06曲線の上に歯車とペンが見えるガイド

<main class="stage">
<div class="sp6 is-demo" id="sp6Root" tabindex="0">
  <canvas class="sp6__canvas" id="sp6Canvas" width="480" height="300"></canvas>
  <p class="sp6__badge" id="sp6Badge"></p>
  <p class="sp6__caption">転がる歯車とペン位置を曲線の上に一緒に描き、今の角度と接点を常に示し続け、歯車が回る方向と軌跡がつながる関係を一目で追えるようにする</p>
</div>
</main>

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

.sp6 {
  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-yellow;
}

.sp6__canvas {
  display: block;
  width: 100%;
  height: 100%;
}

.sp6__badge {
  position: absolute;
  left: $sp-3;
  top: $sp-3;
  margin: 0;
  padding: $sp-1 $sp-3;
  border-radius: $r-pill;
  background: rgba(255, 247, 230, .85);
  color: $subject-ink;
  font-weight: 500;
  font-size: 12px;
  line-height: 1.4;
  pointer-events: none;
}

.sp6__caption {
  position: absolute;
  left: $sp-3;
  bottom: $sp-3;
  max-width: 78%;
  margin: 0;
  padding: $sp-1 $sp-3;
  border-radius: $r-pill;
  background: rgba(255, 247, 230, .85);
  color: $subject-ink;
  font-weight: 500;
  font-size: 12px;
  line-height: 1.4;
  pointer-events: none;
}

@media (max-width: 340px) {
  .sp6__caption, .sp6__badge { font-size: 10px; padding: $sp-1 $sp-2; }
}

@media (prefers-reduced-motion: reduce) {
  .sp6 { cursor: default; }
}

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

.stage {
  box-sizing: border-box;
  min-height: 100vh;
  display: grid;
  place-items: center;
  margin: 0;
  background: #ffd23f;
  font-family: -apple-system, "Segoe UI", "Noto Sans KR", sans-serif;
  padding: clamp(8px, 4vw, 24px);
}

.sp6 {
  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: #ffd23f;
}

.sp6__canvas {
  display: block;
  width: 100%;
  height: 100%;
}

.sp6__badge {
  position: absolute;
  left: 12px;
  top: 12px;
  margin: 0;
  padding: 4px 12px;
  border-radius: 999px;
  background: rgba(255, 247, 230, 0.85);
  color: #17141a;
  font-weight: 500;
  font-size: 12px;
  line-height: 1.4;
  pointer-events: none;
}

.sp6__caption {
  position: absolute;
  left: 12px;
  bottom: 12px;
  max-width: 78%;
  margin: 0;
  padding: 4px 12px;
  border-radius: 999px;
  background: rgba(255, 247, 230, 0.85);
  color: #17141a;
  font-weight: 500;
  font-size: 12px;
  line-height: 1.4;
  pointer-events: none;
}

@media (max-width: 340px) {
  .sp6__caption, .sp6__badge {
    font-size: 10px;
    padding: 4px 8px;
  }
}
@media (prefers-reduced-motion: reduce) {
  .sp6 {
    cursor: default;
  }
}

(function () {
  // 기법: 링 톱니·구름 톱니 두 원과 펜 스포크를 매 프레임 현재 각도로 다시 그려,
  // 곡선이 자라나는 동안에도 "지금 어디를 굴러가는지"가 항상 화면에 남아 있게 한다.
  var root = document.getElementById('sp6Root');
  var canvas = document.getElementById('sp6Canvas');
  var badge = document.getElementById('sp6Badge');
  var ctx = canvas.getContext('2d');
  var wrap = canvas.parentElement;

  var CALC_DIM = 200;
  var GEAR_RING_TEETH = 60;
  var GEAR_ROLL_TEETH = 24;
  var PEN_TIP_RATIO = 0.62;
  var TOOTH_UNIT = 1.3;
  var SEGMENTS_PER_TURN = 200;
  var CYCLE_SECONDS = 6;
  var HOLD_FRACTION = 0.84;

  function gcd(a, b) { while (b) { var t = b; b = a % b; a = t; } return a; }
  var g = gcd(GEAR_RING_TEETH, GEAR_ROLL_TEETH);
  var TURNS = GEAR_ROLL_TEETH / g;
  var AXIS_COUNT = GEAR_RING_TEETH / g;

  var R = GEAR_RING_TEETH * TOOTH_UNIT;
  var r = GEAR_ROLL_TEETH * TOOTH_UNIT;
  var d = r * PEN_TIP_RATIO;
  var K = (R - r) / r;

  function penAt(t) {
    return {
      x: (R - r) * Math.cos(t) + d * Math.cos(K * t),
      y: (R - r) * Math.sin(t) - d * Math.sin(K * t)
    };
  }
  function rollCenterAt(t) {
    return { x: (R - r) * Math.cos(t), y: (R - r) * Math.sin(t) };
  }

  var cw = 480, ch = 300, scale = 1, cx = 240, cy = 150;
  function fit() {
    var rect = wrap.getBoundingClientRect();
    cw = Math.max(1, Math.round(rect.width));
    ch = Math.max(1, Math.round(rect.height));
    canvas.width = cw; canvas.height = ch;
    scale = Math.min(cw, ch) / CALC_DIM * 0.82;
    cx = cw / 2; cy = ch / 2;
  }
  function toScreen(p) { return { x: cx + p.x * scale, y: cy + p.y * scale }; }

  var maxT = 2 * Math.PI * TURNS;
  var dtSample = (2 * Math.PI) / SEGMENTS_PER_TURN;

  function render(progress) {
    var t = maxT * Math.min(progress / HOLD_FRACTION, 1);

    ctx.fillStyle = '#ffd23f';
    ctx.fillRect(0, 0, cw, ch);
    var tipW = toScreen(penAt(t));
    var wash = ctx.createRadialGradient(tipW.x, tipW.y, 0, tipW.x, tipW.y, Math.max(cw, ch) * 0.9);
    wash.addColorStop(0, 'rgba(255,255,255,.62)');
    wash.addColorStop(0.5, 'rgba(255,190,215,.32)');
    wash.addColorStop(1, 'rgba(190,225,255,.14)');
    ctx.fillStyle = wash;
    ctx.fillRect(0, 0, cw, ch);
    var rcW = toScreen(rollCenterAt(t));
    ctx.beginPath();
    ctx.arc(rcW.x, rcW.y, r * scale, 0, Math.PI * 2);
    ctx.fillStyle = 'rgba(190,225,255,.38)';
    ctx.fill();

    var ringCenter = toScreen({ x: 0, y: 0 });
    ctx.beginPath();
    ctx.arc(ringCenter.x, ringCenter.y, R * scale, 0, Math.PI * 2);
    ctx.strokeStyle = 'rgba(23,20,26,.22)';
    ctx.lineWidth = Math.max(1.4, scale * 0.02);
    ctx.stroke();

    ctx.beginPath();
    var first = true;
    for (var tt = 0; tt <= t; tt += dtSample) {
      var p = toScreen(penAt(tt));
      if (first) { ctx.moveTo(p.x, p.y); first = false; } else { ctx.lineTo(p.x, p.y); }
    }
    ctx.save();
    ctx.fillStyle = 'rgba(23,20,26,.10)';
    ctx.fill('evenodd');
    ctx.restore();
    ctx.strokeStyle = 'rgba(23,20,26,.9)';
    ctx.lineWidth = Math.max(3, scale * 0.04);
    ctx.lineJoin = 'round'; ctx.lineCap = 'round';
    ctx.stroke();

    var rc = rollCenterAt(t);
    var rcS = toScreen(rc);
    ctx.beginPath();
    ctx.arc(rcS.x, rcS.y, r * scale, 0, Math.PI * 2);
    ctx.strokeStyle = 'rgba(10,79,232,.75)';
    ctx.lineWidth = Math.max(1.6, scale * 0.024);
    ctx.stroke();

    var pen = toScreen(penAt(t));
    ctx.beginPath();
    ctx.moveTo(rcS.x, rcS.y);
    ctx.lineTo(pen.x, pen.y);
    ctx.strokeStyle = 'rgba(10,79,232,.75)';
    ctx.lineWidth = Math.max(1.4, scale * 0.018);
    ctx.stroke();

    ctx.beginPath();
    ctx.arc(pen.x, pen.y, Math.max(3, scale * 0.05), 0, Math.PI * 2);
    ctx.fillStyle = 'rgba(23,20,26,.92)';
    ctx.fill();

    var deg = Math.round((((t * 180 / Math.PI) % 360) + 360) % 360);
    badge.textContent = '接点角度' + deg + '° · 対称軸' + AXIS_COUNT + '本';
  }

  var reduce = window.matchMedia('(prefers-reduced-motion: reduce)').matches;
  fit();
  if (reduce) {
    root.classList.remove('is-demo');
    render(HOLD_FRACTION);
  } else {
    var startTs = null;
    function tick(ts) {
      if (startTs === null) startTs = ts;
      var elapsed = (ts - startTs) / 1000;
      var progress = (elapsed % CYCLE_SECONDS) / CYCLE_SECONDS;
      render(progress);
      requestAnimationFrame(tick);
    }
    window.addEventListener('resize', function () { fit(); });
    requestAnimationFrame(tick);
  }
})();

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

type Pt = { x: number; y: number };

export default function SpiroSceneGearVisualGuide() {
  const rootRef = useRef<HTMLDivElement>(null);
  const canvasRef = useRef<HTMLCanvasElement>(null);
  const badgeRef = useRef<HTMLParagraphElement>(null);

  useEffect(() => {
    const root = rootRef.current;
    const canvas = canvasRef.current;
    const badge = badgeRef.current;
    if (!root || !canvas || !badge) return;
    const ctx = canvas.getContext("2d");
    if (!ctx) return;
    const wrap = canvas.parentElement as HTMLElement;

    const CALC_DIM = 200;
    const GEAR_RING_TEETH = 60;
    const GEAR_ROLL_TEETH = 24;
    const PEN_TIP_RATIO = 0.62;
    const TOOTH_UNIT = 1.3;
    const SEGMENTS_PER_TURN = 200;
    const CYCLE_SECONDS = 6;
    const HOLD_FRACTION = 0.84;

    function gcd(a: number, b: number): number { while (b) { const t = b; b = a % b; a = t; } return a; }
    const g = gcd(GEAR_RING_TEETH, GEAR_ROLL_TEETH);
    const TURNS = GEAR_ROLL_TEETH / g;
    const AXIS_COUNT = GEAR_RING_TEETH / g;

    const R = GEAR_RING_TEETH * TOOTH_UNIT;
    const r = GEAR_ROLL_TEETH * TOOTH_UNIT;
    const d = r * PEN_TIP_RATIO;
    const K = (R - r) / r;

    function penAt(t: number): Pt {
      return {
        x: (R - r) * Math.cos(t) + d * Math.cos(K * t),
        y: (R - r) * Math.sin(t) - d * Math.sin(K * t)
      };
    }
    function rollCenterAt(t: number): Pt {
      return { x: (R - r) * Math.cos(t), y: (R - r) * Math.sin(t) };
    }

    let cw = 480, ch = 300, scale = 1, cx = 240, cy = 150;
    function fit() {
      const rect = wrap.getBoundingClientRect();
      cw = Math.max(1, Math.round(rect.width));
      ch = Math.max(1, Math.round(rect.height));
      canvas!.width = cw; canvas!.height = ch;
      scale = Math.min(cw, ch) / CALC_DIM * 0.82;
      cx = cw / 2; cy = ch / 2;
    }
    function toScreen(p: Pt): Pt { return { x: cx + p.x * scale, y: cy + p.y * scale }; }

    const maxT = 2 * Math.PI * TURNS;
    const dtSample = (2 * Math.PI) / SEGMENTS_PER_TURN;

    function render(progress: number) {
      const t = maxT * Math.min(progress / HOLD_FRACTION, 1);

      ctx!.fillStyle = "#ffd23f";
      ctx!.fillRect(0, 0, cw, ch);
      const tipW = toScreen(penAt(t));
      const wash = ctx!.createRadialGradient(tipW.x, tipW.y, 0, tipW.x, tipW.y, Math.max(cw, ch) * 0.9);
      wash.addColorStop(0, 'rgba(255,255,255,.62)');
      wash.addColorStop(0.5, 'rgba(255,190,215,.32)');
      wash.addColorStop(1, 'rgba(190,225,255,.14)');
      ctx!.fillStyle = wash;
      ctx!.fillRect(0, 0, cw, ch);
      const rcW = toScreen(rollCenterAt(t));
      ctx!.beginPath();
      ctx!.arc(rcW.x, rcW.y, r * scale, 0, Math.PI * 2);
      ctx!.fillStyle = 'rgba(190,225,255,.38)';
      ctx!.fill();

      const ringCenter = toScreen({ x: 0, y: 0 });
      ctx!.beginPath();
      ctx!.arc(ringCenter.x, ringCenter.y, R * scale, 0, Math.PI * 2);
      ctx!.strokeStyle = "rgba(23,20,26,.22)";
      ctx!.lineWidth = Math.max(1.4, scale * 0.02);
      ctx!.stroke();

      ctx!.beginPath();
      let first = true;
      for (let tt = 0; tt <= t; tt += dtSample) {
        const p = toScreen(penAt(tt));
        if (first) { ctx!.moveTo(p.x, p.y); first = false; } else { ctx!.lineTo(p.x, p.y); }
      }
      ctx!.save();
      ctx!.fillStyle = "rgba(23,20,26,.10)";
      ctx!.fill("evenodd");
      ctx!.restore();
      ctx!.strokeStyle = "rgba(23,20,26,.9)";
      ctx!.lineWidth = Math.max(3, scale * 0.04);
      ctx!.lineJoin = "round"; ctx!.lineCap = "round";
      ctx!.stroke();

      const rc = rollCenterAt(t);
      const rcS = toScreen(rc);
      ctx!.beginPath();
      ctx!.arc(rcS.x, rcS.y, r * scale, 0, Math.PI * 2);
      ctx!.strokeStyle = "rgba(10,79,232,.75)";
      ctx!.lineWidth = Math.max(1.6, scale * 0.024);
      ctx!.stroke();

      const pen = toScreen(penAt(t));
      ctx!.beginPath();
      ctx!.moveTo(rcS.x, rcS.y);
      ctx!.lineTo(pen.x, pen.y);
      ctx!.strokeStyle = "rgba(10,79,232,.75)";
      ctx!.lineWidth = Math.max(1.4, scale * 0.018);
      ctx!.stroke();

      ctx!.beginPath();
      ctx!.arc(pen.x, pen.y, Math.max(3, scale * 0.05), 0, Math.PI * 2);
      ctx!.fillStyle = "rgba(23,20,26,.92)";
      ctx!.fill();

      const deg = Math.round((((t * 180 / Math.PI) % 360) + 360) % 360);
      badge!.textContent = "접점 각도 " + deg + "° · 대칭 축 " + AXIS_COUNT + "개";
    }

    const reduce = window.matchMedia("(prefers-reduced-motion: reduce)").matches;
    fit();
    let raf = 0;
    if (reduce) {
      root.classList.remove("is-demo");
      render(HOLD_FRACTION);
    } else {
      let startTs: number | null = null;
      const onResize = () => { fit(); };
      function tick(ts: number) {
        if (startTs === null) startTs = ts;
        const elapsed = (ts - startTs) / 1000;
        const progress = (elapsed % CYCLE_SECONDS) / CYCLE_SECONDS;
        render(progress);
        raf = requestAnimationFrame(tick);
      }
      window.addEventListener("resize", onResize);
      raf = requestAnimationFrame(tick);
      return () => {
        cancelAnimationFrame(raf);
        window.removeEventListener("resize", onResize);
      };
    }
    return () => { cancelAnimationFrame(raf); };
  }, []);

  return (
    <main className={styles.stage}>
      <div className={`${styles.sp6} is-demo`} ref={rootRef} tabIndex={0}>
        <canvas className={styles.sp6__canvas} ref={canvasRef} width={480} height={300} />
        <p className={styles.sp6__badge} ref={badgeRef} />
        <p className={styles.sp6__caption}>굴러가는 톱니바퀴와 펜 위치를 곡선 위에 함께 그려 지금의 각도와 접점을 계속 보여주고, 톱니가 도는 방향과 궤적이 이어지는 관계를 한눈에 따라갈 수 있게 한다</p>
      </div>
    </main>
  );
}