05自分の線を描く — マウスで引いたら円がその場で蘇らせる

<main class="stage">
<div class="fe is-demo" id="feRoot">
  <p class="fe__hint">
    <span>キャンバスにマウスで好きな線を引くと、その点が即座に複素係数へ変わり、描いたばかりの署名や落書きをエピサイクルが一筆ずつ描き直します</span>
  </p>
  <div class="fe__field" id="feField" role="application" aria-label="自分の線を描く 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"> サンプル落書き・自分でも描いてみて</span></span>
    <span class="fe__meta fe__meta--dim">canvas · live DFT · pointer events</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;
  }
}

// 내 선 그리기(05). 편의 인터랙티브 축 — 손으로 그은 선이 그대로 DFT 입력이 된다.
//   ① 기본 상태: 예시 낙서(물결 서명)를 낮은 알파로 깔아두고 에피사이클이 반복해서 되그린다.
//   ② pointerdown~move 로 점을 모으면(최대 512) 기존 계수를 지우고 즉시 dft() 재계산 —
//     계산은 O(N²) 이지만 N=512 로 순식간이고, 체인이 새 경로를 다시 그리기 시작한다.
//   ③ 같은 재합성 루프(투명 트레일 누적 + 혜성 감쇠)를 공유한다.
//
// 화면이 사는 장치 — 077 기준:
//  · 밑바탕 방사 스윕·스포크가 매 프레임 재계산되어 화면 전면이 살아 있다.
//  · 손 궤적(입력)도 옅은 잔상으로 함께 남는다 — 그은 즉시 바뀌는 계수를 눈으로 읽는다.
(function () {
  // ── 변형 상수 블록 ──
  var MAXPTS = 512;    // 입력 받는 최대 점 수
  var SHOW = 48;       // 화면에 그리는 円の数
  // ──────────────────
  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;

  // ── DFT (03·04 와 같은 계산) ──
  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 = [];
  var normPath = [];   // 정규화된 경로(체인 재현용)

  function normalize() {
    // 그은 점을 무대 중심·단위반지름으로 정규화
    var minx = 1e9, maxx = -1e9, miny = 1e9, maxy = -1e9;
    for (var i = 0; i < PATH.length; i++) {
      if (PATH[i].x < minx) minx = PATH[i].x;
      if (PATH[i].x > maxx) maxx = PATH[i].x;
      if (PATH[i].y < miny) miny = PATH[i].y;
      if (PATH[i].y > maxy) maxy = PATH[i].y;
    }
    var cx = (minx + maxx) / 2, cy = (miny + maxy) / 2;
    var span = Math.max(maxx - minx, maxy - miny) || 1;
    normPath = [];
    for (var j = 0; j < PATH.length; j++) {
      normPath.push({ x: (PATH[j].x - cx) / span, y: (PATH[j].y - cy) / span });
    }
    COEF = dft(normPath);
  }

  function sampleDoodle() {
    // 예시 낙서 — 서명 같은 물결. t 0~1 로 닫힌 물결 무늬
    PATH = [];
    for (var i = 0; i < 200; i++) {
      var t = i / 200;
      PATH.push({
        x: Math.cos(t * TAU) * (0.36 + 0.16 * Math.sin(t * TAU * 3)),
        y: Math.sin(t * TAU) * (0.24 + 0.12 * Math.cos(t * TAU * 2))
      });
    }
    normalize();
  }

  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 (!COEF.length) sampleDoodle();
  }

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

  function chainAt(u, show) {
    var base = Math.min(W, H) * 0.4;
    var cx = W * 0.5, cy = H * 0.5;
    var pts = [{ x: cx, y: cy }];
    var n = show || COEF.length;
    for (var i = 0; i < n && i < COEF.length; i++) {
      var c = COEF[i];
      var a = c.freq * u * TAU;
      var ph = Math.atan2(c.im, c.re);
      var ang = a + ph;
      var px = pts[i].x + Math.cos(ang) * c.amp * base;
      var py = pts[i].y + Math.sin(ang) * c.amp * base;
      pts.push({ x: px, y: py });
    }
    return pts;
  }

  // 밑바탕 — 방사 스윕(계단 밴드) + 스포크
  function drawGrid(t) {
    var ctx = cv.getContext('2d');
    var cx = W * 0.5, cy = H * 0.5;
    var maxR = Math.sqrt(W * W + H * H) * 0.5;
    var sweep = t * 1.1;
    for (var b = 0; b < 16; b++) {
      ctx.fillStyle = rgba(C_GLOW, 0.085 * (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 * 0.26;
    for (var i = 0; i < 16; i++) {
      var a = spin + (i / 16) * TAU;
      ctx.strokeStyle = rgba(C_GLOW, i % 2 === 0 ? 0.08 : 0.05);
      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();
    }
  }

  function draw(u, pulse, show, 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);
    // 손 궤적 잔상 — 사용자가 그은 원본(정규화 전 화면 좌표)을 옅게
    if (handCv) ctx.drawImage(handCv, 0, 0, W, H);
    ctx.drawImage(trailCv, 0, 0, W, H);
    var base = Math.min(W, H) * 0.4;

    var pts = chainAt(u, show);
    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, 0.48);
        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();
    return pen;
  }

  var prevPen = null;
  var handCv = null, handCtx = null;   // 손 궤적 잔상 캔버스

  function stampTrail(pen) {
    if (!prevPen) { prevPen = pen; return; }
    trailCtx.strokeStyle = rgba(C_GLOW, 0.88);
    trailCtx.lineWidth = 1.9;
    trailCtx.lineCap = 'round';
    trailCtx.beginPath();
    trailCtx.moveTo(prevPen.x, prevPen.y);
    trailCtx.lineTo(pen.x, pen.y);
    trailCtx.stroke();
    trailCtx.strokeStyle = rgba(C_GLOW, 0.14);
    trailCtx.lineWidth = 5;
    trailCtx.stroke();
    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) * 0.5;
    var u = lt % 1;
    var pulse = 0.5 + 0.5 * Math.sin(lt * 8.0);
    decayTrail();
    var pen = draw(u, pulse, SHOW, lt * TAU);
    stampTrail(pen);
    if (nOut) nOut.textContent = String(PATH.length);
    raf = requestAnimationFrame(frame);
  }

  // ── 입력 — 그으면 즉시 DFT 재계산 ──
  var drawing = false, lastPt = null;
  function toField(e) {
    var r = cv.getBoundingClientRect();
    return { x: e.clientX - r.left, y: e.clientY - r.top };
  }
  function startDraw(e) {
    drawing = true; lastPt = toField(e);
    PATH = [lastPt];
    if (!handCv) {
      handCv = document.createElement('canvas');
      handCv.width = W * dpr; handCv.height = H * dpr;
      handCtx = handCv.getContext('2d');
      handCtx.scale(dpr, dpr);
    }
    handCtx.clearRect(0, 0, W, H);
    prevPen = null;
    e.preventDefault();
  }
  function moveDraw(e) {
    if (!drawing) return;
    var p = toField(e);
    if (Math.abs(p.x - lastPt.x) + Math.abs(p.y - lastPt.y) < 4) return;
    PATH.push(p);
    if (PATH.length > MAXPTS) PATH.shift();
    handCtx.strokeStyle = rgba(C_HOT, 0.28);
    handCtx.lineWidth = 2;
    handCtx.lineCap = 'round';
    handCtx.beginPath();
    handCtx.moveTo(lastPt.x, lastPt.y);
    handCtx.lineTo(p.x, p.y);
    handCtx.stroke();
    lastPt = p;
    normalize();
    prevPen = null;
    e.preventDefault();
  }
  function endDraw() {
    if (!drawing) return;
    drawing = false;
    if (PATH.length > 8) normalize();
  }
  cv.addEventListener('pointerdown', startDraw);
  cv.addEventListener('pointermove', moveDraw);
  window.addEventListener('pointerup', endDraw);

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

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

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

// FourierDrawYourLine — vanilla 판(run/321/demo/05-fourier-draw-your-line/index.html) 의 React 포트.
// 내 선 그리기 — 편의 인터랙티브 축. 손으로 그은 선이 그대로 DFT 입력이 된다.
//   ① 기본 상태: 예시 낙서(물결 서명)를 낮은 알파로 깔아두고 에피사이클이 반복해서 되그린다.
//   ② pointerdown~move 로 점을 모으면(최대 512) 기존 계수를 지우고 즉시 dft() 재계산 —
//     계산은 O(N²) 이지만 N=512 로 순식간이고, 체인이 새 경로를 다시 그리기 시작한다.
//   ③ 같은 재합성 루프(투명 트레일 누적 + 혜성 감쇠)를 공유한다.
// 화면이 사는 장치 — 밑바탕 방사 스윕·스포크가 매 프레임 재계산,
// 손 궤적(입력)도 옅은 잔상으로 함께 남는다 — 그은 즉시 바뀌는 계수를 눈으로 읽는다.
import { useEffect, useRef, useState } from "react";
import type { CSSProperties, PointerEvent as ReactPointerEvent } from "react";
import styles from "./FourierDrawYourLine.module.scss";

export type FourierDrawYourLineProps = {
  duration?: string;
  easing?: string;
  color?: string;
  maxPts?: number;   // 입력 받는 최대 점 수
  show?: number;     // 화면에 그리는 원 개수
};

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 = "내 선 그리기 에피사이클 실험판";
const TAU = Math.PI * 2;

// ── DFT (03·04 와 같은 계산) ──
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 FourierDrawYourLine({
  duration = "2s",
  easing = "cubic-bezier(.2, .8, .2, 1)",
  color = "#b7c8ff",
  maxPts = 512,
  show = 48
}: FourierDrawYourLineProps) {
  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 handCvRef = useRef<HTMLCanvasElement | null>(null);
  const handCtxRef = useRef<CanvasRenderingContext2D | null>(null);
  const maxPtsRef = useRef(maxPts) as Box<number>;
  const showRef = useRef(show) as Box<number>;
  const pathRef = useRef<Pt[]>([]) as Box<Pt[]>;
  const normPathRef = useRef<Pt[]>([]) as Box<Pt[]>;   // 정규화된 경로(체인 재현용)
  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 drawingRef = useRef(false) as Box<boolean>;
  const lastPtRef = useRef<Pt | null>(null) as Box<Pt | null>;
  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 normalize(): void {
    // 그은 점을 무대 중심·단위반지름으로 정규화
    const PATH = pathRef.current;
    let minx = 1e9, maxx = -1e9, miny = 1e9, maxy = -1e9;
    for (let i = 0; i < PATH.length; i++) {
      if (PATH[i].x < minx) minx = PATH[i].x;
      if (PATH[i].x > maxx) maxx = PATH[i].x;
      if (PATH[i].y < miny) miny = PATH[i].y;
      if (PATH[i].y > maxy) maxy = PATH[i].y;
    }
    const cx = (minx + maxx) / 2, cy = (miny + maxy) / 2;
    const span = Math.max(maxx - minx, maxy - miny) || 1;
    const norm: Pt[] = [];
    for (let j = 0; j < PATH.length; j++) {
      norm.push({ x: (PATH[j].x - cx) / span, y: (PATH[j].y - cy) / span });
    }
    normPathRef.current = norm;
    coefRef.current = dft(norm);
  }

  function sampleDoodle(): void {
    // 예시 낙서 — 서명 같은 물결. t 0~1 로 닫힌 물결 무늬
    const PATH: Pt[] = [];
    for (let i = 0; i < 200; i++) {
      const t = i / 200;
      PATH.push({
        x: Math.cos(t * TAU) * (0.36 + 0.16 * Math.sin(t * TAU * 3)),
        y: Math.sin(t * TAU) * (0.24 + 0.12 * Math.cos(t * TAU * 2))
      });
    }
    pathRef.current = PATH;
    normalize();
  }

  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;
    handCvRef.current = null;
    handCtxRef.current = null;
    if (!coefRef.current.length) sampleDoodle();
  }

  function chainAt(u: number, showCount?: number): Pt[] {
    const W = wRef.current, H = hRef.current;
    const COEF = coefRef.current;
    const base = Math.min(W, H) * 0.4;
    const cx = W * 0.5, cy = H * 0.5;
    const pts: Pt[] = [{ x: cx, y: cy }];
    const n = showCount || COEF.length;
    for (let i = 0; i < n && i < COEF.length; i++) {
      const c = COEF[i];
      const a = c.freq * u * TAU;
      const ph = Math.atan2(c.im, c.re);
      const ang = a + 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;
  }

  // 밑바탕 — 방사 스윕(계단 밴드) + 스포크
  function drawGrid(ctx: CanvasRenderingContext2D, t: number): void {
    const W = wRef.current, H = hRef.current;
    const col = colRef.current;
    if (!col) return;
    const cx = W * 0.5, cy = H * 0.5;
    const maxR = Math.sqrt(W * W + H * H) * 0.5;
    const sweep = t * 1.1;
    for (let b = 0; b < 16; b++) {
      ctx.fillStyle = rgba(col.glow, 0.085 * (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();
    }
    const spin = t * 0.26;
    for (let i = 0; i < 16; i++) {
      const a = spin + (i / 16) * TAU;
      ctx.strokeStyle = rgba(col.glow, i % 2 === 0 ? 0.08 : 0.05);
      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();
    }
  }

  function draw(u: number, pulse: number, showCount: number, gt: number): Pt {
    const ctx = ctxRef.current;
    const trailCv = trailCvRef.current;
    const handCv = handCvRef.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);
    // 손 궤적 잔상 — 사용자가 그은 원본(정규화 전 화면 좌표)을 옅게
    if (handCv) ctx.drawImage(handCv, 0, 0, W, H);
    ctx.drawImage(trailCv, 0, 0, W, H);
    const base = Math.min(W, H) * 0.4;

    const pts = chainAt(u, showCount);
    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, 0.48);
        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();
    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; }
    trailCtx.strokeStyle = rgba(col.glow, 0.88);
    trailCtx.lineWidth = 1.9;
    trailCtx.lineCap = "round";
    trailCtx.beginPath();
    trailCtx.moveTo(prev.x, prev.y);
    trailCtx.lineTo(pen.x, pen.y);
    trailCtx.stroke();
    trailCtx.strokeStyle = rgba(col.glow, 0.14);
    trailCtx.lineWidth = 5;
    trailCtx.stroke();
    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) * 0.5;
    const u = lt % 1;
    const pulse = 0.5 + 0.5 * Math.sin(lt * 8.0);
    decayTrail();
    const pen = draw(u, pulse, showRef.current, lt * TAU);
    stampTrail(pen);
    setCnt(String(pathRef.current.length));
    rafRef.current = requestAnimationFrame(frame);
  }

  // ── 입력 — 그으면 즉시 DFT 재계산 ──
  function toField(e: ReactPointerEvent<HTMLCanvasElement>): Pt {
    const cv = cvRef.current;
    if (!cv) return { x: 0, y: 0 };
    const r = cv.getBoundingClientRect();
    return { x: e.clientX - r.left, y: e.clientY - r.top };
  }
  function startDraw(e: ReactPointerEvent<HTMLCanvasElement>): void {
    const col = colRef.current;
    const W = wRef.current, H = hRef.current;
    const dpr = dprRef.current;
    if (!col) return;
    drawingRef.current = true;
    const p = toField(e);
    lastPtRef.current = p;
    pathRef.current = [p];
    if (!handCvRef.current) {
      const handCv = document.createElement("canvas");
      handCv.width = W * dpr; handCv.height = H * dpr;
      const handCtx = handCv.getContext("2d");
      if (handCtx) handCtx.scale(dpr, dpr);
      handCvRef.current = handCv;
      handCtxRef.current = handCtx;
    }
    const handCtx = handCtxRef.current;
    if (handCtx) handCtx.clearRect(0, 0, W, H);
    prevPenRef.current = null;
    e.preventDefault();
  }
  function moveDraw(e: ReactPointerEvent<HTMLCanvasElement>): void {
    const handCtx = handCtxRef.current;
    const col = colRef.current;
    const last = lastPtRef.current;
    if (!drawingRef.current || !handCtx || !col || !last) return;
    const p = toField(e);
    if (Math.abs(p.x - last.x) + Math.abs(p.y - last.y) < 4) return;
    pathRef.current.push(p);
    if (pathRef.current.length > maxPtsRef.current) pathRef.current.shift();
    handCtx.strokeStyle = rgba(col.hot, 0.28);
    handCtx.lineWidth = 2;
    handCtx.lineCap = "round";
    handCtx.beginPath();
    handCtx.moveTo(last.x, last.y);
    handCtx.lineTo(p.x, p.y);
    handCtx.stroke();
    lastPtRef.current = p;
    normalize();
    prevPenRef.current = null;
    e.preventDefault();
  }
  function endDraw(): void {
    if (!drawingRef.current) return;
    drawingRef.current = false;
    if (pathRef.current.length > 8) normalize();
  }

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

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

  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>캔버스에 마우스로 아무 선이나 그으면 그 점들이 즉시 복소 계수로 바뀌어, 방금 손으로 그은 서명 낙서를 에피사이클이 한 획씩 다시 그려줍니다</span>
        </p>
        <div
          className={styles.field}
          ref={fieldRef}
          role="application"
          aria-label={FIELD_LABEL}
          tabIndex={0}
        >
          <canvas
            className={styles.cv}
            ref={cvRef}
            onPointerDown={startDraw}
            onPointerMove={moveDraw}
          ></canvas>
        </div>
        <div className={styles.bar}>
          <span className={styles.meta}><b className={styles.val}>{cnt}</b> 예시 낙서 · 직접 그려 보세요</span>
          <span className={styles.metaDim}>canvas · live DFT · pointer events</span>
        </div>
      </div>
    </main>
  );
}