From fae63218ada21d6bb1ccaedc802a30ca164377c0 Mon Sep 17 00:00:00 2001
From: DhairyaLGandhi <dhairya@juliacomputing.com>
Date: Tue, 11 Aug 2026 12:13:32 +0200
Subject: [PATCH] feat: add rollercoaster

---
 viz_submission/_data.json     |   1 +
 viz_submission/_loop.png      | Bin 0 -> 108529 bytes
 viz_submission/_over.png      | Bin 0 -> 118452 bytes
 viz_submission/_template.html | 480 ++++++++++++++++++++++++++++++++++
 viz_submission/index.html     | 480 ++++++++++++++++++++++++++++++++++
 5 files changed, 961 insertions(+)
 create mode 100644 viz_submission/_data.json
 create mode 100644 viz_submission/_loop.png
 create mode 100644 viz_submission/_over.png
 create mode 100644 viz_submission/_template.html
 create mode 100644 viz_submission/index.html

diff --git a/viz_submission/_data.json b/viz_submission/_data.json
new file mode 100644
index 0000000..ca2d361
--- /dev/null
+++ b/viz_submission/_data.json
@@ -0,0 +1 @@
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diff --git a/viz_submission/_template.html b/viz_submission/_template.html
new file mode 100644
index 0000000..0235c1a
--- /dev/null
+++ b/viz_submission/_template.html
@@ -0,0 +1,480 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+<meta charset="utf-8" />
+<meta name="viewport" content="width=device-width, initial-scale=1" />
+<title>Rollercoaster — physical simulation</title>
+<link rel="preconnect" href="https://fonts.googleapis.com">
+<link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
+<link href="https://fonts.googleapis.com/css2?family=Instrument+Sans:wght@400;500;600&family=JetBrains+Mono:wght@400;500&display=swap" rel="stylesheet">
+<style>
+  :root{
+    /* surface + ink tokens (spec §3) */
+    --stage:#F3F2F7; --paper:#FAFBFF; --panel2:#FDFCFF;
+    --ink:#1A1330; --ink2:#4A4365; --ink3:#8580A0;
+    --hair:#D8D3E8; --hair-soft:rgba(216,211,232,0.6);
+    --chip:#EFECF8; --dq:#C4574B;
+    --asphalt:#C2BED3; --silver:#8580A0; --tyre:#16111F;
+    /* accent (computed from team slug; overridden in JS) */
+    --acc-deep:#074351; --acc-base:#0E6E86; --acc-lift:#1588A5;
+    --acc-wash:#E9F1F7; --acc-hair:#C6DCE4;
+    --sans:'Instrument Sans', ui-sans-serif, system-ui, sans-serif;
+    --mono:'JetBrains Mono', ui-monospace, 'Courier New', monospace;
+    --shadow:0 10px 34px rgba(20,15,40,0.13);
+  }
+  *{box-sizing:border-box;}
+  html,body{margin:0;}
+  body{
+    background:var(--stage); color:var(--ink2);
+    font-family:var(--sans); font-size:14px; line-height:1.5;
+    -webkit-font-smoothing:antialiased; padding:32px 24px 24px;
+  }
+  .board{max-width:1120px; margin:0 auto;}
+
+  /* ---- header ---- */
+  .head{margin:0 4px 24px;}
+  .kicker{
+    font-family:var(--mono); font-weight:500; font-size:11px;
+    letter-spacing:0.24em; text-transform:uppercase; color:var(--acc-base);
+    margin:0 0 10px;
+  }
+  .kicker .dot{opacity:0.55; margin:0 2px;}
+  h1{
+    font-family:var(--sans); font-weight:500; font-size:30px; line-height:1.15;
+    letter-spacing:-0.02em; color:var(--acc-base); margin:0; max-width:46ch;
+  }
+  h1 .ink{color:var(--ink);}
+  .sub{font-size:14px; color:var(--ink2); margin:10px 0 0; max-width:64ch;}
+
+  /* ---- grid + cards ---- */
+  .grid{display:grid; grid-template-columns:repeat(12,1fr); gap:16px;}
+  .card{
+    background:var(--paper); border-radius:11px;
+    border:1px solid color-mix(in srgb, var(--acc-base) 14%, transparent);
+    box-shadow:var(--shadow); padding:16px 18px; min-width:0;
+  }
+  .card.track{grid-column:1 / -1; border-radius:14px; padding:18px 18px 14px;}
+  .card.hero{grid-column:span 4;}
+  .card.meter{grid-column:span 4;}
+  .card.stat{grid-column:span 2; display:flex; flex-direction:column;}
+  .card.chart{grid-column:span 6;}
+
+  .label{
+    font-family:var(--mono); font-weight:500; font-size:10px;
+    letter-spacing:0.15em; text-transform:uppercase; color:var(--ink3);
+    margin:0;
+  }
+  .cardhead{display:flex; align-items:baseline; justify-content:space-between; gap:12px; margin-bottom:12px;}
+
+  /* ---- hero number ---- */
+  .hero-wrap{display:flex; align-items:flex-end; justify-content:space-between; height:100%;}
+  .hero{
+    font-family:var(--mono); font-weight:500; font-size:52px; line-height:0.95;
+    letter-spacing:-0.02em; color:var(--acc-base);
+  }
+  .hero .unit{font-size:14px; color:var(--ink3); margin-left:8px; letter-spacing:0;}
+  .hero-side{text-align:right;}
+  .hero-side .v{font-family:var(--mono); font-size:24px; color:var(--ink); font-weight:500;}
+  .hero-side .u{font-family:var(--mono); font-size:10px; color:var(--ink3); letter-spacing:0.06em; margin-left:4px;}
+
+  /* ---- segment meter (spec §4) ---- */
+  .meter-val{font-family:var(--mono); font-weight:500; font-size:52px; letter-spacing:-0.02em; color:var(--acc-base); line-height:1;}
+  .meter-val .unit{font-size:14px; color:var(--ink3); margin-left:6px; letter-spacing:0;}
+  .segs{display:flex; gap:3px; margin-top:16px;}
+  .seg{flex:1; height:6px; border-radius:1.5px; background:rgba(26,19,48,0.16); transition:background .12s linear;}
+  .seg.lit{background:var(--acc-base);}
+  .seg.lit.top{background:var(--ink);}
+  .meter-scale{display:flex; justify-content:space-between; margin-top:8px;}
+  .meter-scale span{font-family:var(--mono); font-size:10px; color:var(--ink3); letter-spacing:0.02em;}
+
+  /* ---- stat cards ---- */
+  .stat .v{font-family:var(--mono); font-weight:500; font-size:24px; color:var(--ink); margin-top:auto; letter-spacing:-0.01em;}
+  .stat .v .u{font-size:10px; color:var(--ink3); margin-left:4px; letter-spacing:0.04em;}
+
+  /* ---- track svg ---- */
+  .stage-svg{width:100%; display:block;}
+  .trk-full{fill:none; stroke:var(--hair); stroke-width:2;}
+  .trk-trav{fill:none; stroke:var(--acc-base); stroke-width:2.6; stroke-linecap:round; stroke-linejoin:round;}
+  .trk-area{stroke:none;}
+  .pillar{stroke:var(--silver); stroke-width:1; opacity:0.22;}
+  .ground{stroke:var(--hair); stroke-width:1;}
+
+  /* ---- charts ---- */
+  .spark{width:100%; display:block;}
+  .gl{stroke:var(--hair); stroke-width:1;}
+  .gl.soft{stroke:var(--hair-soft);}
+  .axtx{font-family:var(--mono); font-size:10px; fill:var(--ink3); letter-spacing:0.02em;}
+  .ln-base{fill:none; stroke:var(--acc-base); stroke-width:2.2; stroke-linejoin:round;}
+  .ln-lift{fill:none; stroke:var(--acc-lift); stroke-width:1.8; stroke-linejoin:round;}
+  .ln-ink3{fill:none; stroke:var(--ink3); stroke-width:1.6; stroke-linejoin:round; opacity:0.8;}
+  .legend{display:flex; gap:14px;}
+  .legend span{font-family:var(--mono); font-size:10px; letter-spacing:0.06em; color:var(--ink3); display:flex; align-items:center; gap:5px;}
+  .swatch{width:14px; height:3px; border-radius:1.5px; display:inline-block;}
+
+  /* ---- transport ---- */
+  .transport{display:flex; align-items:center; gap:14px; margin-top:12px;}
+  .play{
+    font-family:var(--mono); font-size:11px; letter-spacing:0.14em; text-transform:uppercase;
+    color:var(--acc-base); background:var(--acc-wash);
+    border:1px solid color-mix(in srgb, var(--acc-base) 24%, transparent);
+    border-radius:7px; padding:7px 14px; cursor:pointer; font-weight:500;
+  }
+  .play:hover{border-color:color-mix(in srgb, var(--acc-base) 45%, transparent);}
+  .clock{font-family:var(--mono); font-size:11px; color:var(--ink3); letter-spacing:0.06em; white-space:nowrap;}
+  .clock b{color:var(--ink); font-weight:500;}
+  input[type=range]{
+    -webkit-appearance:none; appearance:none; flex:1; height:4px; border-radius:2px;
+    background:var(--hair); outline:none; cursor:pointer;
+  }
+  input[type=range]::-webkit-slider-thumb{
+    -webkit-appearance:none; width:14px; height:14px; border-radius:50%;
+    background:var(--acc-base); border:2px solid var(--paper); box-shadow:0 1px 4px rgba(20,15,40,0.25);
+  }
+  input[type=range]::-moz-range-thumb{
+    width:14px; height:14px; border-radius:50%; background:var(--acc-base); border:2px solid var(--paper);
+  }
+
+  /* ---- footer ---- */
+  footer{
+    margin-top:22px; padding-top:14px; border-top:1px solid var(--hair);
+    display:flex; justify-content:space-between; align-items:center; gap:12px; flex-wrap:wrap;
+  }
+  footer .cap, footer .date{font-family:var(--mono); font-size:10.5px; letter-spacing:0.16em; text-transform:uppercase; color:var(--ink3);}
+  footer .sep{color:color-mix(in srgb, var(--acc-base) 55%, transparent); margin:0 10px;}
+
+  /* ---- motion (spec §5) ---- */
+  .reveal{opacity:0; transform:translateY(12px); animation:rv .6s cubic-bezier(.22,.61,.36,1) forwards;}
+  @keyframes rv{to{opacity:1; transform:translateY(0);}}
+  .no-reveal .reveal{opacity:1!important; transform:none!important; animation:none!important;}
+  @media (prefers-reduced-motion: reduce){ *{animation:none!important; transition:none!important;} .reveal{opacity:1; transform:none;} }
+
+  @media (max-width:860px){
+    .card.hero,.card.meter,.card.chart{grid-column:1 / -1;}
+    .card.stat{grid-column:span 6;}
+    .hero,.meter-val{font-size:44px;}
+  }
+</style>
+</head>
+<body>
+<div class="board">
+
+  <header class="head reveal" style="animation-delay:0ms">
+    <p class="kicker">01<span class="dot">·</span>ROLLERCOASTER</p>
+    <h1>A physical <span class="ink">rollercoaster</span>, solved and ridden in real&nbsp;time.</h1>
+    <p class="sub">A point-mass cart on a curved track, integrated by ModelingToolkit. It drops off the lift hill, whips through a vertical loop, and rides out over rolling hills &mdash; gravity trading with speed while drag bleeds the energy away.</p>
+  </header>
+
+  <div class="grid">
+
+    <!-- TRACK -->
+    <section class="card track reveal" style="animation-delay:80ms">
+      <div class="cardhead">
+        <p class="label">The ride <span style="color:color-mix(in srgb,var(--acc-base) 55%,transparent)">·</span> vertical loop + hills</p>
+        <p class="clock">T = <b id="clk">0.0</b> S</p>
+      </div>
+      <svg class="stage-svg" id="track" viewBox="0 0 1040 300" preserveAspectRatio="xMidYMid meet" aria-label="Rollercoaster track"></svg>
+      <div class="transport">
+        <button class="play" id="play">Pause</button>
+        <input type="range" id="scrub" min="0" max="1000" value="0" />
+        <span class="clock"><b id="prog">0</b>%</span>
+      </div>
+    </section>
+
+    <!-- HERO: SPEED -->
+    <section class="card hero reveal" style="animation-delay:160ms">
+      <div class="cardhead"><p class="label">Speed</p></div>
+      <div class="hero-wrap">
+        <div><span class="hero" id="spd">0</span><span class="unit" style="font-family:var(--mono)">km/h</span></div>
+        <div class="hero-side">
+          <div><span class="v" id="spdms">0.0</span><span class="u">m/s</span></div>
+        </div>
+      </div>
+    </section>
+
+    <!-- METER: G-FORCE -->
+    <section class="card meter reveal" style="animation-delay:240ms">
+      <div class="cardhead"><p class="label">Rider g-force <span style="color:color-mix(in srgb,var(--acc-base) 55%,transparent)">·</span> load</p><p class="label" id="peaklbl">peak 0.00 g</p></div>
+      <div class="meter-val" id="gval">1.00<span class="unit">g</span></div>
+      <div class="segs" id="segs"></div>
+      <div class="meter-scale"><span>0</span><span>airtime</span><span>heavy</span><span>5g</span></div>
+    </section>
+
+    <!-- STAT: HEIGHT -->
+    <section class="card stat reveal" style="animation-delay:320ms">
+      <p class="label">Height</p>
+      <div class="v"><span id="hgt">0</span><span class="u">m</span></div>
+    </section>
+
+    <!-- STAT: DISTANCE -->
+    <section class="card stat reveal" style="animation-delay:400ms">
+      <p class="label">Distance</p>
+      <div class="v"><span id="dist">0</span><span class="u">m</span></div>
+    </section>
+
+    <!-- CHART: SPEED -->
+    <section class="card chart reveal" style="animation-delay:480ms">
+      <div class="cardhead"><p class="label">Speed profile</p><p class="label">km/h · t</p></div>
+      <svg class="spark" id="cSpeed" viewBox="0 0 500 200" preserveAspectRatio="none"></svg>
+    </section>
+
+    <!-- CHART: ENERGY -->
+    <section class="card chart reveal" style="animation-delay:560ms">
+      <div class="cardhead">
+        <p class="label">Energy budget</p>
+        <div class="legend">
+          <span><i class="swatch" style="background:var(--acc-base)"></i>total</span>
+          <span><i class="swatch" style="background:var(--acc-lift)"></i>kinetic</span>
+          <span><i class="swatch" style="background:var(--ink3)"></i>potential</span>
+        </div>
+      </div>
+      <svg class="spark" id="cEnergy" viewBox="0 0 500 200" preserveAspectRatio="none"></svg>
+    </section>
+
+  </div>
+
+  <footer class="reveal" style="animation-delay:640ms">
+    <span class="cap">Rollercoaster<span class="sep">|</span>ModelingToolkit &amp; Dyad<span class="sep">|</span><span id="slug">team</span></span>
+    <span class="date">JuliaCon 2026</span>
+  </footer>
+
+</div>
+
+<script>
+const DATA = __DATA_JSON__;
+(function(){
+  "use strict";
+  const A = DATA.accent, M = DATA.meta;
+  const root = document.documentElement.style;
+  root.setProperty('--acc-deep',A.deep); root.setProperty('--acc-base',A.base);
+  root.setProperty('--acc-lift',A.lift); root.setProperty('--acc-wash',A.wash);
+  root.setProperty('--acc-hair',A.hairline);
+  document.getElementById('slug').textContent = DATA.slug;
+
+  const t=DATA.t, X=DATA.x, H=DATA.h, S=DATA.spd, G=DATA.g,
+        KE=DATA.KE, PE=DATA.PE, E=DATA.E, TH=DATA.th, Sa=DATA.s;
+  const n=t.length, T=t[n-1];
+  const NS="http://www.w3.org/2000/svg";
+  const lerp=(a,b,f)=>a+(b-a)*f;
+  const minA=a=>a.reduce((m,v)=>v<m?v:m,Infinity);
+  const maxA=a=>a.reduce((m,v)=>v>m?v:m, -Infinity);
+
+  // ---------- TRACK geometry (equal-aspect so the loop reads as a loop) ----------
+  const TW=1040, THh=300, padL=28, padR=26, padT=18, padB=26;
+  const xMin=0, xMax=maxA(X), hMin=minA(H), hMax=maxA(H);
+  const plotW=TW-padL-padR, plotH=THh-padT-padB;
+  const EXAG=1.25;                                   // gentle vertical emphasis
+  const xr=(xMax-xMin)||1, hr=(hMax-hMin)||1;
+  const sc=Math.min(plotW/xr, plotH/(hr*EXAG));      // px per metre (shared)
+  const scX=sc, scY=sc*EXAG;
+  const drawW=xr*scX, drawH=hr*scY;
+  const ox=padL+(plotW-drawW)/2, oy=padT+(plotH-drawH)/2;
+  const sx=x=>ox+(x-xMin)*scX;
+  const sy=h=>oy+(hMax-h)*scY;                        // higher h -> smaller y
+  const baseY=Math.min(THh-6, oy+drawH+14);
+  const svg=document.getElementById('track');
+  // deep -> base -> lift gradient (the one sanctioned ramp), for the train cars
+  svg.innerHTML =
+    `<defs><linearGradient id="cargrad" x1="0" y1="0" x2="1" y2="0">
+        <stop offset="0%"   stop-color="${A.deep}"/>
+        <stop offset="55%"  stop-color="${A.base}"/>
+        <stop offset="100%" stop-color="${A.lift}"/>
+     </linearGradient></defs>`;
+  // ground line
+  const ground=document.createElementNS(NS,'line');
+  ground.setAttribute('class','ground');
+  ground.setAttribute('x1',padL); ground.setAttribute('x2',TW-padR);
+  ground.setAttribute('y1',baseY); ground.setAttribute('y2',baseY);
+  svg.appendChild(ground);
+  // support pillars — only under gentle (non-inverted) track, so the loop is skipped
+  for(let i=0;i<n;i+=8){
+    if(Math.cos(TH[i])<0.4) continue;
+    const yy=sy(H[i]); if(yy>=baseY-2) continue;
+    const p=document.createElementNS(NS,'line');
+    p.setAttribute('class','pillar');
+    p.setAttribute('x1',sx(X[i]).toFixed(1)); p.setAttribute('x2',sx(X[i]).toFixed(1));
+    p.setAttribute('y1',yy.toFixed(1)); p.setAttribute('y2',baseY.toFixed(1));
+    svg.appendChild(p);
+  }
+  // full track path
+  let dFull="M"+sx(X[0]).toFixed(1)+" "+sy(H[0]).toFixed(1);
+  for(let i=1;i<n;i++) dFull+="L"+sx(X[i]).toFixed(1)+" "+sy(H[i]).toFixed(1);
+  const trkFull=document.createElementNS(NS,'path');
+  trkFull.setAttribute('class','trk-full'); trkFull.setAttribute('d',dFull);
+  svg.appendChild(trkFull);
+  // traveled line (updated per frame)
+  const trkTrav=document.createElementNS(NS,'path'); trkTrav.setAttribute('class','trk-trav');
+  svg.appendChild(trkTrav);
+
+  // ---------- TRAIN: several cars placed by arc length, so it bends through the loop ----------
+  const NCAR=4, CARSPACING=7.5;
+  function carSVG(lead){
+    const nose = lead ? `<path d="M13 -11 Q20 -11 20 -8 L16 -5 H13 Z" fill="${A.deep}"/>` : '';
+    return `
+      <circle cx="-8" cy="-3.2" r="3.5" fill="var(--tyre)"/>
+      <circle cx="8"  cy="-3.2" r="3.5" fill="var(--tyre)"/>
+      <circle cx="-8" cy="-3.2" r="1.3" fill="${A.lift}"/>
+      <circle cx="8"  cy="-3.2" r="1.3" fill="${A.lift}"/>
+      ${nose}
+      <path d="M-13 -5 H13 Q16 -5 16 -9 V-14 Q16 -17 13 -17 H-13 Q-16 -17 -16 -14 V-9 Q-16 -5 -13 -5 Z"
+            fill="url(#cargrad)" stroke="${A.deep}" stroke-width="1"/>
+      <rect x="-12.5" y="-13" width="25" height="3" rx="1.4" fill="${A.wash}" opacity="0.6"/>
+      <circle cx="-5" cy="-19" r="2.6" fill="${A.wash}"/>
+      <circle cx="5"  cy="-19" r="2.6" fill="${A.wash}"/>
+      <path d="M-5 -21.2 v-3 M5 -21.2 v-3" stroke="${A.lift}" stroke-width="1.4" stroke-linecap="round"/>`;
+  }
+  const trainG=document.createElementNS(NS,'g'); svg.appendChild(trainG);
+  const cars=[];
+  for(let k=0;k<NCAR;k++){
+    const gc=document.createElementNS(NS,'g'); gc.innerHTML=carSVG(k===0);
+    trainG.appendChild(gc); cars.push(gc);
+  }
+  // map an arc-length position to screen coords + tangent angle
+  function arcToXY(scArc){
+    scArc=Math.max(Sa[0], Math.min(Sa[n-1], scArc));
+    let lo=0, hi=n-1;
+    while(hi-lo>1){ const mid=(lo+hi)>>1; if(Sa[mid]<=scArc) lo=mid; else hi=mid; }
+    const f=(scArc-Sa[lo])/((Sa[hi]-Sa[lo])||1);
+    const x=lerp(X[lo],X[hi],f), h=lerp(H[lo],H[hi],f);
+    const ang=Math.atan2(sy(H[hi])-sy(H[lo]), sx(X[hi])-sx(X[lo]))*180/Math.PI;
+    return {px:sx(x), py:sy(h), ang};
+  }
+
+  // ---------- SPARKLINE helper ----------
+  function makeChart(id, series, yPad){
+    const el=document.getElementById(id);
+    const W=500,Hh=200,pl=38,pr=10,pt=14,pb=24;
+    const pw=W-pl-pr, ph=Hh-pt-pb;
+    let allY=[]; series.forEach(s=>allY=allY.concat(s.y));
+    let ymin=minA(allY), ymax=maxA(allY); const sp=(ymax-ymin)*0.08+1e-9;
+    ymin-=sp; ymax+=sp;
+    const X2t=i=>pl + (t[i]-t[0])/(T-t[0])*pw;
+    const Y2=v=>pt + (ymax-v)/(ymax-ymin)*ph;
+    let g="";
+    // horizontal gridlines + y ticks
+    for(let k=0;k<=3;k++){
+      const yy=pt+ph*k/3, val=ymax-(ymax-ymin)*k/3;
+      g+=`<line class="gl soft" x1="${pl}" x2="${W-pr}" y1="${yy.toFixed(1)}" y2="${yy.toFixed(1)}"/>`;
+      g+=`<text class="axtx" x="${pl-6}" y="${(yy+3).toFixed(1)}" text-anchor="end">${Math.round(val)}</text>`;
+    }
+    // x ticks
+    for(let k=0;k<=3;k++){
+      const xx=pl+pw*k/3, tv=t[0]+(T-t[0])*k/3;
+      g+=`<text class="axtx" x="${xx.toFixed(1)}" y="${Hh-8}" text-anchor="middle">${tv.toFixed(0)}s</text>`;
+    }
+    el.innerHTML=g;
+    const paths=series.map(s=>{
+      const p=document.createElementNS(NS,'path'); p.setAttribute('class',s.cls); el.appendChild(p); return p;
+    });
+    const dot=document.createElementNS(NS,'circle');
+    dot.setAttribute('r','3.4'); dot.setAttribute('fill',A.base);
+    dot.setAttribute('stroke','var(--paper)'); dot.setAttribute('stroke-width','1.5');
+    el.appendChild(dot);
+    return {series,paths,dot,X2t,Y2};
+  }
+  const chSpeed=makeChart('cSpeed', [{y:S,cls:'ln-base'}]);
+  const chEnergy=makeChart('cEnergy', [
+     {y:E,cls:'ln-base'},{y:KE,cls:'ln-lift'},{y:PE,cls:'ln-ink3'}]);
+
+  function drawChart(ch, iF, i, frac){
+    ch.series.forEach((s,si)=>{
+      let d="M"+ch.X2t(0).toFixed(1)+" "+ch.Y2(s.y[0]).toFixed(1);
+      for(let k=1;k<=i;k++) d+="L"+ch.X2t(k).toFixed(1)+" "+ch.Y2(s.y[k]).toFixed(1);
+      const cx=lerp(ch.X2t(i),ch.X2t(Math.min(i+1,n-1)),frac);
+      const cy=ch.Y2(lerp(s.y[i],s.y[Math.min(i+1,n-1)],frac));
+      d+="L"+cx.toFixed(1)+" "+cy.toFixed(1);
+      ch.paths[si].setAttribute('d',d);
+      if(si===0){ ch.dot.setAttribute('cx',cx); ch.dot.setAttribute('cy',cy); }
+    });
+  }
+
+  // ---------- segment meter ----------
+  const segsEl=document.getElementById('segs'); const SEG=10;
+  for(let i=0;i<SEG;i++){const d=document.createElementNS('http://www.w3.org/1999/xhtml','div');}
+  for(let i=0;i<SEG;i++){const s=document.createElement('div'); s.className='seg'; segsEl.appendChild(s);}
+  const segNodes=[...segsEl.children];
+  const GSCALE=5.0;
+
+  // ---------- update everything from one signal: playT ----------
+  const clk=document.getElementById('clk'), prog=document.getElementById('prog');
+  const spdEl=document.getElementById('spd'), spdms=document.getElementById('spdms');
+  const gval=document.getElementById('gval'), peaklbl=document.getElementById('peaklbl');
+  const hgt=document.getElementById('hgt'), dist=document.getElementById('dist');
+  const scrub=document.getElementById('scrub');
+
+  function update(playT){
+    const idx=Math.max(0,Math.min(n-1, playT/T*(n-1)));
+    const i=Math.min(n-2,Math.floor(idx)), frac=idx-i;
+    const cx=lerp(X[i],X[i+1],frac), ch=lerp(H[i],H[i+1],frac);
+    const spd=lerp(S[i],S[i+1],frac), g=lerp(G[i],G[i+1],frac);
+
+    // train: each car placed by arc length behind the lead, bending through the loop
+    const sLead=lerp(Sa[i],Sa[i+1],frac);
+    for(let k=0;k<NCAR;k++){
+      const p=arcToXY(sLead - k*CARSPACING);
+      cars[k].setAttribute('transform',`translate(${p.px.toFixed(1)},${p.py.toFixed(1)}) rotate(${p.ang.toFixed(2)})`);
+    }
+
+    // traveled track line up to the lead car
+    let d="M"+sx(X[0]).toFixed(1)+" "+sy(H[0]).toFixed(1);
+    for(let k=1;k<=i;k++) d+="L"+sx(X[k]).toFixed(1)+" "+sy(H[k]).toFixed(1);
+    d+="L"+sx(cx).toFixed(1)+" "+sy(ch).toFixed(1);
+    trkTrav.setAttribute('d',d);
+
+    // readouts
+    clk.textContent=(idx/(n-1)*T).toFixed(1);
+    prog.textContent=Math.round(idx/(n-1)*100);
+    spdEl.textContent=Math.round(spd);
+    spdms.textContent=(spd/3.6).toFixed(1);
+    gval.innerHTML=g.toFixed(2)+'<span class="unit">g</span>';
+    hgt.textContent=Math.round(ch);
+    dist.textContent=Math.round(cx);
+    // peak g over the ridden portion
+    let pk=0; for(let k=0;k<=i;k++) if(G[k]>pk) pk=G[k]; if(g>pk) pk=g;
+    peaklbl.textContent='peak '+pk.toFixed(2)+' g';
+
+    // meter
+    const lit=Math.max(0,Math.min(SEG,Math.round(g/GSCALE*SEG)));
+    segNodes.forEach((s,k)=>{
+      s.classList.toggle('lit', k<lit);
+      s.classList.toggle('top', k<lit && k>=SEG-3);
+    });
+
+    // charts
+    drawChart(chSpeed, idx, i, frac);
+    drawChart(chEnergy, idx, i, frac);
+
+    scrub.value=Math.round(idx/(n-1)*1000);
+  }
+
+  // ---------- transport / playback ----------
+  const params=new URLSearchParams(location.search);
+  const reduce=window.matchMedia('(prefers-reduced-motion: reduce)').matches;
+  const forceStill=params.get('anim')==='0';
+  if(reduce||forceStill) document.documentElement.classList.add('no-reveal');
+
+  const PLAY_SECS=26;                     // full 60 s ride plays in ~26 s
+  const rate=T/PLAY_SECS;
+  let playT=0, playing=!(reduce||forceStill), last=null;
+  // deep-link a specific moment: ?t=SECONDS (paused)
+  if(params.has('t')){ playT=Math.max(0,Math.min(T, parseFloat(params.get('t'))||0)); playing=false; }
+  else if(reduce||forceStill){ playT=T*0.28; }   // representative still
+
+  const playBtn=document.getElementById('play');
+  playBtn.textContent=playing?'Pause':'Play';
+
+  function frame(ts){
+    if(last==null) last=ts;
+    const dt=(ts-last)/1000; last=ts;
+    if(playing){ playT+=dt*rate; if(playT>=T) playT=0; }
+    update(playT);
+    requestAnimationFrame(frame);
+  }
+  playBtn.addEventListener('click',()=>{ playing=!playing; playBtn.textContent=playing?'Pause':'Play'; if(playing&&last===null) requestAnimationFrame(frame); });
+  scrub.addEventListener('input',()=>{ playing=false; playBtn.textContent='Play'; playT=scrub.value/1000*T; update(playT); });
+
+  update(playT);                          // always paint the initial frame
+  if(playing) requestAnimationFrame(frame);
+})();
+</script>
+</body>
+</html>
diff --git a/viz_submission/index.html b/viz_submission/index.html
new file mode 100644
index 0000000..0007fab
--- /dev/null
+++ b/viz_submission/index.html
@@ -0,0 +1,480 @@
+<!DOCTYPE html>
+<html lang="en">
+<head>
+<meta charset="utf-8" />
+<meta name="viewport" content="width=device-width, initial-scale=1" />
+<title>Rollercoaster — physical simulation</title>
+<link rel="preconnect" href="https://fonts.googleapis.com">
+<link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
+<link href="https://fonts.googleapis.com/css2?family=Instrument+Sans:wght@400;500;600&family=JetBrains+Mono:wght@400;500&display=swap" rel="stylesheet">
+<style>
+  :root{
+    /* surface + ink tokens (spec §3) */
+    --stage:#F3F2F7; --paper:#FAFBFF; --panel2:#FDFCFF;
+    --ink:#1A1330; --ink2:#4A4365; --ink3:#8580A0;
+    --hair:#D8D3E8; --hair-soft:rgba(216,211,232,0.6);
+    --chip:#EFECF8; --dq:#C4574B;
+    --asphalt:#C2BED3; --silver:#8580A0; --tyre:#16111F;
+    /* accent (computed from team slug; overridden in JS) */
+    --acc-deep:#074351; --acc-base:#0E6E86; --acc-lift:#1588A5;
+    --acc-wash:#E9F1F7; --acc-hair:#C6DCE4;
+    --sans:'Instrument Sans', ui-sans-serif, system-ui, sans-serif;
+    --mono:'JetBrains Mono', ui-monospace, 'Courier New', monospace;
+    --shadow:0 10px 34px rgba(20,15,40,0.13);
+  }
+  *{box-sizing:border-box;}
+  html,body{margin:0;}
+  body{
+    background:var(--stage); color:var(--ink2);
+    font-family:var(--sans); font-size:14px; line-height:1.5;
+    -webkit-font-smoothing:antialiased; padding:32px 24px 24px;
+  }
+  .board{max-width:1120px; margin:0 auto;}
+
+  /* ---- header ---- */
+  .head{margin:0 4px 24px;}
+  .kicker{
+    font-family:var(--mono); font-weight:500; font-size:11px;
+    letter-spacing:0.24em; text-transform:uppercase; color:var(--acc-base);
+    margin:0 0 10px;
+  }
+  .kicker .dot{opacity:0.55; margin:0 2px;}
+  h1{
+    font-family:var(--sans); font-weight:500; font-size:30px; line-height:1.15;
+    letter-spacing:-0.02em; color:var(--acc-base); margin:0; max-width:46ch;
+  }
+  h1 .ink{color:var(--ink);}
+  .sub{font-size:14px; color:var(--ink2); margin:10px 0 0; max-width:64ch;}
+
+  /* ---- grid + cards ---- */
+  .grid{display:grid; grid-template-columns:repeat(12,1fr); gap:16px;}
+  .card{
+    background:var(--paper); border-radius:11px;
+    border:1px solid color-mix(in srgb, var(--acc-base) 14%, transparent);
+    box-shadow:var(--shadow); padding:16px 18px; min-width:0;
+  }
+  .card.track{grid-column:1 / -1; border-radius:14px; padding:18px 18px 14px;}
+  .card.hero{grid-column:span 4;}
+  .card.meter{grid-column:span 4;}
+  .card.stat{grid-column:span 2; display:flex; flex-direction:column;}
+  .card.chart{grid-column:span 6;}
+
+  .label{
+    font-family:var(--mono); font-weight:500; font-size:10px;
+    letter-spacing:0.15em; text-transform:uppercase; color:var(--ink3);
+    margin:0;
+  }
+  .cardhead{display:flex; align-items:baseline; justify-content:space-between; gap:12px; margin-bottom:12px;}
+
+  /* ---- hero number ---- */
+  .hero-wrap{display:flex; align-items:flex-end; justify-content:space-between; height:100%;}
+  .hero{
+    font-family:var(--mono); font-weight:500; font-size:52px; line-height:0.95;
+    letter-spacing:-0.02em; color:var(--acc-base);
+  }
+  .hero .unit{font-size:14px; color:var(--ink3); margin-left:8px; letter-spacing:0;}
+  .hero-side{text-align:right;}
+  .hero-side .v{font-family:var(--mono); font-size:24px; color:var(--ink); font-weight:500;}
+  .hero-side .u{font-family:var(--mono); font-size:10px; color:var(--ink3); letter-spacing:0.06em; margin-left:4px;}
+
+  /* ---- segment meter (spec §4) ---- */
+  .meter-val{font-family:var(--mono); font-weight:500; font-size:52px; letter-spacing:-0.02em; color:var(--acc-base); line-height:1;}
+  .meter-val .unit{font-size:14px; color:var(--ink3); margin-left:6px; letter-spacing:0;}
+  .segs{display:flex; gap:3px; margin-top:16px;}
+  .seg{flex:1; height:6px; border-radius:1.5px; background:rgba(26,19,48,0.16); transition:background .12s linear;}
+  .seg.lit{background:var(--acc-base);}
+  .seg.lit.top{background:var(--ink);}
+  .meter-scale{display:flex; justify-content:space-between; margin-top:8px;}
+  .meter-scale span{font-family:var(--mono); font-size:10px; color:var(--ink3); letter-spacing:0.02em;}
+
+  /* ---- stat cards ---- */
+  .stat .v{font-family:var(--mono); font-weight:500; font-size:24px; color:var(--ink); margin-top:auto; letter-spacing:-0.01em;}
+  .stat .v .u{font-size:10px; color:var(--ink3); margin-left:4px; letter-spacing:0.04em;}
+
+  /* ---- track svg ---- */
+  .stage-svg{width:100%; display:block;}
+  .trk-full{fill:none; stroke:var(--hair); stroke-width:2;}
+  .trk-trav{fill:none; stroke:var(--acc-base); stroke-width:2.6; stroke-linecap:round; stroke-linejoin:round;}
+  .trk-area{stroke:none;}
+  .pillar{stroke:var(--silver); stroke-width:1; opacity:0.22;}
+  .ground{stroke:var(--hair); stroke-width:1;}
+
+  /* ---- charts ---- */
+  .spark{width:100%; display:block;}
+  .gl{stroke:var(--hair); stroke-width:1;}
+  .gl.soft{stroke:var(--hair-soft);}
+  .axtx{font-family:var(--mono); font-size:10px; fill:var(--ink3); letter-spacing:0.02em;}
+  .ln-base{fill:none; stroke:var(--acc-base); stroke-width:2.2; stroke-linejoin:round;}
+  .ln-lift{fill:none; stroke:var(--acc-lift); stroke-width:1.8; stroke-linejoin:round;}
+  .ln-ink3{fill:none; stroke:var(--ink3); stroke-width:1.6; stroke-linejoin:round; opacity:0.8;}
+  .legend{display:flex; gap:14px;}
+  .legend span{font-family:var(--mono); font-size:10px; letter-spacing:0.06em; color:var(--ink3); display:flex; align-items:center; gap:5px;}
+  .swatch{width:14px; height:3px; border-radius:1.5px; display:inline-block;}
+
+  /* ---- transport ---- */
+  .transport{display:flex; align-items:center; gap:14px; margin-top:12px;}
+  .play{
+    font-family:var(--mono); font-size:11px; letter-spacing:0.14em; text-transform:uppercase;
+    color:var(--acc-base); background:var(--acc-wash);
+    border:1px solid color-mix(in srgb, var(--acc-base) 24%, transparent);
+    border-radius:7px; padding:7px 14px; cursor:pointer; font-weight:500;
+  }
+  .play:hover{border-color:color-mix(in srgb, var(--acc-base) 45%, transparent);}
+  .clock{font-family:var(--mono); font-size:11px; color:var(--ink3); letter-spacing:0.06em; white-space:nowrap;}
+  .clock b{color:var(--ink); font-weight:500;}
+  input[type=range]{
+    -webkit-appearance:none; appearance:none; flex:1; height:4px; border-radius:2px;
+    background:var(--hair); outline:none; cursor:pointer;
+  }
+  input[type=range]::-webkit-slider-thumb{
+    -webkit-appearance:none; width:14px; height:14px; border-radius:50%;
+    background:var(--acc-base); border:2px solid var(--paper); box-shadow:0 1px 4px rgba(20,15,40,0.25);
+  }
+  input[type=range]::-moz-range-thumb{
+    width:14px; height:14px; border-radius:50%; background:var(--acc-base); border:2px solid var(--paper);
+  }
+
+  /* ---- footer ---- */
+  footer{
+    margin-top:22px; padding-top:14px; border-top:1px solid var(--hair);
+    display:flex; justify-content:space-between; align-items:center; gap:12px; flex-wrap:wrap;
+  }
+  footer .cap, footer .date{font-family:var(--mono); font-size:10.5px; letter-spacing:0.16em; text-transform:uppercase; color:var(--ink3);}
+  footer .sep{color:color-mix(in srgb, var(--acc-base) 55%, transparent); margin:0 10px;}
+
+  /* ---- motion (spec §5) ---- */
+  .reveal{opacity:0; transform:translateY(12px); animation:rv .6s cubic-bezier(.22,.61,.36,1) forwards;}
+  @keyframes rv{to{opacity:1; transform:translateY(0);}}
+  .no-reveal .reveal{opacity:1!important; transform:none!important; animation:none!important;}
+  @media (prefers-reduced-motion: reduce){ *{animation:none!important; transition:none!important;} .reveal{opacity:1; transform:none;} }
+
+  @media (max-width:860px){
+    .card.hero,.card.meter,.card.chart{grid-column:1 / -1;}
+    .card.stat{grid-column:span 6;}
+    .hero,.meter-val{font-size:44px;}
+  }
+</style>
+</head>
+<body>
+<div class="board">
+
+  <header class="head reveal" style="animation-delay:0ms">
+    <p class="kicker">01<span class="dot">·</span>ROLLERCOASTER</p>
+    <h1>A physical <span class="ink">rollercoaster</span>, solved and ridden in real&nbsp;time.</h1>
+    <p class="sub">A point-mass cart on a curved track, integrated by ModelingToolkit. It drops off the lift hill, whips through a vertical loop, and rides out over rolling hills &mdash; gravity trading with speed while drag bleeds the energy away.</p>
+  </header>
+
+  <div class="grid">
+
+    <!-- TRACK -->
+    <section class="card track reveal" style="animation-delay:80ms">
+      <div class="cardhead">
+        <p class="label">The ride <span style="color:color-mix(in srgb,var(--acc-base) 55%,transparent)">·</span> vertical loop + hills</p>
+        <p class="clock">T = <b id="clk">0.0</b> S</p>
+      </div>
+      <svg class="stage-svg" id="track" viewBox="0 0 1040 300" preserveAspectRatio="xMidYMid meet" aria-label="Rollercoaster track"></svg>
+      <div class="transport">
+        <button class="play" id="play">Pause</button>
+        <input type="range" id="scrub" min="0" max="1000" value="0" />
+        <span class="clock"><b id="prog">0</b>%</span>
+      </div>
+    </section>
+
+    <!-- HERO: SPEED -->
+    <section class="card hero reveal" style="animation-delay:160ms">
+      <div class="cardhead"><p class="label">Speed</p></div>
+      <div class="hero-wrap">
+        <div><span class="hero" id="spd">0</span><span class="unit" style="font-family:var(--mono)">km/h</span></div>
+        <div class="hero-side">
+          <div><span class="v" id="spdms">0.0</span><span class="u">m/s</span></div>
+        </div>
+      </div>
+    </section>
+
+    <!-- METER: G-FORCE -->
+    <section class="card meter reveal" style="animation-delay:240ms">
+      <div class="cardhead"><p class="label">Rider g-force <span style="color:color-mix(in srgb,var(--acc-base) 55%,transparent)">·</span> load</p><p class="label" id="peaklbl">peak 0.00 g</p></div>
+      <div class="meter-val" id="gval">1.00<span class="unit">g</span></div>
+      <div class="segs" id="segs"></div>
+      <div class="meter-scale"><span>0</span><span>airtime</span><span>heavy</span><span>5g</span></div>
+    </section>
+
+    <!-- STAT: HEIGHT -->
+    <section class="card stat reveal" style="animation-delay:320ms">
+      <p class="label">Height</p>
+      <div class="v"><span id="hgt">0</span><span class="u">m</span></div>
+    </section>
+
+    <!-- STAT: DISTANCE -->
+    <section class="card stat reveal" style="animation-delay:400ms">
+      <p class="label">Distance</p>
+      <div class="v"><span id="dist">0</span><span class="u">m</span></div>
+    </section>
+
+    <!-- CHART: SPEED -->
+    <section class="card chart reveal" style="animation-delay:480ms">
+      <div class="cardhead"><p class="label">Speed profile</p><p class="label">km/h · t</p></div>
+      <svg class="spark" id="cSpeed" viewBox="0 0 500 200" preserveAspectRatio="none"></svg>
+    </section>
+
+    <!-- CHART: ENERGY -->
+    <section class="card chart reveal" style="animation-delay:560ms">
+      <div class="cardhead">
+        <p class="label">Energy budget</p>
+        <div class="legend">
+          <span><i class="swatch" style="background:var(--acc-base)"></i>total</span>
+          <span><i class="swatch" style="background:var(--acc-lift)"></i>kinetic</span>
+          <span><i class="swatch" style="background:var(--ink3)"></i>potential</span>
+        </div>
+      </div>
+      <svg class="spark" id="cEnergy" viewBox="0 0 500 200" preserveAspectRatio="none"></svg>
+    </section>
+
+  </div>
+
+  <footer class="reveal" style="animation-delay:640ms">
+    <span class="cap">Rollercoaster<span class="sep">|</span>ModelingToolkit &amp; Dyad<span class="sep">|</span><span id="slug">team</span></span>
+    <span class="date">JuliaCon 2026</span>
+  </footer>
+
+</div>
+
+<script>
+const DATA = 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+(function(){
+  "use strict";
+  const A = DATA.accent, M = DATA.meta;
+  const root = document.documentElement.style;
+  root.setProperty('--acc-deep',A.deep); root.setProperty('--acc-base',A.base);
+  root.setProperty('--acc-lift',A.lift); root.setProperty('--acc-wash',A.wash);
+  root.setProperty('--acc-hair',A.hairline);
+  document.getElementById('slug').textContent = DATA.slug;
+
+  const t=DATA.t, X=DATA.x, H=DATA.h, S=DATA.spd, G=DATA.g,
+        KE=DATA.KE, PE=DATA.PE, E=DATA.E, TH=DATA.th, Sa=DATA.s;
+  const n=t.length, T=t[n-1];
+  const NS="http://www.w3.org/2000/svg";
+  const lerp=(a,b,f)=>a+(b-a)*f;
+  const minA=a=>a.reduce((m,v)=>v<m?v:m,Infinity);
+  const maxA=a=>a.reduce((m,v)=>v>m?v:m, -Infinity);
+
+  // ---------- TRACK geometry (equal-aspect so the loop reads as a loop) ----------
+  const TW=1040, THh=300, padL=28, padR=26, padT=18, padB=26;
+  const xMin=0, xMax=maxA(X), hMin=minA(H), hMax=maxA(H);
+  const plotW=TW-padL-padR, plotH=THh-padT-padB;
+  const EXAG=1.25;                                   // gentle vertical emphasis
+  const xr=(xMax-xMin)||1, hr=(hMax-hMin)||1;
+  const sc=Math.min(plotW/xr, plotH/(hr*EXAG));      // px per metre (shared)
+  const scX=sc, scY=sc*EXAG;
+  const drawW=xr*scX, drawH=hr*scY;
+  const ox=padL+(plotW-drawW)/2, oy=padT+(plotH-drawH)/2;
+  const sx=x=>ox+(x-xMin)*scX;
+  const sy=h=>oy+(hMax-h)*scY;                        // higher h -> smaller y
+  const baseY=Math.min(THh-6, oy+drawH+14);
+  const svg=document.getElementById('track');
+  // deep -> base -> lift gradient (the one sanctioned ramp), for the train cars
+  svg.innerHTML =
+    `<defs><linearGradient id="cargrad" x1="0" y1="0" x2="1" y2="0">
+        <stop offset="0%"   stop-color="${A.deep}"/>
+        <stop offset="55%"  stop-color="${A.base}"/>
+        <stop offset="100%" stop-color="${A.lift}"/>
+     </linearGradient></defs>`;
+  // ground line
+  const ground=document.createElementNS(NS,'line');
+  ground.setAttribute('class','ground');
+  ground.setAttribute('x1',padL); ground.setAttribute('x2',TW-padR);
+  ground.setAttribute('y1',baseY); ground.setAttribute('y2',baseY);
+  svg.appendChild(ground);
+  // support pillars — only under gentle (non-inverted) track, so the loop is skipped
+  for(let i=0;i<n;i+=8){
+    if(Math.cos(TH[i])<0.4) continue;
+    const yy=sy(H[i]); if(yy>=baseY-2) continue;
+    const p=document.createElementNS(NS,'line');
+    p.setAttribute('class','pillar');
+    p.setAttribute('x1',sx(X[i]).toFixed(1)); p.setAttribute('x2',sx(X[i]).toFixed(1));
+    p.setAttribute('y1',yy.toFixed(1)); p.setAttribute('y2',baseY.toFixed(1));
+    svg.appendChild(p);
+  }
+  // full track path
+  let dFull="M"+sx(X[0]).toFixed(1)+" "+sy(H[0]).toFixed(1);
+  for(let i=1;i<n;i++) dFull+="L"+sx(X[i]).toFixed(1)+" "+sy(H[i]).toFixed(1);
+  const trkFull=document.createElementNS(NS,'path');
+  trkFull.setAttribute('class','trk-full'); trkFull.setAttribute('d',dFull);
+  svg.appendChild(trkFull);
+  // traveled line (updated per frame)
+  const trkTrav=document.createElementNS(NS,'path'); trkTrav.setAttribute('class','trk-trav');
+  svg.appendChild(trkTrav);
+
+  // ---------- TRAIN: several cars placed by arc length, so it bends through the loop ----------
+  const NCAR=4, CARSPACING=7.5;
+  function carSVG(lead){
+    const nose = lead ? `<path d="M13 -11 Q20 -11 20 -8 L16 -5 H13 Z" fill="${A.deep}"/>` : '';
+    return `
+      <circle cx="-8" cy="-3.2" r="3.5" fill="var(--tyre)"/>
+      <circle cx="8"  cy="-3.2" r="3.5" fill="var(--tyre)"/>
+      <circle cx="-8" cy="-3.2" r="1.3" fill="${A.lift}"/>
+      <circle cx="8"  cy="-3.2" r="1.3" fill="${A.lift}"/>
+      ${nose}
+      <path d="M-13 -5 H13 Q16 -5 16 -9 V-14 Q16 -17 13 -17 H-13 Q-16 -17 -16 -14 V-9 Q-16 -5 -13 -5 Z"
+            fill="url(#cargrad)" stroke="${A.deep}" stroke-width="1"/>
+      <rect x="-12.5" y="-13" width="25" height="3" rx="1.4" fill="${A.wash}" opacity="0.6"/>
+      <circle cx="-5" cy="-19" r="2.6" fill="${A.wash}"/>
+      <circle cx="5"  cy="-19" r="2.6" fill="${A.wash}"/>
+      <path d="M-5 -21.2 v-3 M5 -21.2 v-3" stroke="${A.lift}" stroke-width="1.4" stroke-linecap="round"/>`;
+  }
+  const trainG=document.createElementNS(NS,'g'); svg.appendChild(trainG);
+  const cars=[];
+  for(let k=0;k<NCAR;k++){
+    const gc=document.createElementNS(NS,'g'); gc.innerHTML=carSVG(k===0);
+    trainG.appendChild(gc); cars.push(gc);
+  }
+  // map an arc-length position to screen coords + tangent angle
+  function arcToXY(scArc){
+    scArc=Math.max(Sa[0], Math.min(Sa[n-1], scArc));
+    let lo=0, hi=n-1;
+    while(hi-lo>1){ const mid=(lo+hi)>>1; if(Sa[mid]<=scArc) lo=mid; else hi=mid; }
+    const f=(scArc-Sa[lo])/((Sa[hi]-Sa[lo])||1);
+    const x=lerp(X[lo],X[hi],f), h=lerp(H[lo],H[hi],f);
+    const ang=Math.atan2(sy(H[hi])-sy(H[lo]), sx(X[hi])-sx(X[lo]))*180/Math.PI;
+    return {px:sx(x), py:sy(h), ang};
+  }
+
+  // ---------- SPARKLINE helper ----------
+  function makeChart(id, series, yPad){
+    const el=document.getElementById(id);
+    const W=500,Hh=200,pl=38,pr=10,pt=14,pb=24;
+    const pw=W-pl-pr, ph=Hh-pt-pb;
+    let allY=[]; series.forEach(s=>allY=allY.concat(s.y));
+    let ymin=minA(allY), ymax=maxA(allY); const sp=(ymax-ymin)*0.08+1e-9;
+    ymin-=sp; ymax+=sp;
+    const X2t=i=>pl + (t[i]-t[0])/(T-t[0])*pw;
+    const Y2=v=>pt + (ymax-v)/(ymax-ymin)*ph;
+    let g="";
+    // horizontal gridlines + y ticks
+    for(let k=0;k<=3;k++){
+      const yy=pt+ph*k/3, val=ymax-(ymax-ymin)*k/3;
+      g+=`<line class="gl soft" x1="${pl}" x2="${W-pr}" y1="${yy.toFixed(1)}" y2="${yy.toFixed(1)}"/>`;
+      g+=`<text class="axtx" x="${pl-6}" y="${(yy+3).toFixed(1)}" text-anchor="end">${Math.round(val)}</text>`;
+    }
+    // x ticks
+    for(let k=0;k<=3;k++){
+      const xx=pl+pw*k/3, tv=t[0]+(T-t[0])*k/3;
+      g+=`<text class="axtx" x="${xx.toFixed(1)}" y="${Hh-8}" text-anchor="middle">${tv.toFixed(0)}s</text>`;
+    }
+    el.innerHTML=g;
+    const paths=series.map(s=>{
+      const p=document.createElementNS(NS,'path'); p.setAttribute('class',s.cls); el.appendChild(p); return p;
+    });
+    const dot=document.createElementNS(NS,'circle');
+    dot.setAttribute('r','3.4'); dot.setAttribute('fill',A.base);
+    dot.setAttribute('stroke','var(--paper)'); dot.setAttribute('stroke-width','1.5');
+    el.appendChild(dot);
+    return {series,paths,dot,X2t,Y2};
+  }
+  const chSpeed=makeChart('cSpeed', [{y:S,cls:'ln-base'}]);
+  const chEnergy=makeChart('cEnergy', [
+     {y:E,cls:'ln-base'},{y:KE,cls:'ln-lift'},{y:PE,cls:'ln-ink3'}]);
+
+  function drawChart(ch, iF, i, frac){
+    ch.series.forEach((s,si)=>{
+      let d="M"+ch.X2t(0).toFixed(1)+" "+ch.Y2(s.y[0]).toFixed(1);
+      for(let k=1;k<=i;k++) d+="L"+ch.X2t(k).toFixed(1)+" "+ch.Y2(s.y[k]).toFixed(1);
+      const cx=lerp(ch.X2t(i),ch.X2t(Math.min(i+1,n-1)),frac);
+      const cy=ch.Y2(lerp(s.y[i],s.y[Math.min(i+1,n-1)],frac));
+      d+="L"+cx.toFixed(1)+" "+cy.toFixed(1);
+      ch.paths[si].setAttribute('d',d);
+      if(si===0){ ch.dot.setAttribute('cx',cx); ch.dot.setAttribute('cy',cy); }
+    });
+  }
+
+  // ---------- segment meter ----------
+  const segsEl=document.getElementById('segs'); const SEG=10;
+  for(let i=0;i<SEG;i++){const d=document.createElementNS('http://www.w3.org/1999/xhtml','div');}
+  for(let i=0;i<SEG;i++){const s=document.createElement('div'); s.className='seg'; segsEl.appendChild(s);}
+  const segNodes=[...segsEl.children];
+  const GSCALE=5.0;
+
+  // ---------- update everything from one signal: playT ----------
+  const clk=document.getElementById('clk'), prog=document.getElementById('prog');
+  const spdEl=document.getElementById('spd'), spdms=document.getElementById('spdms');
+  const gval=document.getElementById('gval'), peaklbl=document.getElementById('peaklbl');
+  const hgt=document.getElementById('hgt'), dist=document.getElementById('dist');
+  const scrub=document.getElementById('scrub');
+
+  function update(playT){
+    const idx=Math.max(0,Math.min(n-1, playT/T*(n-1)));
+    const i=Math.min(n-2,Math.floor(idx)), frac=idx-i;
+    const cx=lerp(X[i],X[i+1],frac), ch=lerp(H[i],H[i+1],frac);
+    const spd=lerp(S[i],S[i+1],frac), g=lerp(G[i],G[i+1],frac);
+
+    // train: each car placed by arc length behind the lead, bending through the loop
+    const sLead=lerp(Sa[i],Sa[i+1],frac);
+    for(let k=0;k<NCAR;k++){
+      const p=arcToXY(sLead - k*CARSPACING);
+      cars[k].setAttribute('transform',`translate(${p.px.toFixed(1)},${p.py.toFixed(1)}) rotate(${p.ang.toFixed(2)})`);
+    }
+
+    // traveled track line up to the lead car
+    let d="M"+sx(X[0]).toFixed(1)+" "+sy(H[0]).toFixed(1);
+    for(let k=1;k<=i;k++) d+="L"+sx(X[k]).toFixed(1)+" "+sy(H[k]).toFixed(1);
+    d+="L"+sx(cx).toFixed(1)+" "+sy(ch).toFixed(1);
+    trkTrav.setAttribute('d',d);
+
+    // readouts
+    clk.textContent=(idx/(n-1)*T).toFixed(1);
+    prog.textContent=Math.round(idx/(n-1)*100);
+    spdEl.textContent=Math.round(spd);
+    spdms.textContent=(spd/3.6).toFixed(1);
+    gval.innerHTML=g.toFixed(2)+'<span class="unit">g</span>';
+    hgt.textContent=Math.round(ch);
+    dist.textContent=Math.round(cx);
+    // peak g over the ridden portion
+    let pk=0; for(let k=0;k<=i;k++) if(G[k]>pk) pk=G[k]; if(g>pk) pk=g;
+    peaklbl.textContent='peak '+pk.toFixed(2)+' g';
+
+    // meter
+    const lit=Math.max(0,Math.min(SEG,Math.round(g/GSCALE*SEG)));
+    segNodes.forEach((s,k)=>{
+      s.classList.toggle('lit', k<lit);
+      s.classList.toggle('top', k<lit && k>=SEG-3);
+    });
+
+    // charts
+    drawChart(chSpeed, idx, i, frac);
+    drawChart(chEnergy, idx, i, frac);
+
+    scrub.value=Math.round(idx/(n-1)*1000);
+  }
+
+  // ---------- transport / playback ----------
+  const params=new URLSearchParams(location.search);
+  const reduce=window.matchMedia('(prefers-reduced-motion: reduce)').matches;
+  const forceStill=params.get('anim')==='0';
+  if(reduce||forceStill) document.documentElement.classList.add('no-reveal');
+
+  const PLAY_SECS=26;                     // full 60 s ride plays in ~26 s
+  const rate=T/PLAY_SECS;
+  let playT=0, playing=!(reduce||forceStill), last=null;
+  // deep-link a specific moment: ?t=SECONDS (paused)
+  if(params.has('t')){ playT=Math.max(0,Math.min(T, parseFloat(params.get('t'))||0)); playing=false; }
+  else if(reduce||forceStill){ playT=T*0.28; }   // representative still
+
+  const playBtn=document.getElementById('play');
+  playBtn.textContent=playing?'Pause':'Play';
+
+  function frame(ts){
+    if(last==null) last=ts;
+    const dt=(ts-last)/1000; last=ts;
+    if(playing){ playT+=dt*rate; if(playT>=T) playT=0; }
+    update(playT);
+    requestAnimationFrame(frame);
+  }
+  playBtn.addEventListener('click',()=>{ playing=!playing; playBtn.textContent=playing?'Pause':'Play'; if(playing&&last===null) requestAnimationFrame(frame); });
+  scrub.addEventListener('input',()=>{ playing=false; playBtn.textContent='Play'; playT=scrub.value/1000*T; update(playT); });
+
+  update(playT);                          // always paint the initial frame
+  if(playing) requestAnimationFrame(frame);
+})();
+</script>
+</body>
+</html>