return b.amp - a.amp; });
    return out;
  }

  var PATH = [], COEF = [];

  function fit() {
    var r = field.getBoundingClientRect();
    W = Math.round(r.width); H = Math.round(r.height);
    dpr = Math.min(2, window.devicePixelRatio || 1);
    cv.width = W * dpr; cv.height = H * dpr;
    cv.style.width = '100%'; cv.style.height = '100%';
    trailCv = document.createElement('canvas');
    trailCv.width = W * dpr; trailCv.height = H * dpr;
    trailCtx = trailCv.getContext('2d');
    trailCtx.scale(dpr, dpr);
    if (!PATH.length) {
      for (var i = 0; i < N; i++) PATH.push(starPath(i / N));
      COEF = dft(PATH);
    }
  }

  function rgba(c, a) { return 'rgba(' + c[0] + ',' + c[1] + ',' + c[2] + ',' + a + ')'; }

  // 위상 오프셋 체인 — d 만큼 각 계수 위상을 민다
  function chainAt(u, d, show) {
    var base = Math.min(W, H) * 0.36;
    var cx = W * 0.32, cy = H * 0.5;
    var pts = [{ x: cx, y: cy }];
    for (var i = 0; i < show && i < COEF.length; i++) {
      var c = COEF[i];
      var ph = Math.atan2(c.im, c.re) + c.freq * d;
      var ang = c.freq * u * TAU + ph;
      pts.push({
        x: pts[i].x + Math.cos(ang) * c.amp * base,
        y: pts[i].y + Math.sin(ang) * c.amp * base
      });
    }
    return pts;
  }

  function drawGrid(t) {
    var ctx = cv.getContext('2d');
    // 왼쪽 체인 자리 스윕
    var cx = W * 0.32, cy = H * 0.5;
    var maxR = Math.min(W, H) * 0.52;
    var sweep = t * 0.8;
    for (var b = 0; b < 16; b++) {
      ctx.fillStyle = rgba(C_GLOW, 0.1 * (1 - b / 16));
      ctx.beginPath();
      ctx.moveTo(cx, cy);
      ctx.arc(cx, cy, maxR, sweep - (b + 1) * 0.06, sweep - b * 0.06);
      ctx.closePath();
      ctx.fill();
    }
    var spin = t * 0.3;
    for (var i = 0; i < 14; i++) {
      var a = spin + (i / 14) * TAU;
      ctx.strokeStyle = rgba(C_GLOW, i % 2 === 0 ? 0.1 : 0.06);
      ctx.lineWidth = 1;
      ctx.beginPath();
      ctx.moveTo(cx + Math.cos(a) * 12, cy + Math.sin(a) * 12);
      ctx.lineTo(cx + Math.cos(a) * maxR, cy + Math.sin(a) * maxR);
      ctx.stroke();
    }
    // 오른쪽 위상 원반 자리 — 반대 방향 스윕(계단 밴드)
    var px = W * 0.78, py = H * 0.5, prad = Math.min(W, H) * 0.42;
    var sweep2 = -t * 0.95;
    for (var b2 = 0; b2 < 12; b2++) {
      ctx.fillStyle = rgba(C_GLOW, 0.1 * (1 - b2 / 12));
      ctx.beginPath();
      ctx.moveTo(px, py);
      ctx.arc(px, py, prad, sweep2 - (b2 + 1) * 0.07, sweep2 - b2 * 0.07);
      ctx.closePath();
      ctx.fill();
    }
    // 하단 가로 스캔 밴드 — 전체 폭을 흐른다(계단 12단)
    var bandY = H - 18 - ((t * 22) % (H - 24));
    for (var sb = 0; sb < 12; sb++) {
      ctx.fillStyle = rgba(C_GLOW, 0.08 * (1 - sb / 12));
      ctx.fillRect(0, bandY + sb * 5, W, 5);
    }
  }

  function draw(u, pulse, d, gt) {
    var ctx = cv.getContext('2d');
    ctx.setTransform(dpr, 0, 0, dpr, 0, 0);
    ctx.fillStyle = 'rgb(' + C_INK[0] + ',' + C_INK[1] + ',' + C_INK[2] + ')';
    ctx.fillRect(0, 0, W, H);
    drawGrid(gt);
    ctx.drawImage(trailCv, 0, 0, W, H);

    var pts = chainAt(u, d, SHOW);
    var base = Math.min(W, H) * 0.36;
    for (var i = 0; i < pts.length - 1; i++) {
      var r = COEF[i].amp * base;
      if (r > 2) {
        ctx.strokeStyle = rgba(C_GLOW, 0.09 + 0.01 * i);
        ctx.lineWidth = 1;
        ctx.beginPath();
        ctx.arc(pts[i].x, pts[i].y, r, 0, TAU);
        ctx.stroke();
      }
      if (i < 4 || r > 3) {
        ctx.strokeStyle = rgba(C_GLOW, 0.46);
        ctx.beginPath();
        ctx.moveTo(pts[i].x, pts[i].y);
        ctx.lineTo(pts[i + 1].x, pts[i + 1].y);
        ctx.stroke();
      }
    }
    var pen = pts[pts.length - 1];
    var pr = 2.4 + pulse * 2.2;
    ctx.fillStyle = rgba(C_HOT, 0.3);
    ctx.beginPath();
    ctx.arc(pen.x, pen.y, pr * 2.3, 0, TAU);
    ctx.fill();
    ctx.fillStyle = rgba(C_HOT, 1);
    ctx.beginPath();
    ctx.arc(pen.x, pen.y, pr, 0, TAU);
    ctx.fill();

    // ── 오른쪽 위상 원반 — 상위 계수의 위상을 단위원 위 점으로 ──
    var px = W * 0.78, py = H * 0.5, prad = Math.min(W, H) * 0.3;
    ctx.strokeStyle = rgba(C_GLOW, 0.22);
    ctx.lineWidth = 1;
    ctx.beginPath();
    ctx.arc(px, py, prad, 0, TAU);
    ctx.stroke();
    ctx.strokeStyle = rgba(C_GLOW, 0.1);
    ctx.beginPath();
    ctx.moveTo(px - prad - 6, py); ctx.lineTo(px + prad + 6, py);
    ctx.moveTo(px, py - prad - 6); ctx.lineTo(px, py + prad + 6);
    ctx.stroke();
    // 계수별 위상 각도(오프셋 적용 뒤)에 점 — 주파수 비례 반지름
    for (var k = 0; k < 12 && k < COEF.length; k++) {
      var c = COEF[k];
      var ph2 = Math.atan2(c.im, c.re) + c.freq * d;
      var rr = prad * (1 - k / 14);
      var qx = px + Math.cos(ph2) * rr, qy = py + Math.sin(ph2) * rr;
      ctx.fillStyle = rgba(k === 0 ? C_HOT : C_GLOW, 0.85);
      ctx.beginPath();
      ctx.arc(qx, qy, k === 0 ? 3 : 2, 0, TAU);
      ctx.fill();
    }
    return pen;
  }

  var prevPen = null;

  function stampTrail(pen) {
    if (!prevPen) { prevPen = pen; return; }
    // globalAlpha 로 코어/확산 두께를 한 경로에서 두 번 칠한다(계수 개수가 흔들려도 잔상이 곱해진다)
    trailCtx.globalAlpha = 0.8;
    trailCtx.strokeStyle = rgba(C_GLOW, 1);
    trailCtx.lineWidth = 1.7;
    trailCtx.lineCap = 'round';
    trailCtx.beginPath();
    trailCtx.moveTo(prevPen.x, prevPen.y);
    trailCtx.lineTo(pen.x, pen.y);
    trailCtx.stroke();
    trailCtx.globalAlpha = 0.12;
    trailCtx.lineWidth = 4.4;
    trailCtx.stroke();
    trailCtx.globalAlpha = 1;
    prevPen = pen;
  }

  function decayTrail() {
    trailCtx.setTransform(1, 0, 0, 1, 0, 0);
    trailCtx.globalCompositeOperation = 'destination-out';
    trailCtx.fillStyle = 'rgba(0,0,0,0.03)';
    trailCtx.fillRect(0, 0, W * dpr, H * dpr);
    trailCtx.globalCompositeOperation = 'source-over';
    trailCtx.setTransform(dpr, 0, 0, dpr, 0, 0);
  }

  function frame(now) {
    if (t0 < 0) t0 = now;
    var lt = (now - t0) / 1000;
    var u = (lt * 0.5) % 1;
    var d = Math.sin(lt * TAU / SWEEP) * 0.8;
    var pulse = 0.5 + 0.5 * Math.sin(lt * 8.0);
    decayTrail();
    var pen = draw(u, pulse, d, lt * TAU);
    stampTrail(pen);
    if (nOut) nOut.textContent = String(SHOW);
    raf = requestAnimationFrame(frame);
  }

  function stillFrame() {
    var prev = chainAt(0, 0, SHOW)[SHOW];
    for (var i = 1; i <= 200; i++) {
      var pen = chainAt(i / 200, 0, SHOW)[SHOW];
      stampTrail(pen);
      prev = pen;
    }
    draw(0.5, 0.5, 0, 2.1);
  }

  window.addEventListener('resize', function () {
    fit(); prevPen = null;
    if (reduce) stillFrame();
  });

  fit();
  if (reduce) {
    stillFrame();
    root.classList.add('is-still');
  } else {
    raf = requestAnimationFrame(frame);
  }
})();

// FourierPhaseCircleMorph — vanilla 판(run/321/demo/07-fourier-phase-circle-morph/index.html) 의 React 포트.
// 위상 모프 — 계수의 두 축(크기·위상) 중 위상만 흔든다.
//   ① 별 경로(03 과 동일)의 DFT 계수에서 진폭은 얼리고 위상에만 오프셋 φ_k = d·k 를 더한다.
//   ② d 가 0 이면 원래 별. d 가 커질수록 각 원의 시각이 어긋나 무늬가 별→꽃잎→소용돌이로 변한다.
//   ③ d 를 사인파로 왕복시키면 무늬가 계속 모프한다 — 크기는 무늬의 "에너지"·위상은 "배치"임을 보여준다.
// 두 번째 시각화: 같은 계수를 오른쪽 위상 원반(각 계수를 단위원 위의 점으로)에 띄운다 —
// 위상이 흔들리면 점들이 원반을 따라 미끄러진다.
// 화면이 사는 장치 — 궤적이 투명 캔버스에 쌓이며 혜성 감쇠, 방사 스윕·스포크가 매 프레임 재계산.
import { useEffect, useRef, useState } from "react";
import type { CSSProperties } from "react";
import styles from "./FourierPhaseCircleMorph.module.scss";

export type FourierPhaseCircleMorphProps = {
  duration?: string;
  easing?: string;
  color?: string;
  n?: number;        // 경로 샘플 점 수
  show?: number;     // 체인에 쓰는 계수 수
  sweep?: number;    // 위상 오프셋 왕복 주기(초)
};

type Vars = CSSProperties & { "--duration"?: string; "--easing"?: string; "--color"?: string };
type Box<T> = { current: T };
type RGB = [number, number, number];
type Pt = { x: number; y: number };
type Coef = { freq: number; re: number; im: number; amp: number };

const FIELD_LABEL = "위상 모프 실험판";
const TAU = Math.PI * 2;

function starPath(u: number): Pt {
  const seg = u * 10;
  const i = Math.floor(seg);
  const f = seg - i;
  const a1 = i / 10 * TAU - Math.PI / 2;
  const a2 = (i + 1) / 10 * TAU - Math.PI / 2;
  const r1 = (i % 2 === 0) ? 1 : 0.42;
  const r2 = (i % 2 === 0) ? 0.42 : 1;
  const x1 = Math.cos(a1) * r1, y1 = Math.sin(a1) * r1;
  const x2 = Math.cos(a2) * r2, y2 = Math.sin(a2) * r2;
  return { x: x1 + (x2 - x1) * f, y: y1 + (y2 - y1) * f };
}
function dft(path: Pt[]): Coef[] {
  const M = path.length;
  const out: Coef[] = [];
  for (let k = 0; k < M; k++) {
    const freq = (k <= M / 2) ? k : k - M;
    let re = 0, im = 0;
    for (let n = 0; n < M; n++) {
      const a = -TAU * k * n / M;
      const c = Math.cos(a), s = Math.sin(a);
      re += path[n].x * c - path[n].y * s;
      im += path[n].x * s + path[n].y * c;
    }
    re /= M; im /= M;
    out.push({ freq: freq, re: re, im: im, amp: Math.sqrt(re * re + im * im) });
  }
  out.sort((a, b) => b.amp - a.amp);
  return out;
}

export default function FourierPhaseCircleMorph({
  duration = "2s",
  easing = "cubic-bezier(.2, .8, .2, 1)",
  color = "#b7c8ff",
  n = 256,
  show = 16,
  sweep = 2.4
}: FourierPhaseCircleMorphProps) {
  const rootRef = useRef<HTMLDivElement | null>(null);
  const fieldRef = useRef<HTMLDivElement | null>(null);
  const cvRef = useRef<HTMLCanvasElement | null>(null);
  const ctxRef = useRef<CanvasRenderingContext2D | null>(null);
  const colRef = useRef<{ ink: RGB; glow: RGB; hot: RGB } | null>(null);
  const trailCvRef = useRef<HTMLCanvasElement | null>(null);
  const trailCtxRef = useRef<CanvasRenderingContext2D | null>(null);
  const nRef = useRef(n) as Box<number>;
  const showRef = useRef(show) as Box<number>;
  const sweepRef = useRef(sweep) as Box<number>;
  const pathRef = useRef<Pt[]>([]) as Box<Pt[]>;
  const coefRef = useRef<Coef[]>([]) as Box<Coef[]>;
  const wRef = useRef(0) as Box<number>;
  const hRef = useRef(0) as Box<number>;
  const dprRef = useRef(1) as Box<number>;
  const rafRef = useRef(0) as Box<number>;
  const [cnt, setCnt] = useState("0");
  const [still, setStill] = useState(false);
  const vars: Vars = { "--duration": duration, "--easing": easing, "--color": color };

  function reduced(): boolean {
    return window.matchMedia("(prefers-reduced-motion: reduce)").matches;
  }

  function tokRGB(root: HTMLDivElement, name: string): RGB {
    const s = getComputedStyle(root).getPropertyValue(name).trim();
    const hx = s.length === 4
      ? s.charAt(1) + s.charAt(1) + s.charAt(2) + s.charAt(2) + s.charAt(3) + s.charAt(3)
      : s.slice(1);
    return [parseInt(hx.slice(0, 2), 16), parseInt(hx.slice(2, 4), 16), parseInt(hx.slice(4, 6), 16)];
  }

  function rgba(c: RGB, a: number): string {
    return "rgba(" + c[0] + "," + c[1] + "," + c[2] + "," + a + ")";
  }

  function fit(): void {
    const field = fieldRef.current;
    const cv = cvRef.current;
    if (!field || !cv) return;
    const r = field.getBoundingClientRect();
    const W = Math.round(r.width), H = Math.round(r.height);
    const dpr = Math.min(2, window.devicePixelRatio || 1);
    wRef.current = W; hRef.current = H; dprRef.current = dpr;
    cv.width = W * dpr; cv.height = H * dpr;
    cv.style.width = "100%"; cv.style.height = "100%";
    ctxRef.current = cv.getContext("2d");
    const trailCv = document.createElement("canvas");
    trailCv.width = W * dpr; trailCv.height = H * dpr;
    const trailCtx = trailCv.getContext("2d");
    if (trailCtx) trailCtx.scale(dpr, dpr);
    trailCvRef.current = trailCv;
    trailCtxRef.current = trailCtx;
    if (!pathRef.current.length) {
      const PATH: Pt[] = [];
      for (let i = 0; i < nRef.current; i++) PATH.push(starPath(i / nRef.current));
      pathRef.current = PATH;
      coefRef.current = dft(PATH);
    }
  }

  // 위상 오프셋 체인 — d 만큼 각 계수 위상을 민다
  function chainAt(u: number, d: number, showCount: number): Pt[] {
    const W = wRef.current, H = hRef.current;
    const COEF = coefRef.current;
    const base = Math.min(W, H) * 0.36;
    const cx = W * 0.32, cy = H * 0.5;
    const pts: Pt[] = [{ x: cx, y: cy }];
    for (let i = 0; i < showCount && i < COEF.length; i++) {
      const c = COEF[i];
      const ph = Math.atan2(c.im, c.re) + c.freq * d;
      const ang = c.freq * u * TAU + ph;
      pts.push({
        x: pts[i].x + Math.cos(ang) * c.amp * base,
        y: pts[i].y + Math.sin(ang) * c.amp * base
      });
    }
    return pts;
  }

  function drawGrid(ctx: CanvasRenderingContext2D, t: number): void {
    const W = wRef.current, H = hRef.current;
    const col = colRef.current;
    if (!col) return;
    // 왼쪽 체인 자리 스윕
    const cx = W * 0.32, cy = H * 0.5;
    const maxR = Math.min(W, H) * 0.52;
    const sweepA = t * 0.8;
    for (let b = 0; b < 16; b++) {
      ctx.fillStyle = rgba(col.glow, 0.1 * (1 - b / 16));
      ctx.beginPath();
      ctx.moveTo(cx, cy);
      ctx.arc(cx, cy, maxR, sweepA - (b + 1) * 0.06, sweepA - b * 0.06);
      ctx.closePath();
      ctx.fill();
    }
    const spin = t * 0.3;
    for (let i = 0; i < 14; i++) {
      const a = spin + (i / 14) * TAU;
      ctx.strokeStyle = rgba(col.glow, i % 2 === 0 ? 0.1 : 0.06);
      ctx.lineWidth = 1;
      ctx.beginPath();
      ctx.moveTo(cx + Math.cos(a) * 12, cy + Math.sin(a) * 12);
      ctx.lineTo(cx + Math.cos(a) * maxR, cy + Math.sin(a) * maxR);
      ctx.stroke();
    }
    // 오른쪽 위상 원반 자리 — 반대 방향 스윕(계단 밴드)
    const px = W * 0.78, py = H * 0.5, prad = Math.min(W, H) * 0.42;
    const sweep2 = -t * 0.95;
    for (let b2 = 0; b2 < 12; b2++) {
      ctx.fillStyle = rgba(col.glow, 0.1 * (1 - b2 / 12));
      ctx.beginPath();
      ctx.moveTo(px, py);
      ctx.arc(px, py, prad, sweep2 - (b2 + 1) * 0.07, sweep2 - b2 * 0.07);
      ctx.closePath();
      ctx.fill();
    }
    // 하단 가로 스캔 밴드 — 전체 폭을 흐른다(계단 12단)
    const bandY = H - 18 - ((t * 22) % (H - 24));
    for (let sb = 0; sb < 12; sb++) {
      ctx.fillStyle = rgba(col.glow, 0.08 * (1 - sb / 12));
      ctx.fillRect(0, bandY + sb * 5, W, 5);
    }
  }

  function draw(u: number, pulse: number, d: number, gt: number): Pt {
    const ctx = ctxRef.current;
    const trailCv = trailCvRef.current;
    const col = colRef.current;
    const dpr = dprRef.current;
    const W = wRef.current, H = hRef.current;
    const COEF = coefRef.current;
    if (!ctx || !trailCv || !col) return { x: 0, y: 0 };
    ctx.setTransform(dpr, 0, 0, dpr, 0, 0);
    ctx.fillStyle = "rgb(" + col.ink[0] + "," + col.ink[1] + "," + col.ink[2] + ")";
    ctx.fillRect(0, 0, W, H);
    drawGrid(ctx, gt);
    ctx.drawImage(trailCv, 0, 0, W, H);

    const S = showRef.current;
    const pts = chainAt(u, d, S);
    const base = Math.min(W, H) * 0.36;
    for (let i = 0; i < pts.length - 1; i++) {
      const r = COEF[i].amp * base;
      if (r > 2) {
        ctx.strokeStyle = rgba(col.glow, 0.09 + 0.01 * i);
        ctx.lineWidth = 1;
        ctx.beginPath();
        ctx.arc(pts[i].x, pts[i].y, r, 0, TAU);
        ctx.stroke();
      }
      if (i < 4 || r > 3) {
        ctx.strokeStyle = rgba(col.glow, 0.46);
        ctx.beginPath();
        ctx.moveTo(pts[i].x, pts[i].y);
        ctx.lineTo(pts[i + 1].x, pts[i + 1].y);
        ctx.stroke();
      }
    }
    const pen = pts[pts.length - 1];
    const pr = 2.4 + pulse * 2.2;
    ctx.fillStyle = rgba(col.hot, 0.3);
    ctx.beginPath();
    ctx.arc(pen.x, pen.y, pr * 2.3, 0, TAU);
    ctx.fill();
    ctx.fillStyle = rgba(col.hot, 1);
    ctx.beginPath();
    ctx.arc(pen.x, pen.y, pr, 0, TAU);
    ctx.fill();

    // ── 오른쪽 위상 원반 — 상위 계수의 위상을 단위원 위 점으로 ──
    const px = W * 0.78, py = H * 0.5, prad = Math.min(W, H) * 0.3;
    ctx.strokeStyle = rgba(col.glow, 0.22);
    ctx.lineWidth = 1;
    ctx.beginPath();
    ctx.arc(px, py, prad, 0, TAU);
    ctx.stroke();
    ctx.strokeStyle = rgba(col.glow, 0.1);
    ctx.beginPath();
    ctx.moveTo(px - prad - 6, py); ctx.lineTo(px + prad + 6, py);
    ctx.moveTo(px, py - prad - 6); ctx.lineTo(px, py + prad + 6);
    ctx.stroke();
    // 계수별 위상 각도(오프셋 적용 뒤)에 점 — 주파수 비례 반지름
    for (let k = 0; k < 12 && k < COEF.length; k++) {
      const c = COEF[k];
      const ph2 = Math.atan2(c.im, c.re) + c.freq * d;
      const rr = prad * (1 - k / 14);
      const qx = px + Math.cos(ph2) * rr, qy = py + Math.sin(ph2) * rr;
      ctx.fillStyle = rgba(k === 0 ? col.hot : col.glow, 0.85);
      ctx.beginPath();
      ctx.arc(qx, qy, k === 0 ? 3 : 2, 0, TAU);
      ctx.fill();
    }
    return pen;
  }

  const prevPenRef = useRef<Pt | null>(null) as Box<Pt | null>;

  function stampTrail(pen: Pt): void {
    const trailCtx = trailCtxRef.current;
    const col = colRef.current;
    const prev = prevPenRef.current;
    if (!trailCtx || !col) return;
    if (!prev) { prevPenRef.current = pen; return; }
    // globalAlpha 로 코어/확산 두께를 한 경로에서 두 번 칠한다(계수 개수가 흔들려도 잔상이 곱해진다)
    trailCtx.globalAlpha = 0.8;
    trailCtx.strokeStyle = rgba(col.glow, 1);
    trailCtx.lineWidth = 1.7;
    trailCtx.lineCap = "round";
    trailCtx.beginPath();
    trailCtx.moveTo(prev.x, prev.y);
    trailCtx.lineTo(pen.x, pen.y);
    trailCtx.stroke();
    trailCtx.globalAlpha = 0.12;
    trailCtx.lineWidth = 4.4;
    trailCtx.stroke();
    trailCtx.globalAlpha = 1;
    prevPenRef.current = pen;
  }

  function decayTrail(): void {
    const trailCtx = trailCtxRef.current;
    const dpr = dprRef.current;
    const W = wRef.current, H = hRef.current;
    if (!trailCtx) return;
    trailCtx.setTransform(1, 0, 0, 1, 0, 0);
    trailCtx.globalCompositeOperation = "destination-out";
    trailCtx.fillStyle = "rgba(0,0,0,0.03)";
    trailCtx.fillRect(0, 0, W * dpr, H * dpr);
    trailCtx.globalCompositeOperation = "source-over";
    trailCtx.setTransform(dpr, 0, 0, dpr, 0, 0);
  }

  let t0 = -1;
  function frame(now: number): void {
    if (t0 < 0) t0 = now;
    const lt = (now - t0) / 1000;
    const u = (lt * 0.5) % 1;
    const d = Math.sin(lt * TAU / sweepRef.current) * 0.8;
    const pulse = 0.5 + 0.5 * Math.sin(lt * 8.0);
    decayTrail();
    const pen = draw(u, pulse, d, lt * TAU);
    stampTrail(pen);
    setCnt(String(showRef.current));
    rafRef.current = requestAnimationFrame(frame);
  }

  function stillFrame(): void {
    const S = showRef.current;
    let prev = chainAt(0, 0, S)[S];
    for (let i = 1; i <= 200; i++) {
      const pen = chainAt(i / 200, 0, S)[S];
      stampTrail(pen);
      prev = pen;
    }
    draw(0.5, 0.5, 0, 2.1);
  }

  useEffect(() => {
    const root = rootRef.current;
    if (!root) return;
    nRef.current = n;
    showRef.current = show;
    sweepRef.current = sweep;
    colRef.current = {
      ink: tokRGB(root, "--fe-ink"),
      glow: tokRGB(root, "--fe-glow"),
      hot: tokRGB(root, "--fe-hot"),
    };
    fit();
    setCnt(String(show));
    function onResize(): void {
      fit(); prevPenRef.current = null;
      if (reduced()) stillFrame();
    }
    window.addEventListener("resize", onResize);
    if (reduced()) {
      stillFrame();
      setStill(true);
    } else {
      t0 = -1;
      rafRef.current = requestAnimationFrame(frame);
    }
    return () => {
      window.removeEventListener("resize", onResize);
      cancelAnimationFrame(rafRef.current);
    };
    // eslint-disable-next-line react-hooks/exhaustive-deps
  }, [n, show, sweep]);

  const rootCls = still ? `${styles.root} ${styles.isStill}` : styles.root;

  return (
    <main className={styles.stage}>
      <div className={rootCls} ref={rootRef} style={vars}>
        <p className={styles.hint}>
          <span>계수 크기는 그대로 두고 위상에만 오프셋을 주면 무늬가 별에서 꽃잎으로, 꽃잎에서 소용돌이로 연속 변형되는데, 크기와 위상이 그림에서 각각 무엇을 담당하는지 보여주는 실험입니다</span>
        </p>
        <div
          className={styles.field}
          ref={fieldRef}
          role="application"
          aria-label={FIELD_LABEL}
          tabIndex={0}
        >
          <canvas className={styles.cv} ref={cvRef}></canvas>
        </div>
        <div className={styles.bar}>
          <span className={styles.meta}><b className={styles.val}>{cnt}</b> 위상 오프셋 진동 · 크기 고정</span>
          <span className={styles.metaDim}>canvas · phase offset · requestAnimationFrame</span>
        </div>
      </div>
    </main>
  );
}