04質量差で跳ねる高さが分かれるボール

<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">ボールごとに異なる大きさを質量として使い落下時の力を計算するため、同じ高さから落としても軽いボールは高く跳ね、重いボールは低く跳ねる。</p>
</div>
</main>

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

.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-paper;
}

.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: #ffffff;
  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: #ffffff;
}

.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: 공의 반지름을 그대로 질량으로 쓰고, 바닥에 닿을 때 되튀는 반발계수를
  // BASE_MASS_REST * BALL_MASS_BOUNCE_FACTOR / mass 로 계산한다 — 질량이 작을수록
  // 나눗셈 결과가 커져 반발계수가 크고, 질량이 클수록 작아 낮게 튄다. 네 공이 같은
  // 높이·같은 시각에 떨어지므로 튀는 높이 차이가 질량 하나로만 갈린다.
  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 BALL_MASS_BOUNCE_FACTOR = 1.4;
  var BASE_MASS_REST = 6;
  var SLEEP_THRESHOLD = 24;
  var SLEEP_HOLD_MS = 300;
  var STAGE_BG = '255,255,255';

  var MASSES = [10, 16, 22, 30];
  var COLORS = ['#6ec8ff', '#4cd4a6', '#b9a0ff', '#ff9ebb'];
  var XPOS = [0.16, 0.4, 0.64, 0.86];

  function restitutionFor(mass) {
    return Math.max(0.22, Math.min(0.95, BASE_MASS_REST * BALL_MASS_BOUNCE_FACTOR / mass));
  }

  var balls = [];
  function reset() {
    balls = [];
    for (var i = 0; i < MASSES.length; i += 1) {
      balls.push({
        x: CALC_W * XPOS[i],
        y: 26,
        vy: 0,
        mass: MASSES[i],
        r: MASSES[i] * 0.5,
        color: COLORS[i],
        rest: restitutionFor(MASSES[i]),
        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 (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;
        } 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 * b.rest;
        }
      }
      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 < 260) 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;
    ctx.beginPath();
    ctx.moveTo(0, (CALC_H - 2) * sy);
    ctx.lineTo(cw, (CALC_H - 2) * sy);
    ctx.stroke();
    for (var j = 0; j < balls.length; j += 1) {
      var b = balls[j];
      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) / 130);
      var shw = pr * (0.9 + shf * 0.4);
      ctx.beginPath();
      ctx.ellipse(px, (CALC_H - 3) * sy, shw, shw * 0.24, 0, 0, Math.PI * 2);
      ctx.fillStyle = 'rgba(23,20,26,' + (0.08 + shf * 0.14) + ')';
      ctx.fill();
      var sqX = 1 + b.squash * 0.5, sqY = 1 - b.squash * 0.35;
      ctx.save();
      ctx.translate(px, py + pr * b.squash * 0.35);
      ctx.scale(sqX, sqY);
      ctx.beginPath();
      ctx.arc(0, 0, pr, 0, Math.PI * 2);
      ctx.fillStyle = b.color;
      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;
  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 > SLEEP_HOLD_MS) { settledAt = null; 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 "./BallPhysicsMassBounceHeight.module.scss";

type Ball = { x: number; y: number; vy: number; mass: number; r: number; color: string; rest: number; squash: number; settled: boolean };

export default function BallPhysicsMassBounceHeight() {
  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 BALL_MASS_BOUNCE_FACTOR = 1.4;
    const BASE_MASS_REST = 6;
    const SLEEP_THRESHOLD = 24;
    const SLEEP_HOLD_MS = 300;

    const MASSES = [10, 16, 22, 30];
    const COLORS = ["#6ec8ff", "#4cd4a6", "#b9a0ff", "#ff9ebb"];
    const XPOS = [0.16, 0.4, 0.64, 0.86];

    function restitutionFor(mass: number) {
      return Math.max(0.22, Math.min(0.95, (BASE_MASS_REST * BALL_MASS_BOUNCE_FACTOR) / mass));
    }

    let balls: Ball[] = [];
    let impacts: { x: number; y: number; born: number; strength: number }[] = [];
    function reset() {
      balls = MASSES.map((mass, i) => ({
        x: CALC_W * XPOS[i], y: 26, vy: 0, mass, r: mass * 0.5,
        color: COLORS[i], rest: restitutionFor(mass), squash: 0, settled: false
      }));
      impacts = [];
    }
    reset();

    function stepSim(dtMs: number, nowMs: number) {
      const dtS = dtMs / 1000;
      for (const b of balls) {
        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;
          } 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 * b.rest;
          }
        }
        b.squash = Math.max(0, b.squash - dtS * 3.5);
      }
      impacts = impacts.filter((im) => nowMs - im.born < 260);
    }

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

    let cw = 480, ch = 300;
    function draw() {
      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;
      ctx!.beginPath();
      ctx!.moveTo(0, (CALC_H - 2) * sy);
      ctx!.lineTo(cw, (CALC_H - 2) * sy);
      ctx!.stroke();
      for (const b of balls) {
        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) / 130);
        const shw = pr * (0.9 + shf * 0.4);
        ctx!.beginPath();
        ctx!.ellipse(px, (CALC_H - 3) * sy, shw, shw * 0.24, 0, 0, Math.PI * 2);
        ctx!.fillStyle = "rgba(23,20,26," + (0.08 + shf * 0.14) + ")";
        ctx!.fill();
        const sqX = 1 + b.squash * 0.5, sqY = 1 - b.squash * 0.35;
        ctx!.save();
        ctx!.translate(px, py + pr * b.squash * 0.35);
        ctx!.scale(sqX, sqY);
        ctx!.beginPath();
        ctx!.arc(0, 0, pr, 0, Math.PI * 2);
        ctx!.fillStyle = b.color;
        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();
    }

    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 > SLEEP_HOLD_MS) { settledAt = null; elapsed = 0; reset(); }
          }
          acc -= FIXED_DT;
        }
        draw();
      }
      raf = requestAnimationFrame(tick);
    }
    fit();
    window.addEventListener("resize", fit);
    draw();
    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}>공마다 다른 크기를 질량값으로 써서 떨어질 때 힘을 계산해, 같은 높이에서 떨어져도 가벼운 공은 높이 튀어 오르고 무거운 공은 낮게 튄다</p>
      </div>
    </main>
  );
}