02Ball Falling Under Gravity and Settling on the Floor

<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">Every frame adds downward velocity to drop the ball, and each floor hit shaves off speed until the ball finally settles still.</p>
</div>
</main>

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

.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-yellow;
}

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

.bp__caption {
  position: absolute;
  left: $sp-3;
  top: $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: #ffd23f;
  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: #ffd23f;
}

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

.bp__caption {
  position: absolute;
  left: 12px;
  top: 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 () {
  // 기법: 반고정 시간 스텝마다 속도에 GRAVITY * dt 를 더해 적분한다(오일러). 바닥에
  // 닿으면 속도를 FLOOR_RESTITUTION 배로 줄여 되튕기고, 절대값이 SLEEP_THRESHOLD 보다
  // 작아지면 움직임을 0으로 잠가 공이 멈춰 눕는다. 완전히 멈춘 뒤엔 일정 시간 뒤 같은
  // 시퀀스를 처음부터 다시 시작해 2초 캡처창 안에 낙하-안정 사이클이 2회 들어온다.
  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 GRAVITY = 900;
  var FLOOR_RESTITUTION = 0.55;
  var SLEEP_THRESHOLD = 26;
  var SLEEP_HOLD_MS = 320;
  var STAGE_BG = '255,247,230';
  var REST_MS = 620;

  function seedRand(seed) {
    var s = seed >>> 0;
    return function () { s = (s * 1664525 + 1013904223) >>> 0; return s / 4294967296; };
  }
  var rand = seedRand(427021);

  var DROPS = [
    { x: 0.22, r: 13, color: '#ff9ebb', delay: 0 },
    { x: 0.5, r: 17, color: '#4cd4a6', delay: 200 },
    { x: 0.78, r: 11, color: '#b9a0ff', delay: 420 }
  ];

  var balls = [];
  function reset() {
    balls = [];
    for (var i = 0; i < DROPS.length; i += 1) {
      var d = DROPS[i];
      balls.push({
        x0: CALC_W * d.x,
        x: CALC_W * d.x,
        y: 30,
        vy: 0,
        r: d.r,
        color: d.color,
        startAt: d.delay,
        born: 0,
        squash: 0,
        settled: false
      });
    }
    impacts = [];
  }
  var impacts = [];

  function stepSim(dtMs, nowMs) {
    var dtS = dtMs / 1000;
    for (var i = 0; i < balls.length; i += 1) {
      var b = balls[i];
      if (nowMs < b.startAt) continue;
      if (b.settled) {
        b.squash = Math.max(0, b.squash - dtS * 6);
        continue;
      }
      b.vy += GRAVITY * dtS;
      b.y += b.vy * dtS;
      var floor = CALC_H - b.r;
      if (b.y >= floor) {
        b.y = floor;
        if (Math.abs(b.vy) < SLEEP_THRESHOLD) {
          b.vy = 0;
          b.settled = true;
          b.squash = 0.5;
          impacts.push({ x: b.x, y: floor, born: nowMs, strength: 0.35 });
        } else {
          impacts.push({ x: b.x, y: floor, born: nowMs, strength: Math.min(1, Math.abs(b.vy) / 320) });
          b.squash = Math.max(b.squash, Math.min(0.85, Math.abs(b.vy) / 300));
          b.vy = -b.vy * FLOOR_RESTITUTION;
        }
      }
      b.squash = Math.max(0, b.squash - dtS * 3.5);
    }
    var live = [];
    for (var k = 0; k < impacts.length; k += 1) {
      if (nowMs - impacts[k].born < 300) live.push(impacts[k]);
    }
    impacts = live;
  }

  function allSettled() {
    for (var i = 0; i < balls.length; i += 1) {
      if (!balls[i].settled) return false;
    }
    return true;
  }

  function draw(nowMs) {
    var sx = cw / CALC_W, sy = ch / CALC_H;
    ctx.clearRect(0, 0, cw, ch);
    ctx.strokeStyle = 'rgba(23,20,26,0.08)';
    ctx.lineWidth = 1;
    for (var gy = 0; gy < CALC_H; gy += 40) {
      ctx.beginPath();
      ctx.moveTo(0, gy * sy);
      ctx.lineTo(cw, gy * sy);
      ctx.stroke();
    }
    for (var i = 0; i < impacts.length; i += 1) {
      var im = impacts[i];
      var f = (nowMs - im.born) / 300;
      var px = im.x * sx, py = im.y * sy;
      var pr = (8 + f * 22) * ((sx + sy) / 2);
      ctx.beginPath();
      ctx.ellipse(px, py, pr, pr * 0.32, 0, 0, Math.PI * 2);
      ctx.strokeStyle = 'rgba(23,20,26,' + (im.strength * (1 - f) * 0.3) + ')';
      ctx.lineWidth = 2;
      ctx.stroke();
    }
    for (var j = 0; j < balls.length; j += 1) {
      var b = balls[j];
      if (nowMs < b.startAt) continue;
      var px = b.x * sx, py = b.y * sy, pr = b.r * ((sx + sy) / 2);
      var shf = Math.max(0, 1 - (CALC_H - b.r - b.y) / 120);
      var shw = pr * (0.9 + shf * 0.4);
      ctx.beginPath();
      ctx.ellipse(px, (CALC_H - 4) * sy, shw, shw * 0.26, 0, 0, Math.PI * 2);
      ctx.fillStyle = 'rgba(23,20,26,' + (0.10 + shf * 0.16) + ')';
      ctx.fill();
      var sqX = 1 + b.squash * 0.55;
      var sqY = 1 - b.squash * 0.38;
      ctx.save();
      ctx.translate(px, py + pr * b.squash * 0.38);
      ctx.scale(sqX, sqY);
      ctx.beginPath();
      ctx.arc(0, 0, pr, 0, Math.PI * 2);
      ctx.fillStyle = b.color;
      ctx.fill();
      var hg = ctx.createRadialGradient(-pr * 0.3, -pr * 0.35, pr * 0.1, -pr * 0.3, -pr * 0.35, pr * 0.75);
      hg.addColorStop(0, 'rgba(255,255,255,0.5)');
      hg.addColorStop(1, 'rgba(255,255,255,0)');
      ctx.fillStyle = hg;
      ctx.fill();
      ctx.restore();
    }
  }

  var cw = 480, ch = 300;
  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;
    draw(elapsed);
  }

  var reduce = window.matchMedia('(prefers-reduced-motion: reduce)').matches;
  var elapsed = 0;
  if (reduce) root.classList.remove('is-demo');
  reset();

  var lastTs = null;
  var acc = 0;
  var FIXED_DT = 16;
  var settledAt = null;
  var cycle = 0;
  function tick(ts) {
    if (lastTs === null) lastTs = ts;
    var frameDt = Math.min(ts - lastTs, 48);
    lastTs = ts;
    if (!reduce) {
      acc += frameDt;
      while (acc >= FIXED_DT) {
        elapsed += FIXED_DT;
        stepSim(FIXED_DT, elapsed);
        if (allSettled()) {
          if (settledAt === null) settledAt = elapsed;
          else if (elapsed - settledAt > REST_MS) {
            settledAt = null;
            cycle += 1;
            elapsed = 0;
            reset();
          }
        }
        acc -= FIXED_DT;
      }
      draw(elapsed);
    }
    requestAnimationFrame(tick);
  }
  fit();
  window.addEventListener('resize', fit);
  draw(elapsed);
  requestAnimationFrame(tick);
})();

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

type Ball = {
  x0: number; x: number; y: number; vy: number; r: number; color: string;
  startAt: number; squash: number; settled: boolean;
};
type Impact = { x: number; y: number; born: number; strength: number };

export default function BallPhysicsGravityDropSettle() {
  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_W = 320, CALC_H = 200;
    const GRAVITY = 900;
    const FLOOR_RESTITUTION = 0.55;
    const SLEEP_THRESHOLD = 26;
    const REST_MS = 620;

    const DROPS = [
      { x: 0.22, r: 13, color: "#ff9ebb", delay: 0 },
      { x: 0.5, r: 17, color: "#4cd4a6", delay: 200 },
      { x: 0.78, r: 11, color: "#b9a0ff", delay: 420 }
    ];

    let balls: Ball[] = [];
    let impacts: Impact[] = [];
    function reset() {
      balls = DROPS.map((d) => ({
        x0: CALC_W * d.x, x: CALC_W * d.x, y: 30, vy: 0,
        r: d.r, color: d.color, startAt: d.delay, squash: 0, settled: false
      }));
      impacts = [];
    }
    reset();

    function stepSim(dtMs: number, nowMs: number) {
      const dtS = dtMs / 1000;
      for (const b of balls) {
        if (nowMs < b.startAt) continue;
        if (b.settled) { b.squash = Math.max(0, b.squash - dtS * 6); continue; }
        b.vy += GRAVITY * dtS;
        b.y += b.vy * dtS;
        const floor = CALC_H - b.r;
        if (b.y >= floor) {
          b.y = floor;
          if (Math.abs(b.vy) < SLEEP_THRESHOLD) {
            b.vy = 0; b.settled = true; b.squash = 0.5;
            impacts.push({ x: b.x, y: floor, born: nowMs, strength: 0.35 });
          } else {
            impacts.push({ x: b.x, y: floor, born: nowMs, strength: Math.min(1, Math.abs(b.vy) / 320) });
            b.squash = Math.max(b.squash, Math.min(0.85, Math.abs(b.vy) / 300));
            b.vy = -b.vy * FLOOR_RESTITUTION;
          }
        }
        b.squash = Math.max(0, b.squash - dtS * 3.5);
      }
      impacts = impacts.filter((im) => nowMs - im.born < 300);
    }

    function allSettled() { return balls.every((b) => b.settled); }

    let cw = 480, ch = 300;
    function draw(nowMs: number) {
      const sx = cw / CALC_W, sy = ch / CALC_H;
      ctx!.clearRect(0, 0, cw, ch);
      ctx!.strokeStyle = "rgba(23,20,26,0.08)";
      ctx!.lineWidth = 1;
      for (let gy = 0; gy < CALC_H; gy += 40) {
        ctx!.beginPath();
        ctx!.moveTo(0, gy * sy);
        ctx!.lineTo(cw, gy * sy);
        ctx!.stroke();
      }
      for (const im of impacts) {
        const f = (nowMs - im.born) / 300;
        const px = im.x * sx, py = im.y * sy;
        const pr = (8 + f * 22) * ((sx + sy) / 2);
        ctx!.beginPath();
        ctx!.ellipse(px, py, pr, pr * 0.32, 0, 0, Math.PI * 2);
        ctx!.strokeStyle = "rgba(23,20,26," + (im.strength * (1 - f) * 0.3) + ")";
        ctx!.lineWidth = 2;
        ctx!.stroke();
      }
      for (const b of balls) {
        if (nowMs < b.startAt) continue;
        const px = b.x * sx, py = b.y * sy, pr = b.r * ((sx + sy) / 2);
        const shf = Math.max(0, 1 - (CALC_H - b.r - b.y) / 120);
        const shw = pr * (0.9 + shf * 0.4);
        ctx!.beginPath();
        ctx!.ellipse(px, (CALC_H - 4) * sy, shw, shw * 0.26, 0, 0, Math.PI * 2);
        ctx!.fillStyle = "rgba(23,20,26," + (0.10 + shf * 0.16) + ")";
        ctx!.fill();
        const sqX = 1 + b.squash * 0.55, sqY = 1 - b.squash * 0.38;
        ctx!.save();
        ctx!.translate(px, py + pr * b.squash * 0.38);
        ctx!.scale(sqX, sqY);
        ctx!.beginPath();
        ctx!.arc(0, 0, pr, 0, Math.PI * 2);
        ctx!.fillStyle = b.color;
        ctx!.fill();
        const hg = ctx!.createRadialGradient(-pr * 0.3, -pr * 0.35, pr * 0.1, -pr * 0.3, -pr * 0.35, pr * 0.75);
        hg.addColorStop(0, "rgba(255,255,255,0.5)");
        hg.addColorStop(1, "rgba(255,255,255,0)");
        ctx!.fillStyle = hg;
        ctx!.fill();
        ctx!.restore();
      }
    }

    function fit() {
      const 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;
      draw(elapsed);
    }

    const reduce = window.matchMedia("(prefers-reduced-motion: reduce)").matches;
    let elapsed = 0;
    if (reduce) root.classList.remove("is-demo");

    let lastTs: number | null = null;
    let acc = 0;
    const FIXED_DT = 16;
    let settledAt: number | null = null;
    let raf = 0;
    function tick(ts: number) {
      if (lastTs === null) lastTs = ts;
      const frameDt = Math.min(ts - lastTs, 48);
      lastTs = ts;
      if (!reduce) {
        acc += frameDt;
        while (acc >= FIXED_DT) {
          elapsed += FIXED_DT;
          stepSim(FIXED_DT, elapsed);
          if (allSettled()) {
            if (settledAt === null) settledAt = elapsed;
            else if (elapsed - settledAt > REST_MS) { settledAt = null; elapsed = 0; reset(); }
          }
          acc -= FIXED_DT;
        }
        draw(elapsed);
      }
      raf = requestAnimationFrame(tick);
    }
    fit();
    window.addEventListener("resize", fit);
    draw(elapsed);
    raf = requestAnimationFrame(tick);

    return () => {
      cancelAnimationFrame(raf);
      window.removeEventListener("resize", fit);
    };
  }, []);

  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}>매 프레임 아래 방향으로 속도를 더해 공을 떨어뜨리고, 바닥에 닿을 때마다 속도를 줄여 나가 결국 공이 멈춰 눕는다</p>
      </div>
    </main>
  );
}