02Outer Curve Drawn by a Gear Rolling Around the Outside

<main class="stage">
<div class="sp2 is-demo" id="sp2Root" tabindex="0">
  <canvas class="sp2__canvas" id="sp2Canvas" width="480" height="300"></canvas>
  <p class="sp2__caption">Recalculates the contact angle every frame as a small gear rolls around the outside of the ring, drawing a petal-shaped trace that extends outward, the opposite of the inward curve</p>
</div>
</main>

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

.sp2 {
  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;
}

.sp2__canvas {
  display: block;
  width: 100%;
  height: 100%;
}

.sp2__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) {
  .sp2__caption { font-size: 10px; padding: $sp-1 $sp-2; }
}

@media (prefers-reduced-motion: reduce) {
  .sp2 { 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);
}

.sp2 {
  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;
}

.sp2__canvas {
  display: block;
  width: 100%;
  height: 100%;
}

.sp2__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) {
  .sp2__caption {
    font-size: 10px;
    padding: 4px 8px;
  }
}
@media (prefers-reduced-motion: reduce) {
  .sp2 {
    cursor: default;
  }
}

(function () {
  // 기법: 에피트로코이드(외접 톱니) — 톱니가 고정된 링 바깥을 미끄러지지 않고 굴러갈 때
  // 펜 구멍이 그리는 좌표를 매 프레임 각도 t 로 다시 계산한다.
  // x(t) = (R+r)cos(t) - d cos(((R+r)/r) t) · y(t) = (R+r)sin(t) - d sin(((R+r)/r) t)
  var root = document.getElementById('sp2Root');
  var canvas = document.getElementById('sp2Canvas');
  var ctx = canvas.getContext('2d');
  var wrap = canvas.parentElement;

  var CALC_DIM = 200;
  var GEAR_TEETH_OUTER = 96;
  var GEAR_ROLL_TEETH = 36;
  var PEN_TIP_RATIO = 0.6;
  var TOOTH_UNIT = 0.6;
  var SEGMENTS_PER_TURN = 240;

  function gcd(a, b) { a = Math.abs(a); b = Math.abs(b); while (b) { var t = b; b = a % b; a = t; } return a; }

  var R = GEAR_TEETH_OUTER * TOOTH_UNIT;
  var r = GEAR_ROLL_TEETH * TOOTH_UNIT;
  var d = r * PEN_TIP_RATIO;
  var g = gcd(GEAR_TEETH_OUTER, GEAR_ROLL_TEETH);
  var TURNS = GEAR_ROLL_TEETH / g;
  var TOTAL_T = TURNS * Math.PI * 2;
  var CYCLE_SECONDS = 6;
  var SPEED = TOTAL_T / CYCLE_SECONDS;

  function point(t) {
    var k = (R + r) / r;
    return {
      x: (R + r) * Math.cos(t) - d * Math.cos(k * t),
      y: (R + r) * Math.sin(t) - d * Math.sin(k * 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 * 0.92;
    cx = cw / 2; cy = ch / 2;
  }

  function toScreen(p) { return { x: cx + p.x * scale, y: cy + p.y * scale }; }

  function drawFull(tMax) {
    ctx.clearRect(0, 0, cw, ch);
    var tipW = toScreen(point(tMax));
    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,.60)');
    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 fillSteps = Math.max(2, Math.round((tMax / (Math.PI * 2)) * SEGMENTS_PER_TURN));
    ctx.beginPath();
    for (var fi = 0; fi <= fillSteps; fi += 1) {
      var fs = toScreen(point((fi / fillSteps) * tMax));
      if (fi === 0) ctx.moveTo(fs.x, fs.y); else ctx.lineTo(fs.x, fs.y);
    }
    ctx.closePath();
    ctx.fillStyle = 'rgba(23,20,26,.12)';
    ctx.fill('evenodd');
    ctx.beginPath();
    ctx.strokeStyle = 'rgba(23,20,26,.16)';
    ctx.lineWidth = Math.max(1, scale * 0.012);
    ctx.arc(cx, cy, R * scale, 0, Math.PI * 2);
    ctx.stroke();

    ctx.lineWidth = Math.max(3, scale * 0.04);
    ctx.strokeStyle = 'rgba(23,20,26,.92)';
    ctx.lineJoin = 'round';
    ctx.lineCap = 'round';
    var steps = Math.max(2, Math.round((tMax / (Math.PI * 2)) * SEGMENTS_PER_TURN));
    ctx.beginPath();
    for (var i = 0; i <= steps; i += 1) {
      var t = (i / steps) * tMax;
      var s = toScreen(point(t));
      if (i === 0) ctx.moveTo(s.x, s.y); else ctx.lineTo(s.x, s.y);
    }
    ctx.stroke();
    if (tMax > 0.001) {
      var tip = toScreen(point(tMax));
      ctx.fillStyle = 'rgba(23,20,26,1)';
      ctx.beginPath();
      ctx.arc(tip.x, tip.y, Math.max(3, scale * 0.05), 0, Math.PI * 2);
      ctx.fill();
    }
  }

  var reduce = window.matchMedia('(prefers-reduced-motion: reduce)').matches;
  if (reduce) root.classList.remove('is-demo');
  fit();

  if (reduce) {
    drawFull(TOTAL_T);
  } else {
    var elapsed = 0.3;
    var lastTs = null;
    function tick(ts) {
      if (lastTs === null) lastTs = ts;
      var dt = Math.min(ts - lastTs, 48);
      lastTs = ts;
      elapsed += dt / 1000;
      var t = elapsed * SPEED;
      if (t > TOTAL_T) { elapsed = 0; t = 0; }
      drawFull(t);
      requestAnimationFrame(tick);
    }
    drawFull(elapsed * SPEED);
    window.addEventListener('resize', function () { fit(); drawFull(elapsed * SPEED); });
    requestAnimationFrame(tick);
  }
})();

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

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

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

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

    const CALC_DIM = 200;
    const GEAR_TEETH_OUTER = 96;
    const GEAR_ROLL_TEETH = 36;
    const PEN_TIP_RATIO = 0.6;
    const TOOTH_UNIT = 0.6;
    const SEGMENTS_PER_TURN = 240;

    function gcd(a: number, b: number): number {
      a = Math.abs(a); b = Math.abs(b);
      while (b) { const t = b; b = a % b; a = t; }
      return a;
    }

    const R = GEAR_TEETH_OUTER * TOOTH_UNIT;
    const r = GEAR_ROLL_TEETH * TOOTH_UNIT;
    const d = r * PEN_TIP_RATIO;
    const g = gcd(GEAR_TEETH_OUTER, GEAR_ROLL_TEETH);
    const TURNS = GEAR_ROLL_TEETH / g;
    const TOTAL_T = TURNS * Math.PI * 2;
    const CYCLE_SECONDS = 6;
    const SPEED = TOTAL_T / CYCLE_SECONDS;

    function point(t: number): Pt {
      const k = (R + r) / r;
      return {
        x: (R + r) * Math.cos(t) - d * Math.cos(k * t),
        y: (R + r) * Math.sin(t) - d * Math.sin(k * 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 * 0.92;
      cx = cw / 2; cy = ch / 2;
    }

    function toScreen(p: Pt): Pt { return { x: cx + p.x * scale, y: cy + p.y * scale }; }

    function drawFull(tMax: number) {
      ctx!.clearRect(0, 0, cw, ch);
      const tipW = toScreen(point(tMax));
      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,.60)');
      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 fillSteps = Math.max(2, Math.round((tMax / (Math.PI * 2)) * SEGMENTS_PER_TURN));
      ctx!.beginPath();
      for (let fi = 0; fi <= fillSteps; fi += 1) {
        const fs = toScreen(point((fi / fillSteps) * tMax));
        if (fi === 0) ctx!.moveTo(fs.x, fs.y); else ctx!.lineTo(fs.x, fs.y);
      }
      ctx!.closePath();
      ctx!.fillStyle = 'rgba(23,20,26,.12)';
      ctx!.fill('evenodd');
      ctx!.beginPath();
      ctx!.strokeStyle = "rgba(23,20,26,.16)";
      ctx!.lineWidth = Math.max(1, scale * 0.012);
      ctx!.arc(cx, cy, R * scale, 0, Math.PI * 2);
      ctx!.stroke();

      ctx!.lineWidth = Math.max(3, scale * 0.04);
      ctx!.strokeStyle = "rgba(23,20,26,.92)";
      ctx!.lineJoin = "round";
      ctx!.lineCap = "round";
      const steps = Math.max(2, Math.round((tMax / (Math.PI * 2)) * SEGMENTS_PER_TURN));
      ctx!.beginPath();
      for (let i = 0; i <= steps; i += 1) {
        const t = (i / steps) * tMax;
        const s = toScreen(point(t));
        if (i === 0) ctx!.moveTo(s.x, s.y); else ctx!.lineTo(s.x, s.y);
      }
      ctx!.stroke();
      if (tMax > 0.001) {
        const tip = toScreen(point(tMax));
        ctx!.fillStyle = "rgba(23,20,26,1)";
        ctx!.beginPath();
        ctx!.arc(tip.x, tip.y, Math.max(3, scale * 0.05), 0, Math.PI * 2);
        ctx!.fill();
      }
    }

    const reduce = window.matchMedia("(prefers-reduced-motion: reduce)").matches;
    if (reduce) root.classList.remove("is-demo");
    fit();

    let raf = 0;
    if (reduce) {
      drawFull(TOTAL_T);
    } else {
      let elapsed = 0.3;
      let lastTs: number | null = null;
      const onResize = () => { fit(); drawFull(elapsed * SPEED); };
      function tick(ts: number) {
        if (lastTs === null) lastTs = ts;
        const dt = Math.min(ts - lastTs, 48);
        lastTs = ts;
        elapsed += dt / 1000;
        let t = elapsed * SPEED;
        if (t > TOTAL_T) { elapsed = 0; t = 0; }
        drawFull(t);
        raf = requestAnimationFrame(tick);
      }
      drawFull(elapsed * SPEED);
      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.sp2} is-demo`} ref={rootRef} tabIndex={0}>
        <canvas className={styles.sp2__canvas} ref={canvasRef} width={480} height={300} />
        <p className={styles.sp2__caption}>작은 톱니가 링 바깥을 돌 때의 접점 각도를 매 프레임 다시 계산해, 안쪽 곡선과 반대로 바깥으로 뻗는 꽃잎 모양 궤적을 그린다</p>
      </div>
    </main>
  );
}