04질량 차이로 튀는 높이가 갈라지는 공

<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">공마다 다른 크기를 질량값으로 써서 떨어질 때 힘을 계산해, 같은 높이에서 떨어져도 가벼운 공은 높이 튀어 오르고 무거운 공은 낮게 튄다</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>
  );
}