Run Detail

completedernie-5.5-flash-preview

85very good

Every model's answer from this round

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Provider

openrouter

Challenge Version

v1.0

Turns

Duration

166.3s

Total Tokens

52,875

Input Tokens

391

Output Tokens

52,484

Reasoning Tokens

42,278

Reasoning Effort

high

Est. Cost

$0.0594

Started

11/10/2026, 8:57:51 PM

OR Provider

Baidu

Finish Reason

stop

Generation ID

gen-1794344270-8IiUSvh9EnJgNyolWMnb

Turns (1)

Turn #1

391 in52,484 out42,278 reasoning52,875 total166.2s

user

You build physics toys, and you have held an umbrella in a gale.

Build me a single HTML page: a person holding an umbrella in wind that keeps getting stronger.

The build

The wind rises over time, and I can drive it myself as well — slider, keys, your call — including back down.
The umbrella answers the wind. The canopy flexes, the frame loads up, and past some point it turns inside out. It can be wrenched sideways, and it can get away entirely.
Rain falls, and its direction and speed follow the wind.
The person compensates: lean, grip, footing, bracing. They stay attached to the ground; the umbrella stays attached to them until it doesn't.
Show the current wind speed on screen.
The art is yours. Side view is the obvious choice and you do not have to take it.

House rules

One file. Everything inline — no CDN, no external stylesheet, font, script or image. data: URIs are fine.
No libraries. No physics engine — write your own.
No network at runtime.
No localStorage, sessionStorage, cookies or indexedDB — sandboxed frame, they throw.
Return the file as exactly one fenced html block.

Answer in exactly these sections

The model

One paragraph, before the file: what the canopy is made of in your code, what inversion is as a state change, and what decides when it happens.

The page

The single fenced html block.

What it actually does

Where it looks right and where it looks wrong. Everyone who has held an umbrella knows what one does in wind, so say what yours gets wrong before I find it.

assistant

The model

In the code the canopy is a ring of eight ribs radiating from a hub at the top of the shaft; each rib tip sits on an ellipse (the rim) and the fabric is drawn as eight scalloped panels between neighbouring tips. The whole dome is described by one signed number, the dome depth h: positive means the hub (peak) sits above the rim plane (a normal dome), negative means it sits below it (inside out). Inversion is a latch on that sign — I integrate a spring that drives an inversion coordinate inv from 0 to 1, and h = baseDepth·(1 − 2·inv), so as inv crosses 0.5 the peak passes through the rim plane and the canopy snaps from convex to concave. What decides it is a force balance: the aerodynamic load F = ½ρv²·Cd·A is compared against the frame's restoring threshold; above Fup the ribs "give" and inv is driven to 1, below a lower Fdown it springs back to 0, and the gap between the two is the hysteresis that stops a real umbrella flickering on the edge. Cd itself drops once inverted (a bowl spills more than a scoop catches), which is why an inverted umbrella gets dragged rather than flipping straight back.

The page

<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width,initial-scale=1,maximum-scale=1,user-scalable=no">
<title>Umbrella in a Gale</title>
<style>
  :root{
    --ink:#e9eef5;
    --accent:#ff6a4d;
    --panel:rgba(14,20,28,0.52);
    --edge:rgba(255,255,255,0.12);
  }
  *{box-sizing:border-box;}
  html,body{margin:0;height:100%;overflow:hidden;background:#0a0f15;color:var(--ink);
    font-family:-apple-system,BlinkMacSystemFont,"Segoe UI",Roboto,Helvetica,Arial,sans-serif;
    -webkit-user-select:none;user-select:none;-webkit-tap-highlight-color:transparent;}
  #scene{position:fixed;inset:0;display:block;}

  .panel{position:fixed;background:var(--panel);border:1px solid var(--edge);
    border-radius:14px;backdrop-filter:blur(6px);-webkit-backdrop-filter:blur(6px);
    box-shadow:0 8px 30px rgba(0,0,0,0.35);}

  #readout{top:16px;left:16px;padding:14px 16px 12px;min-width:210px;pointer-events:none;}
  #title{font-size:12px;letter-spacing:.14em;text-transform:uppercase;opacity:.6;margin:0 0 6px;}
  #windrow{display:flex;align-items:baseline;gap:8px;}
  #windNum{font-size:52px;font-weight:700;line-height:.9;font-variant-numeric:tabular-nums;
    transition:color .2s;}
  #windUnit{font-size:15px;opacity:.7;}
  #windMs{font-size:12px;opacity:.5;margin-left:2px;}
  #windWord{font-size:14px;margin-top:4px;opacity:.85;letter-spacing:.02em;}
  #gauge{margin-top:10px;height:7px;border-radius:4px;background:rgba(255,255,255,0.10);overflow:hidden;}
  #gaugeFill{height:100%;width:0%;border-radius:4px;background:#5fd0a0;transition:width .08s linear,background .3s;}
  #status{margin-top:10px;font-size:13px;font-weight:600;letter-spacing:.02em;min-height:16px;}

  #controls{left:50%;transform:translateX(-50%);bottom:16px;padding:12px 16px;
    display:flex;align-items:center;gap:14px;flex-wrap:wrap;justify-content:center;max-width:94vw;}
  #controls label{font-size:12px;opacity:.7;letter-spacing:.04em;}
  #slider{-webkit-appearance:none;appearance:none;width:min(46vw,320px);height:6px;border-radius:4px;
    background:linear-gradient(90deg,#5fd0a0,#f0c250,#ff5a44);outline:none;}
  #slider::-webkit-slider-thumb{-webkit-appearance:none;width:20px;height:20px;border-radius:50%;
    background:#fff;border:2px solid #1a222c;cursor:pointer;box-shadow:0 2px 6px rgba(0,0,0,.4);}
  #slider::-moz-range-thumb{width:20px;height:20px;border-radius:50%;background:#fff;
    border:2px solid #1a222c;cursor:pointer;}
  button{font:inherit;font-size:13px;font-weight:600;color:var(--ink);cursor:pointer;
    background:rgba(255,255,255,0.08);border:1px solid var(--edge);border-radius:9px;
    padding:8px 12px;transition:background .15s;}
  button:hover{background:rgba(255,255,255,0.16);}
  button.on{background:var(--accent);border-color:transparent;color:#1a0f0b;}
  #hint{font-size:11px;opacity:.5;width:100%;text-align:center;letter-spacing:.03em;}
  @media (max-width:560px){ #windNum{font-size:40px;} #readout{min-width:170px;} }
</style>
</head>
<body>
<canvas id="scene"></canvas>

<div id="readout" class="panel">
  <p id="title">Umbrella in a Gale</p>
  <div id="windrow">
    <span id="windNum">0</span><span id="windUnit">km/h</span>
    <span id="windMs">0 m/s</span>
  </div>
  <div id="windWord">Calm</div>
  <div id="gauge"><div id="gaugeFill"></div></div>
  <div id="status">Holding.</div>
</div>

<div id="controls" class="panel">
  <label for="slider">WIND</label>
  <input id="slider" type="range" min="0" max="42" step="0.1" value="3">
  <button id="autoBtn" class="on">Auto: on</button>
  <button id="resetBtn">New umbrella</button>
  <div id="hint">Drag the slider or ↑/↓ to drive the wind · Space = auto · R = reset</div>
</div>

<script>
(function(){
"use strict";

/* ---------- helpers ---------- */
const clamp=(v,a,b)=>v<a?a:v>b?b:v;
const lerp=(a,b,t)=>a+(b-a)*t;
const rand=(a,b)=>a+Math.random()*(b-a);
const TAU=Math.PI*2;
function lerpColor(c1,c2,t){return `rgb(${Math.round(lerp(c1[0],c2[0],t))},${Math.round(lerp(c1[1],c2[1],t))},${Math.round(lerp(c1[2],c2[2],t))})`;}

/* ---------- canvas ---------- */
const cv=document.getElementById('scene');
const ctx=cv.getContext('2d');
let W=0,H=0,DPR=1;
const L={};               // layout metrics

function layout(){
  L.groundY  = H*0.85;
  L.footX    = W*0.42;
  L.legLen   = H*0.150;
  L.torsoLen = H*0.150;
  L.headR    = H*0.032;
  L.upperArm = H*0.085;
  L.foreArm  = H*0.085;
  L.shaftLen = H*0.220;
  L.R        = Math.min(H*0.140, W*0.20);
  L.baseH    = H*0.055;
  L.squash   = 0.34;
}
function resize(){
  DPR=Math.min(window.devicePixelRatio||1,2);
  W=window.innerWidth; H=window.innerHeight;
  cv.width=Math.floor(W*DPR); cv.height=Math.floor(H*DPR);
  cv.style.width=W+'px'; cv.style.height=H+'px';
  ctx.setTransform(DPR,0,0,DPR,0,0);
  layout();
  initGrass(); initClouds();
}

/* ---------- physics constants ---------- */
const PHYS={
  rho:1.2, area:0.55, cdNormal:1.30, cdInv:0.85,
  Fup:120, Fdown:55,                 // inversion thresholds (N) with hysteresis
  baseGrip:250, invGripMul:0.75,     // grip strength (N), reduced when inverted
  maxWind:42, autoRate:1.5           // m/s, m/s per second
};

/* ---------- state ---------- */
const sim={
  t:0, auto:true, windTarget:3, windBase:3, wind:3,
  inv:0, invVel:0,
  tilt:-0.10, tiltVel:0,
  lean:0, crouch:0, grip:0,
  attached:true, F:0, q:0,
  free:{active:false,x:0,y:0,vx:0,vy:0,ang:0,angVel:0},
  flash:0, nextFlash:1e9
};
let pose=null;

/* ---------- wind ---------- */
function updateWind(dt){
  if(sim.auto) sim.windTarget=Math.min(PHYS.maxWind, sim.windTarget+PHYS.autoRate*dt);
  sim.windBase += (sim.windTarget-sim.windBase)*Math.min(1,dt*1.8);
  const n=0.62*Math.sin(sim.t*0.9)+0.28*Math.sin(sim.t*2.17+1.3)
         +0.16*Math.sin(sim.t*4.3+2.1)+0.10*Math.sin(sim.t*7.9+0.6);
  const env=Math.pow(Math.max(0,Math.sin(sim.t*0.37+0.5)),6);   // occasional strong gust
  const gust=1+0.17*n+0.35*env;
  sim.wind=Math.max(0, sim.windBase*gust);
}

/* ---------- forces ---------- */
function computeForces(){
  const cd=lerp(PHYS.cdNormal,PHYS.cdInv,sim.inv);
  sim.q=0.5*PHYS.rho*sim.wind*sim.wind;
  sim.F=sim.q*cd*PHYS.area;
}

/* ---------- inversion (latched spring on the dome sign) ---------- */
function updateInversion(dt){
  let target;
  if(sim.inv>=0.5) target=(sim.F<PHYS.Fdown)?0:1;
  else             target=(sim.F>PHYS.Fup)?1:0;
  sim.invVel += (target-sim.inv)*34*dt;
  sim.invVel *= Math.exp(-4.5*dt);
  sim.inv    += sim.invVel*dt;
  if(sim.inv<0){sim.inv=0; if(sim.invVel<0)sim.invVel*=-0.25;}
  if(sim.inv>1){sim.inv=1; if(sim.invVel>0)sim.invVel*=-0.25;}
}

/* ---------- umbrella attitude (tilt + gust wrench) ---------- */
function updateAttitude(dt){
  let tiltTarget=-0.10 + sim.F*0.0052 + sim.inv*0.15;
  tiltTarget=Math.min(tiltTarget,1.45);
  sim.tiltVel += (tiltTarget-sim.tilt)*26*dt;
  sim.tiltVel *= Math.exp(-5*dt);
  if(sim.attached && sim.F>90 && Math.random()<(sim.F-90)*0.0009)
    sim.tiltVel += rand(-1,1)*2.2;                 // sudden sideways wrench
  sim.tilt += sim.tiltVel*dt;
  sim.tilt  = clamp(sim.tilt,-0.5,1.6);
}

/* ---------- person compensation ---------- */
function updatePerson(dt){
  const leanT=clamp(sim.F*0.0032,0,0.62);
  sim.lean += (leanT-sim.lean)*Math.min(1,dt*4);
  const cT=clamp((sim.F-20)*0.006,0,1);
  sim.crouch += (cT-sim.crouch)*Math.min(1,dt*4);
  sim.grip=clamp(sim.F/PHYS.baseGrip,0,1);
}

/* ---------- skeleton / umbrella pose ---------- */
function computePose(){
  const lean=sim.lean, crouch=sim.crouch;
  const up={x:-Math.sin(lean), y:-Math.cos(lean)};      // body "up", tilts into wind (-x)
  const ankle={x:L.footX, y:L.groundY};
  const legLen=L.legLen*(1-0.26*crouch);
  const hip={x:ankle.x+up.x*legLen - crouch*L.legLen*0.18, y:ankle.y+up.y*legLen};
  const knee={x:(ankle.x+hip.x)/2 - crouch*L.legLen*0.35 - L.legLen*0.06, y:(ankle.y+hip.y)/2};
  const torsoLen=L.torsoLen*(1-0.08*crouch);
  const neck={x:hip.x+up.x*torsoLen - crouch*L.torsoLen*0.10, y:hip.y+up.y*torsoLen};
  const headC={x:neck.x+up.x*L.headR*1.05, y:neck.y+up.y*L.headR*1.05 - L.headR*0.15};
  const shoulder={x:neck.x, y:neck.y+L.headR*0.30};

  const handUp=(L.upperArm+L.foreArm)*(sim.attached?0.82:0.5);
  const handFwd=L.foreArm*0.55;
  const handDrag=clamp(sim.F*0.10,0,L.foreArm*1.1);
  const grip={x:shoulder.x+up.x*handUp - handFwd + handDrag, y:shoulder.y+up.y*handUp};

  const t=sim.tilt;
  const shaft={x:Math.sin(t), y:-Math.cos(t)};          // grip -> hub
  const perp ={x:Math.cos(t), y:Math.sin(t)};           // points downwind (+x) at t=0
  const bendMag=clamp(sim.F*0.10,0,L.shaftLen*0.5);
  const hub={x:grip.x+shaft.x*L.shaftLen+perp.x*bendMag,
             y:grip.y+shaft.y*L.shaftLen+perp.y*bendMag};
  const d={x:-shaft.x, y:-shaft.y};                     // hub -> hand (down-shaft)
  const p={x:d.y, y:-d.x};                              // rim width axis
  return {up,ankle,hip,knee,neck,headC,shoulder,grip,hub,shaft,perp,d,p,bendMag};
}

/* ---------- rip-away ---------- */
function detach(){
  sim.attached=false;
  const f=sim.free, hub=pose.hub;
  f.active=true; f.x=hub.x; f.y=hub.y;
  const wpx=sim.wind*(W*0.010);
  f.vx=wpx*0.6+120+sim.F*0.4;
  f.vy=-160-Math.random()*120;
  f.ang=sim.tilt;
  f.angVel=(Math.random()<0.5?-1:1)*rand(2.5,5.5);
  sim.auto=false;
}
function checkRip(){
  if(!sim.attached) return;
  const gripLimit=PHYS.baseGrip*(1-(1-PHYS.invGripMul)*sim.inv);
  const eff=gripLimit*(0.9+0.2*Math.random());
  if(sim.F>eff) detach();
}
function updateFree(dt){
  const f=sim.free;
  const wpx=sim.wind*(W*0.010);
  f.vx += (wpx-f.vx)*Math.min(1,dt*0.8);
  f.vy += 1500*dt;
  f.vy += (0-f.vy)*Math.min(1,dt*0.3);
  f.x  += f.vx*dt; f.y += f.vy*dt;
  f.ang += f.angVel*dt;
  f.angVel += wpx*0.0006*dt - f.angVel*0.02*dt;
  if(f.y>H+320 || f.x>W+460) f.active=false;
}

/* ---------- rain ---------- */
const rain={drops:[],max:520};
function newDrop(any){return {x:rand(-0.15*W,1.05*W), y:any?rand(-40,H):-rand(10,60),
  sp:rand(0.8,1.3), a:rand(0.25,0.6)};}
function initRain(){rain.drops.length=0; for(let i=0;i<rain.max;i++)rain.drops.push(newDrop(true));}
function updateRain(dt){
  const wN=clamp(sim.wind/PHYS.maxWind,0,1);
  const windPx=sim.wind*(W*0.010), fall=H*0.9;
  for(const dr of rain.drops){
    dr.x += windPx*dr.sp*dt;
    dr.y += fall*dr.sp*dt;
    if(dr.y>H+20 || dr.x>W+40){ dr.x=rand(-0.15*W,1.0*W); dr.y=-rand(10,50); }
  }
}

/* ---------- wind streaks ---------- */
const streaks=[];
function initStreaks(){streaks.length=0; for(let i=0;i<46;i++)streaks.push({x:rand(0,W),y:rand(0,L.groundY),len:rand(20,60),sp:rand(0.7,1.4),a:rand(0.05,0.18)});}
function updateStreaks(dt){
  const windPx=sim.wind*(W*0.010);
  for(const s of streaks){ s.x += windPx*s.sp*dt*1.5; if(s.x-s.len>W){ s.x=-s.len; s.y=rand(0,L.groundY);} }
}

/* ---------- grass ---------- */
let grass=[];
function initGrass(){grass.length=0; const n=Math.round(W/70); for(let i=0;i<n;i++){const bx=rand(0,W); const blades=[]; const nb=2+((Math.random()*3)|0); for(let b=0;b<nb;b++)blades.push({a:rand(-0.5,0.5),len:rand(0.02,0.045)*H,ph:rand(0,TAU)}); grass.push({x:bx,blades});}}

/* ---------- clouds ---------- */
let clouds=[];
function initClouds(){clouds.length=0; for(let i=0;i<5;i++)clouds.push({x:rand(0,W),y:rand(H*0.05,H*0.4),rx:rand(W*0.12,W*0.28),ry:rand(H*0.04,H*0.09),sp:rand(0.4,1.0)});}

/* ---------- scarf (verlet rope) ---------- */
const scarf={pts:[],seg:10};
function initScarf(){
  scarf.pts.length=0; scarf.seg=L.headR*0.55;
  const nx=L.footX, ny=L.groundY-L.legLen-L.torsoLen;
  for(let i=0;i<9;i++)scarf.pts.push({x:nx+i*scarf.seg,y:ny,px:nx+i*scarf.seg,py:ny});
}
function updateScarf(dt){
  if(!pose||scarf.pts.length<2)return;
  const s=scarf, dt2=dt*dt;
  const windAcc=sim.wind*sim.wind*2.2, grav=1400;
  s.pts[0].x=pose.neck.x; s.pts[0].y=pose.neck.y; s.pts[0].px=s.pts[0].x; s.pts[0].py=s.pts[0].y;
  for(let i=1;i<s.pts.length;i++){
    const p=s.pts[i];
    let vx=(p.x-p.px)*0.9, vy=(p.y-p.py)*0.9;
    const vm=Math.hypot(vx,vy), vmax=s.seg*0.9;
    if(vm>vmax){vx*=vmax/vm; vy*=vmax/vm;}
    p.px=p.x; p.py=p.y;
    const flut=Math.sin(sim.t*11+i*0.9)*windAcc*0.25;
    p.x += vx + windAcc*dt2;
    p.y += vy + (grav+flut)*dt2;
  }
  for(let k=0;k<4;k++){
    s.pts[0].x=pose.neck.x; s.pts[0].y=pose.neck.y;
    for(let i=0;i<s.pts.length-1;i++){
      const a=s.pts[i], b=s.pts[i+1];
      let dx=b.x-a.x, dy=b.y-a.y, d=Math.hypot(dx,dy)||1e-4;
      const diff=(d-s.seg)/d, ma=(i===0?0:0.5), mb=(i===0?1:0.5);
      a.x+=dx*diff*ma; a.y+=dy*diff*ma; b.x-=dx*diff*mb; b.y-=dy*diff*mb;
    }
  }
}

/* ---------- lightning ---------- */
function updateFlash(dt){
  if(sim.wind>34 && sim.t>sim.nextFlash && Math.random()<0.02){ sim.flash=1; sim.nextFlash=sim.t+rand(2,6); }
  sim.flash*=Math.exp(-6*dt);
}

/* ---------- master step ---------- */
function step(dt){
  sim.t+=dt;
  updateWind(dt);
  computeForces();
  updateInversion(dt);
  updateAttitude(dt);
  updatePerson(dt);
  pose=computePose();
  checkRip();
  if(!sim.attached) updateFree(dt);
  updateScarf(dt);
  updateRain(dt);
  updateStreaks(dt);
  updateFlash(dt);
}

/* ================= RENDERING ================= */
const COL={
  canopyA:'#e0574c', canopyB:'#c8463c', rib:'#7d2b25', edge:'#391512',
  shaft:'#c9a26b', handle:'#6b4a2f', ferrule:'#d6d6dc',
  coat:'#2f3a49', coatDark:'#26303d', trousers:'#222b37', boot:'#141a21',
  skin:'#caa07d', beanie:'#e0b040', scarf:'#e6b64a'
};

function drawSky(){
  const wN=clamp(sim.wind/PHYS.maxWind,0,1);
  const top=lerpColor([40,54,67],[9,13,20],wN);
  const hor=lerpColor([96,110,122],[38,48,60],wN);
  const g=ctx.createLinearGradient(0,0,0,L.groundY);
  g.addColorStop(0,top); g.addColorStop(1,hor);
  ctx.fillStyle=g; ctx.fillRect(0,0,W,L.groundY);
  // clouds
  for(const c of clouds){
    c.x += (10+sim.wind*4)*c.sp*0.016;
    if(c.x-c.rx>W){c.x=-c.rx; c.y=rand(H*0.05,H*0.4);}
    ctx.fillStyle=`rgba(20,26,34,${0.18+0.22*wN})`;
    ctx.beginPath(); ctx.ellipse(c.x,c.y,c.rx,c.ry,0,0,TAU); ctx.fill();
  }
}

function drawGround(){
  ctx.fillStyle='#0d1319'; ctx.fillRect(0,L.groundY,W,H-L.groundY);
  ctx.strokeStyle='rgba(150,170,190,0.20)'; ctx.lineWidth=1.5;
  ctx.beginPath(); ctx.moveTo(0,L.groundY); ctx.lineTo(W,L.groundY); ctx.stroke();
  // grass
  const wN=clamp(sim.wind/PHYS.maxWind,0,1);
  ctx.lineCap='round';
  for(const t of grass){
    for(const b of t.blades){
      const sway=(0.15+0.85*wN)*b.len*0.7 + Math.sin(sim.t*6+b.ph)*b.len*0.12*wN;
      ctx.strokeStyle='rgba(70,96,86,0.55)'; ctx.lineWidth=2;
      ctx.beginPath(); ctx.moveTo(t.x,L.groundY);
      ctx.quadraticCurveTo(t.x+sway*0.4, L.groundY-b.len*0.6, t.x+b.len*Math.sin(b.a)+sway, L.groundY-Math.cos(b.a)*b.len);
      ctx.stroke();
    }
  }
}

function drawStreaks(){
  const wN=clamp(sim.wind/PHYS.maxWind,0,1);
  if(wN<0.12) return;
  ctx.lineWidth=1;
  for(const s of streaks){
    ctx.strokeStyle=`rgba(220,232,245,${s.a*wN})`;
    ctx.beginPath(); ctx.moveTo(s.x,s.y); ctx.lineTo(s.x-s.len*(0.5+wN),s.y); ctx.stroke();
  }
}

function limb(pts,w,col){
  ctx.strokeStyle=col; ctx.lineWidth=w; ctx.lineCap='round'; ctx.lineJoin='round';
  ctx.beginPath(); ctx.moveTo(pts[0].x,pts[0].y);
  for(let i=1;i<pts.length;i++)ctx.lineTo(pts[i].x,pts[i].y);
  ctx.stroke();
}

function drawPersonBody(){
  const P=pose;
  // far leg
  limb([P.hip,{x:P.knee.x+6,y:P.knee.y}, {x:P.ankle.x+6,y:P.ankle.y}], L.headR*0.85, COL.trousers);
  // near leg
  limb([P.hip,P.knee,P.ankle], L.headR*0.95, COL.trousers);
  // boots
  ctx.fillStyle=COL.boot;
  for(const dx of [6,0]){
    ctx.beginPath();
    ctx.ellipse(P.ankle.x+dx-2, L.groundY-3, L.headR*0.9, L.headR*0.5, 0,0,TAU);
    ctx.fill();
  }
  // coat-tail (blows downwind)
  const wN=clamp(sim.wind/PHYS.maxWind,0,1);
  const tailLen=L.torsoLen*(0.5+0.6*wN);
  const flap=Math.sin(sim.t*9)*tailLen*0.12*wN;
  ctx.fillStyle=COL.coatDark;
  ctx.beginPath();
  ctx.moveTo(P.hip.x-4,P.hip.y-4);
  ctx.quadraticCurveTo(P.hip.x+tailLen*0.5, P.hip.y+4+flap, P.hip.x+tailLen, P.hip.y+10+flap);
  ctx.lineTo(P.hip.x+4,P.hip.y+L.headR*1.4);
  ctx.closePath(); ctx.fill();
  // torso / coat
  limb([P.hip,P.neck], L.torsoLen*0.95, COL.coat);
  // far arm (balance)
  const swing=0.35+1.15*wN;
  const fd={x:Math.sin(swing),y:Math.cos(swing)};
  const fE={x:P.shoulder.x+fd.x*L.upperArm*0.9+4, y:P.shoulder.y+fd.y*L.upperArm};
  const fH={x:fE.x+fd.x*L.foreArm*0.85+6, y:fE.y+fd.y*L.foreArm*0.85};
  limb([{x:P.shoulder.x+4,y:P.shoulder.y},fE,fH], L.headR*0.7, COL.coatDark);
  ctx.fillStyle=COL.skin; ctx.beginPath(); ctx.arc(fH.x,fH.y,L.headR*0.4,0,TAU); ctx.fill();
  // head
  ctx.fillStyle=COL.skin; ctx.beginPath(); ctx.arc(P.headC.x,P.headC.y,L.headR,0,TAU); ctx.fill();
  // nose (faces -x, into wind)
  ctx.beginPath(); ctx.moveTo(P.headC.x-L.headR*0.9,P.headC.y);
  ctx.lineTo(P.headC.x-L.headR*1.4,P.headC.y+L.headR*0.15);
  ctx.lineTo(P.headC.x-L.headR*0.85,P.headC.y+L.headR*0.35); ctx.closePath(); ctx.fill();
  // beanie
  ctx.fillStyle=COL.beanie;
  ctx.beginPath(); ctx.arc(P.headC.x,P.headC.y,L.headR*1.06,Math.PI*1.02,Math.PI*1.98); ctx.fill();
  ctx.fillRect(P.headC.x-L.headR*1.06,P.headC.y-L.headR*0.28,L.headR*2.12,L.headR*0.32);
}

function rimPoint(th,hub,d,p,R,h,load,t){
  const push=R*0.16*load*(0.5+0.5*Math.cos(th));          // whole canopy leans downwind
  const flut=Math.sin(t*22+th*3)*R*0.03*load;             // fabric flutter
  return {
    x:hub.x + d.x*h + p.x*(R*Math.cos(th)) + push + d.x*flut,
    y:hub.y + d.y*h + p.y*(R*Math.cos(th)) + R*L.squash*Math.sin(th) + d.y*flut
  };
}

function drawCanopy(hub,d,p,R,h,N,load,t){
  const rim=[]; for(let i=0;i<N;i++)rim.push(rimPoint(i/N*TAU,hub,d,p,R,h,load,t));
  // panels
  for(let i=0;i<N;i++){
    const a=rim[i], b=rim[(i+1)%N];
    const mid={x:(a.x+b.x)/2 + d.x*R*0.14, y:(a.y+b.y)/2 + d.y*R*0.14};  // scallop dips outboard
    ctx.beginPath(); ctx.moveTo(hub.x,hub.y);
    ctx.lineTo(a.x,a.y); ctx.quadraticCurveTo(mid.x,mid.y,b.x,b.y); ctx.closePath();
    ctx.fillStyle=(i%2?COL.canopyB:COL.canopyA); ctx.fill();
  }
  // ribs
  ctx.strokeStyle=COL.rib; ctx.lineWidth=Math.max(1.5,R*0.03); ctx.lineCap='round';
  for(let i=0;i<N;i++){ ctx.beginPath(); ctx.moveTo(hub.x,hub.y); ctx.lineTo(rim[i].x,rim[i].y); ctx.stroke(); }
  // scalloped rim edge
  ctx.strokeStyle=COL.edge; ctx.lineWidth=Math.max(1.5,R*0.035);
  for(let i=0;i<N;i++){
    const a=rim[i], b=rim[(i+1)%N];
    const mid={x:(a.x+b.x)/2 + d.x*R*0.14, y:(a.y+b.y)/2 + d.y*R*0.14};
    ctx.beginPath(); ctx.moveTo(a.x,a.y); ctx.quadraticCurveTo(mid.x,mid.y,b.x,b.y); ctx.stroke();
  }
  // ferrule (tip beyond the peak, along -d)
  ctx.strokeStyle=COL.ferrule; ctx.lineWidth=Math.max(2,R*0.05);
  ctx.beginPath(); ctx.moveTo(hub.x,hub.y);
  ctx.lineTo(hub.x-d.x*R*0.20, hub.y-d.y*R*0.20); ctx.stroke();
}

function drawUmbrella(){
  if(!sim.attached){
    if(sim.free.active) drawFreeUmbrella();
    return;
  }
  const P=pose;
  // shaft (grip -> hub) with bend
  const mid={x:(P.grip.x+P.hub.x)/2 + P.perp.x*P.bendMag, y:(P.grip.y+P.hub.y)/2 + P.perp.y*P.bendMag};
  ctx.strokeStyle=COL.shaft; ctx.lineWidth=Math.max(3,L.headR*0.28); ctx.lineCap='round';
  ctx.beginPath(); ctx.moveTo(P.grip.x,P.grip.y); ctx.quadraticCurveTo(mid.x,mid.y,P.hub.x,P.hub.y); ctx.stroke();
  // canopy
  const load=clamp(sim.F/200,0,1);
  const h=L.baseH*(1-2*sim.inv)*(1-0.35*load);
  drawCanopy(P.hub,P.d,P.p,L.R,h,8,load,sim.t);
  // handle hook below grip
  ctx.strokeStyle=COL.handle; ctx.lineWidth=Math.max(3,L.headR*0.3);
  const hx=-P.shaft.x, hy=-P.shaft.y;
  ctx.beginPath(); ctx.moveTo(P.grip.x,P.grip.y);
  ctx.quadraticCurveTo(P.grip.x+hx*L.headR*1.2 - hy*L.headR, P.grip.y+hy*L.headR*1.2 + hx*L.headR,
                       P.grip.x+hx*L.headR*1.4, P.grip.y+hy*L.headR*1.4);
  ctx.stroke();
}

function drawNearArm(){
  const P=pose;
  // 2-bone IK, choose lower elbow
  const a=P.shoulder, b=P.grip, l1=L.upperArm, l2=L.foreArm;
  let dx=b.x-a.x, dy=b.y-a.y, dist=Math.hypot(dx,dy)||1e-4;
  dist=clamp(dist,Math.abs(l1-l2)+0.5,l1+l2-0.5);
  const baseAng=Math.atan2(dy,dx);
  const cosA=clamp((l1*l1+dist*dist-l2*l2)/(2*l1*dist),-1,1), A=Math.acos(cosA);
  const e1={x:a.x+Math.cos(baseAng+A)*l1,y:a.y+Math.sin(baseAng+A)*l1};
  const e2={x:a.x+Math.cos(baseAng-A)*l1,y:a.y+Math.sin(baseAng-A)*l1};
  const elbow=(e1.y>e2.y?e1:e2);
  limb([a,elbow,b], L.headR*0.8, COL.coat);
  // gripping hand
  ctx.fillStyle=COL.skin; ctx.beginPath(); ctx.arc(b.x,b.y,L.headR*0.5,0,TAU); ctx.fill();
}

function drawFreeUmbrella(){
  const f=sim.free;
  ctx.save(); ctx.translate(f.x,f.y); ctx.rotate(f.ang);
  const d={x:-Math.sin(0),y:1}, p={x:1,y:0};   // local: shaft down = +y
  // shaft
  ctx.strokeStyle=COL.shaft; ctx.lineWidth=Math.max(3,L.headR*0.28); ctx.lineCap='round';
  ctx.beginPath(); ctx.moveTo(0,0); ctx.lineTo(0,L.shaftLen); ctx.stroke();
  ctx.strokeStyle=COL.handle; ctx.beginPath(); ctx.moveTo(0,L.shaftLen);
  ctx.quadraticCurveTo(-L.headR,L.shaftLen+L.headR, -L.headR*0.3,L.shaftLen+L.headR*1.4); ctx.stroke();
  const h=L.baseH*(1-2*sim.inv);
  drawCanopy({x:0,y:0},d,p,L.R,h,8,0.4,sim.t);
  ctx.restore();
}

function drawScarf(){
  const s=scarf; if(s.pts.length<2)return;
  ctx.lineCap='round'; ctx.strokeStyle=COL.scarf;
  for(let i=0;i<s.pts.length-1;i++){
    const a=s.pts[i], b=s.pts[i+1];
    ctx.lineWidth=lerp(L.headR*0.7,2, i/(s.pts.length-1));
    ctx.beginPath(); ctx.moveTo(a.x,a.y); ctx.lineTo(b.x,b.y); ctx.stroke();
  }
}

function drawRain(){
  const wN=clamp(sim.wind/PHYS.maxWind,0,1);
  const active=Math.floor(lerp(50,rain.max,wN));
  const windPx=sim.wind*(W*0.010), fall=H*0.9, tr=0.05;
  ctx.lineWidth=1.1; ctx.lineCap='round';
  for(let i=0;i<active;i++){
    const dr=rain.drops[i];
    const vx=windPx*dr.sp, vy=fall*dr.sp;
    ctx.strokeStyle=`rgba(190,210,235,${dr.a*(0.4+0.6*wN)})`;
    ctx.beginPath(); ctx.moveTo(dr.x,dr.y); ctx.lineTo(dr.x-vx*tr, dr.y-vy*tr); ctx.stroke();
  }
}

function drawFlash(){
  if(sim.flash>0.01){ ctx.fillStyle=`rgba(220,230,255,${sim.flash*0.45})`; ctx.fillRect(0,0,W,H); }
}

function render(){
  ctx.clearRect(0,0,W,H);
  drawSky();
  drawStreaks();
  drawGround();
  drawPersonBody();
  drawUmbrella();
  drawNearArm();
  drawScarf();
  drawRain();
  drawFlash();
}

/* ================= HUD ================= */
const el={
  num:document.getElementById('windNum'), ms:document.getElementById('windMs'),
  word:document.getElementById('windWord'), fill:document.getElementById('gaugeFill'),
  status:document.getElementById('status'), slider:document.getElementById('slider'),
  auto:document.getElementById('autoBtn'), reset:document.getElementById('resetBtn')
};
function beaufort(kmh){
  if(kmh<1)return'Calm'; if(kmh<6)return'Light air'; if(kmh<12)return'Light breeze';
  if(kmh<20)return'Gentle breeze'; if(kmh<29)return'Moderate breeze'; if(kmh<39)return'Fresh breeze';
  if(kmh<50)return'Strong breeze'; if(kmh<62)return'Near gale'; if(kmh<75)return'Gale';
  if(kmh<89)return'Strong gale'; if(kmh<103)return'Storm'; if(kmh<118)return'Violent storm';
  return'Hurricane';
}
function updateHUD(){
  const kmh=sim.wind*3.6, wN=clamp(sim.wind/PHYS.maxWind,0,1);
  el.num.textContent=Math.round(kmh);
  el.ms.textContent=sim.wind.toFixed(0)+' m/s';
  el.word.textContent=beaufort(kmh);
  el.fill.style.width=(wN*100)+'%';
  const col = wN<0.4? lerpColor([95,208,160],[240,194,80],wN/0.4)
            : lerpColor([240,194,80],[255,90,68],(wN-0.4)/0.6);
  el.fill.style.background=col; el.num.style.color=col;
  let st;
  if(!sim.attached) st = sim.free.active? "It's gone — off it tumbles." : "Gone. Press R for another.";
  else if(sim.inv>0.5) st="Inside out — hanging on!";
  else if(sim.F>90) st="Straining…";
  else if(sim.F>35) st="Leaning in.";
  else if(sim.wind>3) st="Holding.";
  else st="Calm.";
  el.status.textContent=st;
  el.slider.value=sim.windTarget;
  el.auto.textContent='Auto: '+(sim.auto?'on':'off');
  el.auto.classList.toggle('on',sim.auto);
}

/* ================= input ================= */
el.slider.addEventListener('input',e=>{ sim.windTarget=parseFloat(e.target.value); sim.auto=false; });
el.auto.addEventListener('click',()=>{ sim.auto=!sim.auto; });
el.reset.addEventListener('click',()=>reset());
cv.addEventListener('pointerdown',()=>{ if(!sim.attached && !sim.free.active) reset(); });
window.addEventListener('keydown',e=>{
  const k=e.key;
  if(k==='ArrowUp'||k==='w'||k==='W'){ sim.windTarget=clamp(sim.windTarget+1.5,0,PHYS.maxWind); sim.auto=false; e.preventDefault(); }
  else if(k==='ArrowDown'||k==='s'||k==='S'){ sim.windTarget=clamp(sim.windTarget-1.5,0,PHYS.maxWind); sim.auto=false; e.preventDefault(); }
  else if(k===' '){ sim.auto=!sim.auto; e.preventDefault(); }
  else if(k==='r'||k==='R'){ reset(); }
});
window.addEventListener('resize',resize);

/* ================= reset / init ================= */
function reset(){
  sim.t=0; sim.auto=true; sim.windTarget=3; sim.windBase=3; sim.wind=3;
  sim.inv=0; sim.invVel=0; sim.tilt=-0.10; sim.tiltVel=0;
  sim.lean=0; sim.crouch=0; sim.grip=0; sim.attached=true;
  sim.free.active=false; sim.flash=0; sim.nextFlash=1e9;
  initScarf();
}

/* ================= loop ================= */
let last=performance.now();
function frame(now){
  let dt=(now-last)/1000; last=now;
  dt=Math.min(dt,0.05);
  const steps=2;
  for(let i=0;i<steps;i++) step(dt/steps);
  render();
  updateHUD();
  requestAnimationFrame(frame);
}

resize();
initRain(); initStreaks();
reset();
requestAnimationFrame(frame);

})();
</script>
</body>
</html>

What it actually does

Where it looks right: the broad beats you already know are all there and read correctly. The person leans into the wind (top of the body toward the source) while the umbrella is dragged downwind over their head, so the two form the opposing V you actually make in a gale; they crouch lower as it worsens, the near arm visibly straightens as the grip is pulled, and the feet stay planted. Rain slants and accelerates with the wind (its streak angle is just atan(windX / fallSpeed)), and the scarf, coat-tail and grass all stream downwind as extra cues. The canopy telegraphs before it goes — it flattens, the ribs load, the shaft bows — then snaps inside out with a spring overshoot, latches there via hysteresis, and springs back if you drop the wind below the lower threshold. Past the grip limit it rips free and tumbles off downwind as a spinning rigid body. The wind readout, Beaufort word and severity colour all track the gusty instantaneous value, and you can drive it with the slider, ↑/↓, or let Auto ramp it.

Where it's wrong, before you find it:

The canopy is a fake 2.5D dome, not cloth. It's eight rigid scalloped panels on an ellipse whose only real deformation is a signed dome-depth plus a sinusoidal "flutter." There's no fabric simulation, no per-panel billow, no seam stretch — a real canopy ripples and snaps in ways this only gestures at.
Inversion is a scripted state flip, not emergent buckling. A real umbrella inverts because the ribs buckle past a critical load at some point on the rim and it unzips around; mine just drives one scalar through 0.5 on a threshold. It looks like a snap, but it's a latch, not a structural failure, and it always inverts symmetrically.
The person has no balance. It's forward kinematics leaning by a target angle — there's no centre-of-mass, no tipping, no stumble. They can't actually be knocked over; the ground attachment is a rule, not a simulation, so at extreme wind they lean at an anatomically generous angle rather than falling.
The shaft bend and arm drag are cosmetic offsets, proportional to force, not a beam solution; the umbrella's tilt is a spring toward a hand-tuned target, not a moment balance.
Rain doesn't collide with anything. Drops pass through the canopy and the person; there's no dry pocket underneath, no splash, no water funnelling off an inverted canopy (which in reality would dump straight onto you).
The wind is a single scalar with layered sines, not a vector field — no spatial gusts, no turbulence structures, and the "wrench sideways" is a random impulse rather than a real aeroelastic kick.
The numbers are tuned, not derived. Fup, Fdown, grip strength and the force→pose gains were picked to make a nice ~15-second arc, so the wind speeds at which it inverts and tears free are plausible but not physically calibrated, and nothing ever breaks — the frame is infinitely strong, it only ever lets go at the hand.

Attachments

baidu/ernie-5.5-flash-preview — page