Run Detail

completedclaude-opus-5.5

95excellent

Every model's answer from this round

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Provider

openrouter

Challenge Version

v1.0

Turns

Duration

Batched — not timed

Total Tokens

91,971

Input Tokens

536

Output Tokens

91,435

Reasoning Tokens

68,944

Reasoning Effort

default

Est. Cost

$0.9154

Started

10/7/2026, 8:15:51 PM

OR Provider

Anthropic

Finish Reason

stop

Generation ID

gen-batch-1791404153-c3d82e0e58cbeb148473

Turns (1)

Turn #1

536 in91,435 out68,944 reasoning91,971 total

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

The canopy is two ribs seen edge-on, one for each half of the umbrella in the side view. Each rib is a short chain of point masses. The crown and the inner rib (crown to the stretcher joint) are rigid in the shaft's frame, because the crown–runner–stretcher triangle holds them there. The three outer segments are free Verlet particles. Torsion springs at each joint give the rib its curve. A tension-only hoop limit stands in for the fabric, so the rim cannot spread past the cloth.

Each segment feels the air relative to its own motion:

Air striking the concave underside pushes harder (C≈1.5) than air striking the convex top (C≈0.8).
Air flowing along the surface adds suction off the top face.
The summed forces and moments go to the shaft. A wrist with a stiffness limit and a torque limit holds the shaft, and that wrist is attached to a person who balances at the ankles.

Inversion is a discrete state on the "knuckle", the joint where the stretcher meets the rib. That spring has two rest wells: normal (outer rib continues the dome, −10°) and inside-out (outer rib flipped up, +85°). When the outer rib is pushed upward past the over-centre angle of +35°, the state flips and the spring starts pulling toward the inverted well. That is the snap. It flips back only below +27° (hysteresis), which in practice means the person's hand pulls it back.

What decides when it happens is the lifting moment about the knuckle against the knuckle stiffness. That moment comes from:

gusts with an upward component;
suction over the dome;
how badly the canopy is angled to the flow, which depends on the person's reaction lag.

Each inversion permanently bends the rib a few degrees, so the next inversion comes easier.

Three separate limits handle the rest:

Rib snaps: the stretcher breaks when its load (crown moment ÷ lever) exceeds 320 N.
Ripped away: the grip slips when the pull exceeds what one or two hands can hold.
Wrenched away: the umbrella twists out of the wrist when the twisting torque exceeds the wrist's limit for long enough.

The page

<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width,initial-scale=1">
<title>Umbrella in a rising gale</title>
<style>
html,body{margin:0;height:100%;overflow:hidden;background:#0b0f16;color:#dde5ee;font:14px/1.35 system-ui,-apple-system,"Segoe UI",Roboto,sans-serif}
canvas{display:block;position:fixed;left:0;top:0;width:100vw;height:100vh}
#hud{position:fixed;left:14px;top:12px;padding:10px 14px;background:rgba(10,14,20,.6);border:1px solid rgba(255,255,255,.08);border-radius:10px;width:270px;pointer-events:none}
#spd{font-size:40px;font-weight:700;letter-spacing:-.5px;font-variant-numeric:tabular-nums;line-height:1.1}
#spd small{font-size:16px;font-weight:500;opacity:.7}
#sub{opacity:.88}
#gust,#mode{opacity:.7;font-variant-numeric:tabular-nums;font-size:13px}
.lbl{font-size:12px;opacity:.7;margin-top:7px}
.bar{height:6px;background:rgba(255,255,255,.1);border-radius:3px;margin:3px 0 2px;overflow:hidden}
.bar i{display:block;height:100%;width:0;background:#7fc4ff}
#stat{margin-top:8px;min-height:4.2em;white-space:pre-line;font-size:13px}
#ctl{position:fixed;left:14px;right:14px;bottom:12px;display:flex;gap:10px;align-items:center;padding:8px 12px;background:rgba(10,14,20,.6);border-radius:10px;border:1px solid rgba(255,255,255,.08)}
#ctl input{flex:1;accent-color:#e2525c}
button{background:#222b38;color:#dde5ee;border:1px solid #3a4658;border-radius:7px;padding:6px 10px;font:inherit;cursor:pointer;white-space:nowrap}
button.on{background:#7a2a30;border-color:#c24852}
#keys{font-size:12px;opacity:.6;white-space:nowrap}
</style>
</head>
<body>
<canvas id="c"></canvas>
<div id="hud">
  <div id="spd">0.0 <small>m/s</small></div>
  <div id="sub"></div>
  <div id="gust"></div>
  <div id="mode"></div>
  <div class="lbl">grip load</div><div class="bar"><i id="bGrip"></i></div>
  <div class="lbl">frame load (worst stretcher)</div><div class="bar"><i id="bFrame"></i></div>
  <div id="stat"></div>
</div>
<div id="ctl">
  <button id="auto" class="on">Auto: rising</button>
  <span>wind</span>
  <input id="sl" type="range" min="0" max="40" step="0.1" value="2">
  <button id="newu">New umbrella</button>
  <span id="keys">↑/↓ wind · A auto · N new · R reset</span>
</div>
<script>
'use strict';
const cv=document.getElementById('c'),ctx=cv.getContext('2d');
const D2R=Math.PI/180,RHO=1.2,GRAV=9.81;
let DPR=1,CW=0,CH=0,S=100,OX=0,OY=0;
const X=x=>OX+x*S,Y=y=>OY-y*S;
const viewL=()=>-OX/S,viewR=()=>(CW-OX)/S,viewT=()=>OY/S;
function clamp(v,a,b){return v<a?a:v>b?b:v}

/* ---------------- background ---------------- */
const bgc=document.createElement('canvas'),bgx=bgc.getContext('2d');
function buildBG(){
  bgc.width=cv.width;bgc.height=cv.height;const c=bgx;c.setTransform(DPR,0,0,DPR,0,0);
  const g=c.createLinearGradient(0,0,0,OY);g.addColorStop(0,'#0c121d');g.addColorStop(1,'#283240');
  c.fillStyle=g;c.fillRect(0,0,CW,OY);
  let seed=11;const rnd=()=>{seed=(seed*16807)%2147483647;return seed/2147483647;};
  for(let layer=0;layer<2;layer++){
    let x=-30;const col=layer?'#131922':'#1c2532',sc=CH/800;
    while(x<CW+30){
      const w=(layer?70:45)+rnd()*(layer?110:80),hg=((layer?70:130)+rnd()*(layer?150:190))*sc;
      c.fillStyle=col;c.fillRect(x,OY-hg,w,hg);
      for(let wy=OY-hg+10*sc;wy<OY-14*sc;wy+=16*sc)for(let wx=x+6;wx<x+w-8;wx+=13){
        if(rnd()<(layer?0.12:0.07)){c.fillStyle=layer?'rgba(255,200,120,0.32)':'rgba(255,210,150,0.16)';c.fillRect(wx,wy,6,8*sc);}
      }
      x+=w+rnd()*14;
    }
  }
  const gg=c.createLinearGradient(0,OY,0,CH);gg.addColorStop(0,'#1e242d');gg.addColorStop(1,'#0b0e13');
  c.fillStyle=gg;c.fillRect(0,OY,CW,CH-OY);
  c.fillStyle='rgba(170,190,220,0.14)';c.fillRect(0,OY,CW,1.5);
}
function resize(){
  DPR=Math.min(2,window.devicePixelRatio||1);CW=innerWidth;CH=innerHeight;
  cv.width=Math.round(CW*DPR);cv.height=Math.round(CH*DPR);
  S=Math.min(CW/9.5,CH/5.0);OX=CW*0.40;OY=CH*0.80;buildBG();
}
addEventListener('resize',resize);resize();

/* ---------------- wind ---------------- */
let windSet=2,Umean=2,auto=true,T=0,Dadv=0,LULL=1;
const RAMP=0.25,WMAX=40;
let WX=0,WY=0;
function gn1(z){return 0.5*Math.sin(0.61*z+1.3)+0.33*Math.sin(1.37*z+0.2)+0.22*Math.sin(2.71*z+2.1)+0.12*Math.sin(4.9*z+4.0);}
function gn2(z){return 0.5*Math.sin(0.83*z+0.7)+0.35*Math.sin(1.91*z+2.9)+0.2*Math.sin(3.7*z+1.1);}
function wind(x,y){
  const U=Umean,z=(Dadv-x)/6,yy=y>0.05?y:0.05;
  const prof=Math.min(1.1,Math.pow(yy/1.6,0.16));
  WX=U*(1+0.22*gn1(z))*prof*LULL;
  WY=U*0.17*gn2(z*1.3+5)*Math.min(1,yy/0.6);
}

/* ---------------- umbrella ---------------- */
const A_IN=0.22,L_OUT=0.11,PHI0=100*D2R,RUN=0.22,HAND_B=0.10,SHAFT=0.85,COM_B=0.64;
const TH_N=-10*D2R,TH_I=85*D2R,TH_B=35*D2R,TH_HYS=8*D2R,TH_J=-12*D2R;
const K_KN=3.2,K_J=1.8,C_KN=0.02,C_J=0.012;
const MN=0.03,M_K=0.35,M_FREE=0.53,I_HAND=0.24,I_FREE=0.06,KG=60,CG=4;
const SPAN=[0.75,0.62,0.62,0.62];
const C_TOP=0.8,C_UND=1.5,C_SUC=0.3;
const STRUT_ARM=0.168,STRUT_BREAK=320,HSTEP=1/720;
const RA=[0],RR=[0],RMAX=[0,0,0,0,0];
(function(){let a=A_IN*Math.cos(PHI0),r=A_IN*Math.sin(PHI0);RA.push(a);RR.push(r);
  let phi=PHI0-TH_N;for(let j=2;j<=4;j++){a+=L_OUT*Math.cos(phi);r+=L_OUT*Math.sin(phi);RA.push(a);RR.push(r);RMAX[j]=r*1.1;phi-=TH_J;}})();
const G={};
function geom(u,Hx,Hy){
  const ux=Math.sin(u.alpha),uy=Math.cos(u.alpha);
  G.ux=ux;G.uy=uy;G.px=uy;G.py=-ux;
  if(u.held){G.bx=Hx-ux*HAND_B;G.by=Hy-uy*HAND_B;}else{G.bx=u.cx-ux*COM_B;G.by=u.cy-uy*COM_B;}
  G.cx=G.bx+ux*SHAFT;G.cy=G.by+uy*SHAFT;G.rx=G.cx-ux*RUN;G.ry=G.cy-uy*RUN;
}
function newSide(s){const n=[];for(let j=0;j<5;j++)n.push({x:0,y:0,px:0,py:0,fx:0,fy:0});
  return {s,n,state:0,broken:false,restKn:TH_N,thp:[0,TH_N,TH_J,TH_J,0],load:0,invT:0,inv:0,M:0};}
function makeUmb(){return {held:true,alpha:0,omega:0,alphaT:0,tauMax:14,fGrip:140,cx:0,cy:0,vx:0,vy:0,
  sides:[newSide(-1),newSide(1)],slip:0,wrenchT:0,sat:false,why:'',freeT:0,gone:false,goneT:0,accFx:0,accFy:0,accN:0};}
function place(u,Hx,Hy){
  geom(u,Hx,Hy);
  for(const sd of u.sides)for(let j=0;j<5;j++){const nd=sd.n[j];
    nd.x=nd.px=G.cx+G.ux*RA[j]+G.px*sd.s*RR[j];nd.y=nd.py=G.cy+G.uy*RA[j]+G.py*sd.s*RR[j];}
}
function bend(sd,j,k,rest,cd,h,lo,hi){
  const s=sd.s,n=sd.n,p=n[j-1],c=n[j],q=n[j+1];
  const d1x=c.x-p.x,d1y=c.y-p.y,d2x=q.x-c.x,d2y=q.y-c.y;
  const L1=Math.hypot(d1x,d1y)||1e-6,L2=Math.hypot(d2x,d2y)||1e-6;
  const th=s*Math.atan2(d1x*d2y-d1y*d2x,d1x*d2x+d1y*d2y);
  const thd=clamp((th-sd.thp[j])/h,-300,300);sd.thp[j]=th;
  let tau=-k*(th-rest)-cd*thd;
  if(th<lo)tau+=-25*(th-lo);else if(th>hi)tau+=-25*(th-hi);
  const tw=s*tau;
  const fq=tw/L2,qx=-d2y/L2*fq,qy=d2x/L2*fq;
  q.fx+=qx;q.fy+=qy;c.fx-=qx;c.fy-=qy;
  const fp=-tw/L1,ppx=d1y/L1*fp,ppy=-d1x/L1*fp;
  p.fx+=ppx;p.fy+=ppy;c.fx-=ppx;c.fy-=ppy;
  return th;
}
function angAt(n,j,s){const p=n[j-1],c=n[j],q=n[j+1];const d1x=c.x-p.x,d1y=c.y-p.y,d2x=q.x-c.x,d2y=q.y-c.y;
  return s*Math.atan2(d1x*d2y-d1y*d2x,d1x*d2x+d1y*d2y);}
function rootBroken(sd,h){
  const s=sd.s,n=sd.n,a=n[0],b=n[1];
  const rx=G.ux*Math.cos(PHI0)+G.px*s*Math.sin(PHI0),ry=G.uy*Math.cos(PHI0)+G.py*s*Math.sin(PHI0);
  const dx=b.x-a.x,dy=b.y-a.y,L=Math.hypot(dx,dy)||1e-6;
  const th=s*Math.atan2(rx*dy-ry*dx,rx*dx+ry*dy);
  const thd=clamp((th-sd.thp[0])/h,-300,300);sd.thp[0]=th;
  let tau=-0.35*th-0.01*thd;if(th<-1.2)tau+=-6*(th+1.2);if(th>1.6)tau+=-6*(th-1.6);
  const f=s*tau/L;b.fx+=-dy/L*f;b.fy+=dx/L*f;
}
function distFix(a,b,L){const dx=b.x-a.x,dy=b.y-a.y,d=Math.hypot(dx,dy)||1e-6;b.x=a.x+dx/d*L;b.y=a.y+dy/d*L;}
function distBoth(a,b,L){const dx=b.x-a.x,dy=b.y-a.y,d=Math.hypot(dx,dy)||1e-6,k=(d-L)/d*0.5;a.x+=dx*k;a.y+=dy*k;b.x-=dx*k;b.y-=dy*k;}
function contact(u,x,y){
  if(y>=0)return;
  const rx=x-u.cx,ry=y-u.cy;u.cy-=y;
  const wc=-u.omega,vpx=u.vx-wc*ry,vpy=u.vy+wc*rx;
  if(vpy<0){
    const kn=1/M_FREE+rx*rx/I_FREE,jn=-1.25*vpy/kn,kt=1/M_FREE+ry*ry/I_FREE;
    let jt=clamp(-vpx/kt,-0.6*jn,0.6*jn);
    u.vx+=jt/M_FREE;u.vy+=jn/M_FREE;u.omega-=(rx*jn-ry*jt)/I_FREE;
  }
}
function release(u,why,Hx,Hy,Hvx,Hvy){
  geom(u,Hx,Hy);
  const comx=G.bx+G.ux*COM_B,comy=G.by+G.uy*COM_B,rx=comx-Hx,ry=comy-Hy,wc=-u.omega;
  u.held=false;u.why=why;u.cx=comx;u.cy=comy;u.vx=Hvx-wc*ry;u.vy=Hvy+wc*rx;u.freeT=0;
  P.reach=1.4;P.fix=null;
}
function stepUmb(u,h,Hx,Hy,Hvx,Hvy){
  geom(u,Hx,Hy);
  const ux=G.ux,uy=G.uy,pX=G.px,pY=G.py,cx=G.cx,cy=G.cy,c0=Math.cos(PHI0),s0=Math.sin(PHI0);
  for(const sd of u.sides){const s=sd.s,n=sd.n;
    n[0].px=n[0].x;n[0].py=n[0].y;n[0].x=cx;n[0].y=cy;
    if(!sd.broken){const a=n[1];a.px=a.x;a.py=a.y;a.x=cx+(ux*c0+pX*s*s0)*A_IN;a.y=cy+(uy*c0+pY*s*s0)*A_IN;}
  }
  const pvx=u.held?Hx:u.cx,pvy=u.held?Hy:u.cy;
  let Fx=0,Fy=0,Tq=0;
  for(const sd of u.sides){const s=sd.s,n=sd.n;let M=0;
    for(let j=0;j<5;j++){n[j].fx=0;n[j].fy=(j>=2||(j===1&&sd.broken))?-MN*GRAV:0;}
    for(let j=0;j<4;j++){const a=n[j],b=n[j+1];
      let tx=b.x-a.x,ty=b.y-a.y;const L=Math.hypot(tx,ty)||1e-6;tx/=L;ty/=L;
      const mx=(a.x+b.x)/2,my=(a.y+b.y)/2;
      const vmx=((a.x-a.px)+(b.x-b.px))/(2*h),vmy=((a.y-a.py)+(b.y-b.py))/(2*h);
      wind(mx,my);const Vx=WX-vmx,Vy=WY-vmy;
      const nx=-s*ty,ny=s*tx,q=Vx*nx+Vy*ny,vt=Vx*tx+Vy*ty;
      const fn=0.5*RHO*SPAN[j]*L*((q>0?C_UND:C_TOP)*Math.abs(q)*q+C_SUC*vt*vt);
      const fx=fn*nx,fy=fn*ny;
      a.fx+=fx/2;a.fy+=fy/2;b.fx+=fx/2;b.fy+=fy/2;
      Fx+=fx;Fy+=fy;Tq+=(mx-pvx)*fy-(my-pvy)*fx;M+=(mx-cx)*fy-(my-cy)*fx;
    }
    for(let j=1;j<5;j++){if(j===1&&!sd.broken)continue;const w=-MN*GRAV;Fy+=w;Tq+=(n[j].x-pvx)*w;M+=(n[j].x-cx)*w;}
    sd.M=M;
  }
  if(P.fix&&u.held&&P.fix.t>0.45){const sd=u.sides[P.fix.i],s=sd.s,k=260*Math.min(1,(P.fix.t-0.45)*3);
    for(let j=2;j<5;j++){const nd=sd.n[j],tx=cx+ux*RA[j]+pX*s*RR[j],ty=cy+uy*RA[j]+pY*s*RR[j];
      nd.fx+=k*(tx-nd.x)-1.5*(nd.x-nd.px)/h;nd.fy+=k*(ty-nd.y)-1.5*(nd.y-nd.py)/h;}}
  for(const sd of u.sides){
    if(sd.broken)rootBroken(sd,h);
    const th=angAt(sd.n,1,sd.s);
    if(sd.state===0&&th>TH_B){sd.state=1;sd.inv++;sd.restKn=Math.min(TH_N+18*D2R,sd.restKn+3*D2R);}
    else if(sd.state===1&&th<TH_B-TH_HYS){sd.state=0;}
    bend(sd,1,K_KN,sd.state?TH_I:sd.restKn,C_KN,h,-60*D2R,125*D2R);
    bend(sd,2,K_J,TH_J,C_J,h,-75*D2R,75*D2R);
    bend(sd,3,K_J,TH_J,C_J,h,-75*D2R,75*D2R);
    sd.invT=sd.state?sd.invT+h:0;
  }
  if(u.held){
    const comx=G.bx+ux*COM_B,tg=(comx-Hx)*(-M_K*GRAV);
    const Gext=-(Tq+tg);
    let gr=KG*(u.alphaT-u.alpha)-CG*u.omega;
    u.sat=Math.abs(gr)>u.tauMax*0.98;gr=clamp(gr,-u.tauMax,u.tauMax);
    u.omega+=(Gext+gr)/I_HAND*h;u.alpha+=u.omega*h;
    const fy=Fy-M_K*GRAV;u.accFx+=Fx;u.accFy+=fy;u.accN++;
    const Fm=Math.hypot(Fx,fy);
    if(Fm>u.fGrip)u.slip+=(Fm/u.fGrip-1)*h*4;else u.slip=Math.max(0,u.slip-h*0.5);
    if(Math.abs(u.alpha-u.alphaT)>1.7)u.wrenchT+=h;else u.wrenchT=Math.max(0,u.wrenchT-h);
    if(u.slip>0.3)release(u,'ripped out of their hands',Hx,Hy,Hvx,Hvy);
    else if(u.wrenchT>0.35)release(u,'wrenched out of their grip',Hx,Hy,Hvx,Hvy);
  }else{
    u.vx+=(Fx/M_FREE-0.05*u.vx)*h;u.vy+=((Fy-M_K*GRAV)/M_FREE)*h;
    u.cx+=u.vx*h;u.cy+=u.vy*h;
    u.omega+=-Tq/I_FREE*h;u.omega*=1-0.2*h;u.alpha+=u.omega*h;
    geom(u,0,0);
    contact(u,G.bx,G.by);geom(u,0,0);contact(u,G.cx,G.cy);
    for(const sd of u.sides){geom(u,0,0);const s=sd.s;
      contact(u,G.cx+(G.ux*c0+G.px*s*s0)*A_IN,G.cy+(G.uy*c0+G.py*s*s0)*A_IN);}
  }
  const h2=h*h;
  for(const sd of u.sides)for(let j=sd.broken?1:2;j<5;j++){const nd=sd.n[j];
    const vx=(nd.x-nd.px)*0.9985,vy=(nd.y-nd.py)*0.9985;nd.px=nd.x;nd.py=nd.y;
    nd.x+=vx+nd.fx/MN*h2;nd.y+=vy+nd.fy/MN*h2;}
  for(let it=0;it<4;it++)for(const sd of u.sides){const s=sd.s,n=sd.n;
    if(sd.broken)distFix(n[0],n[1],A_IN);
    for(let j=1;j<4;j++){if(j===1&&!sd.broken)distFix(n[1],n[2],L_OUT);else distBoth(n[j],n[j+1],L_OUT);}
    for(let j=2;j<5;j++){const nd=n[j],r=s*((nd.x-cx)*pX+(nd.y-cy)*pY);
      if(r>RMAX[j]){const d=(r-RMAX[j])*0.6;nd.x-=s*pX*d;nd.y-=s*pY*d;}}
    for(let j=1;j<5;j++){if(j===1&&!sd.broken)continue;const nd=n[j];
      if(nd.y<0){nd.y=0;nd.py=0;nd.px=nd.x-(nd.x-nd.px)*0.6;}}
  }
  for(const sd of u.sides){
    if(sd.broken){sd.load*=0.99;continue;}
    const f=Math.abs(sd.M)/STRUT_ARM;sd.load+=(f-sd.load)*Math.min(1,h/0.03);
    if(sd.load>STRUT_BREAK){sd.broken=true;sd.thp[0]=0;}
  }
}

/* ---------------- person ---------------- */
const P={beta:0,bdot:0,stance:0,crouch:0,two:0,Us:2,Ug:2,Vg:0,tauS:0,Fsx:0,Fsy:0,Fax:0,Fay:0,
  Hx:0,Hy:1.5,Hnx:0,Hny:1.5,at:0,reach:0,hitRate:0,hits:0,fix:null,fixCool:0,J:null};
let umb=null,umbCount=0;
function ik(ax,ay,bx,by,l1,l2,sgn){
  const dx=bx-ax,dy=by-ay,d=Math.hypot(dx,dy)||1e-6;
  const dn=Math.max(Math.min(d,l1+l2-1e-4),Math.abs(l1-l2)+1e-4);
  const ux=dx/d,uy=dy/d,a=(l1*l1-l2*l2+dn*dn)/(2*dn),hh=Math.sqrt(Math.max(0,l1*l1-a*a));
  return {ex:ax+ux*a-uy*hh*sgn,ey:ay+uy*a+ux*hh*sgn,hx:ax+ux*dn,hy:ay+uy*dn};
}
function armIK(sh,tx,ty){const a=ik(sh.x,sh.y,tx,ty,0.30,0.29,1),b=ik(sh.x,sh.y,tx,ty,0.30,0.29,-1);return a.ey<b.ey?a:b;}
function pose(){
  const st=P.stance,cr=P.crouch,b=P.beta;
  const aF={x:-0.13-0.12*st,y:0.08},aR={x:0.13+0.30*st,y:0.08};
  const pivx=(aF.x+aR.x)/2,pivy=0.07,hipH=0.92-0.17*cr;
  const hip={x:pivx-Math.sin(b)*hipH,y:pivy+Math.cos(b)*hipH};
  for(let k=0;k<3;k++)for(const a of [aF,aR]){const dx=hip.x-a.x,dy=hip.y-a.y,d=Math.hypot(dx,dy);
    if(d>0.88){hip.x=a.x+dx/d*0.88;hip.y=a.y+dy/d*0.88;}}
  const ta=b+0.18*cr+0.05;
  const neck={x:hip.x-Math.sin(ta)*0.54,y:hip.y+Math.cos(ta)*0.54};
  const sh={x:neck.x+Math.sin(ta)*0.05,y:neck.y-Math.cos(ta)*0.05};
  const hd=ta+0.25*cr+0.12;
  const head={x:neck.x-Math.sin(hd)*0.15,y:neck.y+Math.cos(hd)*0.15};
  const kF=ik(hip.x,hip.y,aF.x,aF.y,0.45,0.45,-1),kR=ik(hip.x,hip.y,aR.x,aR.y,0.45,0.45,-1);
  return {aF,aR,pivx,pivy,hip,neck,sh,head,ta,kF:{x:kF.ex,y:kF.ey},kR:{x:kR.ex,y:kR.ey}};
}
function personPrep(dt){
  wind(-0.2,1.4);
  P.Us+=(Umean-P.Us)*Math.min(1,dt/1.0);
  P.Ug+=(WX-P.Ug)*Math.min(1,dt/0.7);
  P.Vg+=(WY-P.Vg)*Math.min(1,dt/0.7);
  P.crouch+=(clamp((P.Us-9)/18,0,1)-P.crouch)*Math.min(1,dt/1.5);
  P.stance+=(clamp((P.Us-4)/14,0,1)-P.stance)*Math.min(1,dt/1.2);
  const held=!!(umb&&umb.held&&!umb.gone);
  let inv=false;if(held)for(const sd of umb.sides)if(sd.state)inv=true;
  const Fm=Math.hypot(P.Fsx,P.Fsy);
  P.two+=(((held&&(P.Us>10||Fm>45||inv))?1:0)-P.two)*Math.min(1,dt/0.35);
  P.at=clamp(Math.atan2(-P.Ug,6.5-P.Vg),-1.25,0.35);
  if(held){
    umb.alphaT=inv?Math.max(-1.45,P.at-0.3):P.at;
    umb.tauMax=14+21*P.two;umb.fGrip=140+150*P.two;
  }
  P.fixCool-=dt;
  if(P.fix){P.fix.t+=dt;const sd=held?umb.sides[P.fix.i]:null;
    if(!sd||sd.state===0||sd.broken||P.fix.t>2.4||P.Us>16){P.fix=null;P.fixCool=1.5;}}
  else if(held&&P.fixCool<=0&&P.Us<15){for(let i=0;i<2;i++){const sd=umb.sides[i];
    if(sd.state&&!sd.broken&&sd.invT>1.2){P.fix={i,t:0};break;}}}
  P.reach=Math.max(0,P.reach-dt);
  P.J=pose();
  const sh=P.J.sh,at=held?umb.alphaT:P.at,tilt=clamp(-at,0,1.45);
  let hx=sh.x-0.17-0.10*tilt,hy=sh.y+0.24-0.26*tilt;
  const kA=1600+1600*P.two;
  hx+=clamp(P.Fsx/kA,-0.16,0.16);hy+=clamp(P.Fsy/kA,-0.16,0.16);
  const dx=hx-sh.x,dy=hy-sh.y,d=Math.hypot(dx,dy);
  if(d>0.56){hx=sh.x+dx/d*0.56;hy=sh.y+dy/d*0.56;}
  P.Hnx=hx;P.Hny=hy;
}
function personDyn(dt){
  const J=P.J;
  wind(J.hip.x,1.1);
  const A=0.72-0.2*P.crouch,Fb=0.5*RHO*A*WX*Math.abs(WX);
  let tw=-(1.05-0.15*P.crouch-J.pivy)*Fb;
  if(umb&&umb.held&&!umb.gone)tw+=(P.Hx-J.pivx)*P.Fay-(P.Hy-J.pivy)*P.Fax;
  const Mgh=72*GRAV*1.0;
  P.tauS+=(tw-P.tauS)*Math.min(1,dt/0.5);
  const bref=Math.asin(clamp(-P.tauS/Mgh,-0.35,0.62));
  const acc=(tw+Mgh*Math.sin(P.beta)-1500*(P.beta-bref)-420*P.bdot)/85;
  P.bdot+=acc*dt;P.beta+=P.bdot*dt;
  if(P.beta>0.62){P.beta=0.62;if(P.bdot>0)P.bdot=0;}
  if(P.beta<-0.3){P.beta=-0.3;if(P.bdot<0)P.bdot=0;}
}
function newUmb(){
  umb=makeUmb();umbCount++;umb.alpha=umb.alphaT=P.at;P.fix=null;P.reach=0;
  personPrep(0);P.Hx=P.Hnx;P.Hy=P.Hny;place(umb,P.Hx,P.Hy);
}

/* ---------------- rain, splashes, air streaks ---------------- */
const NR=700,rx=new Float32Array(NR),ry=new Float32Array(NR),rvx=new Float32Array(NR),rvy=new Float32Array(NR);
const splashes=[];
const NS=50,sx=new Float32Array(NS),sy=new Float32Array(NS);
function spawnDrop(i){
  const L=viewL()-0.5,R=viewR()+0.5,Tp=viewT()+0.3;
  wind(0,2);const vx=WX,hfl=Math.abs(vx)*Tp,vfl=6.5*(R-L);
  if(Math.random()<hfl/(hfl+vfl)){rx[i]=L;ry[i]=Math.random()*Tp;}
  else{const back=Math.min(30,vx/6.5*Tp);rx[i]=L-back*Math.random()+Math.random()*(R-L+back*0.0);ry[i]=Tp;}
  rvx[i]=vx;rvy[i]=-6.5+WY;
}
function rainInit(){for(let i=0;i<NR;i++){spawnDrop(i);rx[i]=viewL()+Math.random()*(viewR()-viewL());ry[i]=Math.random()*viewT();}
  for(let i=0;i<NS;i++){sx[i]=viewL()+Math.random()*(viewR()-viewL());sy[i]=0.2+Math.random()*(viewT()-0.2);}}
function segHit(x0,y0,x1,y1,ax,ay,bx,by){
  const rX=x1-x0,rY=y1-y0,sX=bx-ax,sY=by-ay,den=rX*sY-rY*sX;
  if(Math.abs(den)<1e-12)return -1;
  const qx=ax-x0,qy=ay-y0,t=(qx*sY-qy*sX)/den,v=(qx*rY-qy*rX)/den;
  return (t>=0&&t<=1&&v>=0&&v<=1)?t:-1;
}
function distSeg(px,py,ax,ay,bx,by){const dx=bx-ax,dy=by-ay,l=dx*dx+dy*dy||1e-9;
  const t=clamp(((px-ax)*dx+(py-ay)*dy)/l,0,1);return Math.hypot(px-ax-dx*t,py-ay-dy*t);}
function addSplash(x,y,n){if(splashes.length>400)return;for(let k=0;k<n;k++)
  splashes.push({x,y,vx:(Math.random()-0.5)*1.5+Umean*0.05,vy:0.8+Math.random()*1.4,l:0.25+Math.random()*0.15});}
function rainStep(dt){
  const k=Math.min(1,dt/0.1),segs=[];let bx0=1e9,by0=1e9,bx1=-1e9,by1=-1e9;
  if(umb&&!umb.gone)for(const sd of umb.sides)for(let j=0;j<4;j++){const a=sd.n[j],b=sd.n[j+1];
    segs.push(a.x,a.y,b.x,b.y);bx0=Math.min(bx0,a.x,b.x);bx1=Math.max(bx1,a.x,b.x);by0=Math.min(by0,a.y,b.y);by1=Math.max(by1,a.y,b.y);}
  const J=P.J;let hits=0;const R=viewR()+1;
  for(let i=0;i<NR;i++){
    wind(rx[i],ry[i]);rvx[i]+=(WX-rvx[i])*k;rvy[i]+=(-6.5+WY-rvy[i])*k;
    const x0=rx[i],y0=ry[i],x1=x0+rvx[i]*dt,y1=y0+rvy[i]*dt;
    let hit=false,hx=0,hy=0;
    if(segs.length&&Math.max(x0,x1)>=bx0-0.05&&Math.min(x0,x1)<=bx1+0.05&&Math.max(y0,y1)>=by0-0.05&&Math.min(y0,y1)<=by1+0.05){
      for(let s=0;s<segs.length;s+=4){const t=segHit(x0,y0,x1,y1,segs[s],segs[s+1],segs[s+2],segs[s+3]);
        if(t>=0){hit=true;hx=x0+(x1-x0)*t;hy=y0+(y1-y0)*t;break;}}
    }
    if(!hit&&y1<2&&y1>0.6&&Math.abs(x1-J.hip.x)<0.6){
      if(Math.hypot(x1-J.head.x,y1-J.head.y)<0.13||distSeg(x1,y1,J.hip.x,J.hip.y,J.neck.x,J.neck.y)<0.16){hit=true;hx=x1;hy=y1;hits++;}
    }
    if(!hit&&y1<=0){hit=true;hx=x1;hy=0;}
    if(hit){if(Math.random()<0.5)addSplash(hx,hy,hy===0?1:2);spawnDrop(i);}
    else{rx[i]=x1;ry[i]=y1;if(x1>R||x1<viewL()-40)spawnDrop(i);}
  }
  P.hitRate+=(hits/dt-P.hitRate)*Math.min(1,dt/1.0);
  for(let i=splashes.length-1;i>=0;i--){const s=splashes[i];s.vy-=9.8*dt;s.x+=s.vx*dt;s.y+=s.vy*dt;s.l-=dt;
    if(s.l<=0||s.y<-0.02)splashes.splice(i,1);}
  for(let i=0;i<NS;i++){wind(sx[i],sy[i]);sx[i]+=WX*dt;sy[i]+=WY*dt*0.5;
    if(sx[i]>viewR()+1||sy[i]<0.1||sy[i]>viewT()){sx[i]=viewL()-1-Math.random()*2;sy[i]=0.2+Math.random()*(viewT()-0.2);}}
}

/* ---------------- drawing ---------------- */
function line(ax,ay,bx,by){ctx.beginPath();ctx.moveTo(X(ax),Y(ay));ctx.lineTo(X(bx),Y(by));ctx.stroke();}
function limb(a,b,c,w,col){ctx.strokeStyle=col;ctx.lineWidth=w*S;ctx.beginPath();ctx.moveTo(X(a.x),Y(a.y));ctx.lineTo(X(b.x),Y(b.y));ctx.lineTo(X(c.x),Y(c.y));ctx.stroke();}
function dot(x,y,r,col){ctx.fillStyle=col;ctx.beginPath();ctx.arc(X(x),Y(y),r*S,0,Math.PI*2);ctx.fill();}
function drawLamp(){
  const lx=-2.9;
  const g=ctx.createRadialGradient(X(lx+0.5),Y(3.2),0,X(lx+0.5),Y(3.2),2.6*S);
  g.addColorStop(0,'rgba(255,214,150,0.22)');g.addColorStop(1,'rgba(255,214,150,0)');
  ctx.fillStyle=g;ctx.fillRect(X(lx-2.3),Y(5.8),5.6*S,5.8*S);
  ctx.fillStyle='rgba(255,210,150,0.10)';ctx.beginPath();ctx.ellipse(X(lx+0.5),Y(0),1.6*S,0.12*S,0,0,Math.PI*2);ctx.fill();
  ctx.strokeStyle='#161b23';ctx.lineCap='round';ctx.lineWidth=0.07*S;line(lx,0,lx,3.25);
  ctx.lineWidth=0.045*S;line(lx,3.25,lx+0.5,3.3);
  dot(lx+0.5,3.22,0.06,'#ffe2b0');
}
function drawStreaks(){
  const a=clamp((Umean-3)/45,0,0.22);if(a<=0.005)return;
  ctx.strokeStyle='rgba(210,225,245,'+a+')';ctx.lineWidth=1;ctx.beginPath();
  for(let i=0;i<NS;i++){wind(sx[i],sy[i]);ctx.moveTo(X(sx[i]),Y(sy[i]));ctx.lineTo(X(sx[i]-WX*0.12),Y(sy[i]-WY*0.06));}
  ctx.stroke();
}
function smoothPath(pts){
  ctx.moveTo(X(pts[0].x),Y(pts[0].y));
  for(let i=1;i<pts.length-1;i++){const p=pts[i],q=pts[i+1];
    ctx.quadraticCurveTo(X(p.x),Y(p.y),X((p.x+q.x)/2),Y((p.y+q.y)/2));}
  const l=pts[pts.length-1];ctx.lineTo(X(l.x),Y(l.y));
}
function drawUmb(u){
  if(u.gone)return;
  geom(u,P.Hx,P.Hy);
  ctx.lineCap='round';ctx.lineJoin='round';
  const Ln=u.sides[0].n,Rn=u.sides[1].n;
  const pts=[Ln[4],Ln[3],Ln[2],Ln[1],Ln[0],Rn[1],Rn[2],Rn[3],Rn[4]];
  ctx.strokeStyle='#2c3138';ctx.lineWidth=Math.max(2,0.016*S);
  line(G.bx,G.by,G.cx+G.ux*0.07,G.cy+G.uy*0.07);
  // J handle
  ctx.lineWidth=Math.max(3,0.03*S);ctx.strokeStyle='#4a2f1f';
  const hk=0.05;ctx.beginPath();
  const hcx=G.bx+G.px*hk,hcy=G.by+G.py*hk,ang0=Math.atan2(-(G.by-hcy),(G.bx-hcx));
  ctx.arc(X(hcx),Y(hcy),hk*S,ang0,ang0+Math.PI*0.95,false);ctx.stroke();
  line(G.bx,G.by,G.bx+G.ux*0.1,G.by+G.uy*0.1);
  // stretchers
  for(const sd of u.sides){
    const f=clamp(sd.load/STRUT_BREAK,0,1);
    ctx.lineWidth=Math.max(1.2,0.009*S);
    if(!sd.broken){ctx.strokeStyle='rgb('+(90+165*f|0)+','+(95-50*f|0)+','+(105-60*f|0)+')';line(G.rx,G.ry,sd.n[1].x,sd.n[1].y);}
    else{ctx.strokeStyle='#c45a3a';const dx=sd.n[1].x-G.rx,dy=sd.n[1].y-G.ry,d=Math.hypot(dx,dy)||1;
      line(G.rx,G.ry,G.rx+dx/d*0.09,G.ry+dy/d*0.09-0.03);}
  }
  ctx.fillStyle='#3a3f47';const rw=0.02;ctx.beginPath();
  ctx.moveTo(X(G.rx-G.px*rw-G.ux*0.03),Y(G.ry-G.py*rw-G.uy*0.03));ctx.lineTo(X(G.rx+G.px*rw-G.ux*0.03),Y(G.ry+G.py*rw-G.uy*0.03));
  ctx.lineTo(X(G.rx+G.px*rw+G.ux*0.03),Y(G.ry+G.py*rw+G.uy*0.03));ctx.lineTo(X(G.rx-G.px*rw+G.ux*0.03),Y(G.ry-G.py*rw+G.uy*0.03));ctx.fill();
  // canopy
  ctx.beginPath();smoothPath(pts);ctx.closePath();
  ctx.fillStyle='rgba(158,34,44,0.9)';ctx.fill('evenodd');
  ctx.beginPath();smoothPath(pts);ctx.strokeStyle='#e0525c';ctx.lineWidth=Math.max(2,0.02*S);ctx.stroke();
  ctx.strokeStyle='rgba(30,10,12,0.55)';ctx.lineWidth=Math.max(1,0.006*S);ctx.beginPath();smoothPath(pts);ctx.stroke();
  for(const p of [Ln[4],Rn[4]])dot(p.x,p.y,0.012,'#ddd');
  dot(G.cx+G.ux*0.07,G.cy+G.uy*0.07,0.014,'#888');
}
function drawPerson(){
  const J=P.J;ctx.lineCap='round';ctx.lineJoin='round';
  const coat='#d39a26',coatD='#93681a',trou='#2a3343',trouD='#1b222d',boot='#11151b',skin='#deb08e';
  const held=umb&&umb.held&&!umb.gone;
  if(held)geom(umb,P.Hx,P.Hy);
  // targets
  const sh=J.sh,tuck={x:sh.x-0.15,y:sh.y-0.22},hood={x:J.head.x-0.06,y:J.head.y+0.02};
  let nT,fT;
  if(held){
    nT={x:P.Hx,y:P.Hy};
    const h2={x:P.Hx+G.ux*0.2,y:P.Hy+G.uy*0.2};
    fT={x:tuck.x+(h2.x-tuck.x)*P.two,y:tuck.y+(h2.y-tuck.y)*P.two};
    if(P.fix){const tip=umb.sides[P.fix.i].n[4],r=clamp(P.fix.t/0.45,0,1);fT={x:fT.x+(tip.x-fT.x)*r,y:fT.y+(tip.y-fT.y)*r};}
  }else if(P.reach>0&&umb&&!umb.gone){const dx=umb.cx-sh.x,dy=umb.cy-sh.y,d=Math.hypot(dx,dy)||1;
    nT={x:sh.x+dx/d*0.6,y:sh.y+dy/d*0.6};fT={x:sh.x+dx/d*0.55,y:sh.y+dy/d*0.5};}
  else{nT=hood;fT=tuck;}
  const fa=armIK({x:sh.x+0.03,y:sh.y},fT.x,fT.y),na=armIK(sh,nT.x,nT.y);
  // far leg & boot
  limb(J.hip,J.kR,J.aR,0.12,trouD);
  ctx.strokeStyle=boot;ctx.lineWidth=0.08*S;line(J.aR.x+0.03,0.035,J.aR.x-0.1,0.035);
  // far arm
  limb({x:sh.x+0.03,y:sh.y},{x:fa.ex,y:fa.ey},{x:fa.hx,y:fa.hy},0.085,coatD);dot(fa.hx,fa.hy,0.04,'#c39778');
  // near leg
  limb(J.hip,J.kF,J.aF,0.125,trou);
  ctx.strokeStyle=boot;ctx.lineWidth=0.085*S;line(J.aF.x+0.03,0.038,J.aF.x-0.11,0.038);
  // coat
  const ta=J.ta,tdx=-Math.sin(ta),tdy=Math.cos(ta),pxv=Math.cos(ta),pyv=Math.sin(ta);
  const fl=clamp(Umean/28,0,1),flap=fl*(0.13+0.05*Math.sin(T*13)+0.03*Math.sin(T*29));
  ctx.fillStyle=coat;ctx.beginPath();
  ctx.moveTo(X(J.neck.x-pxv*0.11),Y(J.neck.y-pyv*0.11));
  ctx.lineTo(X(J.neck.x+pxv*0.12),Y(J.neck.y+pyv*0.12));
  ctx.lineTo(X(J.hip.x+pxv*0.15),Y(J.hip.y+pyv*0.15));
  ctx.lineTo(X(J.hip.x-tdx*0.22+pxv*0.17+flap),Y(J.hip.y-tdy*0.22+pyv*0.17+0.05*fl));
  ctx.lineTo(X(J.hip.x-tdx*0.2-pxv*0.15+flap*0.4),Y(J.hip.y-tdy*0.2-pyv*0.15));
  ctx.lineTo(X(J.hip.x-pxv*0.14),Y(J.hip.y-pyv*0.14));
  ctx.closePath();ctx.fill();
  ctx.strokeStyle=coat;ctx.lineWidth=0.25*S;line(J.hip.x+tdx*0.08,J.hip.y+tdy*0.08,J.neck.x-tdx*0.04,J.neck.y-tdy*0.04);
  // head with hood
  dot(J.head.x+0.015,J.head.y+0.005,0.125,coat);
  dot(J.head.x-0.035,J.head.y-0.012,0.078,skin);
  ctx.strokeStyle=coatD;ctx.lineWidth=0.02*S;ctx.beginPath();ctx.arc(X(J.head.x+0.015),Y(J.head.y+0.005),0.125*S,Math.PI*0.65,Math.PI*1.45);ctx.stroke();
  // near arm
  limb(sh,{x:na.ex,y:na.ey},{x:na.hx,y:na.hy},0.09,coat);dot(na.hx,na.hy,0.043,skin);
}
function drawRain(){
  ctx.strokeStyle='rgba(185,205,235,0.38)';ctx.lineWidth=1;ctx.beginPath();
  for(let i=0;i<NR;i++){ctx.moveTo(X(rx[i]),Y(ry[i]));ctx.lineTo(X(rx[i]-rvx[i]*0.025),Y(ry[i]-rvy[i]*0.025));}
  ctx.stroke();
  ctx.fillStyle='rgba(200,220,245,0.6)';
  for(const s of splashes){ctx.fillRect(X(s.x)-1,Y(s.y)-1,2,2);}
}
function draw(){
  ctx.setTransform(1,0,0,1,0,0);ctx.drawImage(bgc,0,0);
  ctx.setTransform(DPR,0,0,DPR,0,0);
  drawLamp();drawStreaks();
  if(umb)drawUmb(umb);
  drawPerson();
  drawRain();
}

/* ---------------- HUD & input ---------------- */
const elS=document.getElementById('spd'),elSub=document.getElementById('sub'),elG=document.getElementById('gust'),
  elM=document.getElementById('mode'),elSt=document.getElementById('stat'),bGrip=document.getElementById('bGrip'),
  bFrame=document.getElementById('bFrame'),sl=document.getElementById('sl'),bAuto=document.getElementById('auto');
const BF=[0.5,1.6,3.4,5.5,8,10.8,13.9,17.2,20.8,24.5,28.5,32.7];
const BN=['Calm','Light air','Light breeze','Gentle breeze','Moderate breeze','Fresh breeze','Strong breeze','Near gale','Gale','Strong gale','Storm','Violent storm','Hurricane force'];
function beaufort(v){let b=0;while(b<BF.length&&v>=BF[b])b++;return b;}
function setAuto(on){auto=on;bAuto.classList.toggle('on',on);bAuto.textContent=on?'Auto: rising':'Auto: off';}
bAuto.onclick=()=>setAuto(!auto);
sl.oninput=()=>{windSet=+sl.value;setAuto(false);};
document.getElementById('newu').onclick=()=>newUmb();
function resetAll(){windSet=2;Umean=2;setAuto(true);sl.value=2;umbCount=0;P.beta=0;P.bdot=0;P.tauS=0;P.Fsx=P.Fsy=0;newUmb();}
addEventListener('keydown',e=>{
  const k=e.key;
  if(k==='ArrowUp'||k==='+'||k==='='){windSet=Math.min(WMAX,windSet+1);setAuto(false);sl.value=windSet;e.preventDefault();}
  else if(k==='ArrowDown'||k==='-'){windSet=Math.max(0,windSet-1);setAuto(false);sl.value=windSet;e.preventDefault();}
  else if(k==='a'||k==='A')setAuto(!auto);
  else if(k==='n'||k==='N')newUmb();
  else if(k==='r'||k==='R')resetAll();
});
function hud(){
  const b=beaufort(Umean);
  elS.innerHTML=Umean.toFixed(1)+' <small>m/s mean</small>';
  elSub.textContent=Math.round(Umean*3.6)+' km/h · Beaufort '+b+' — '+BN[b];
  let gx=-0.2,gy=1.6;if(umb&&!umb.gone){geom(umb,P.Hx,P.Hy);gx=G.cx;gy=G.cy;}
  wind(gx,gy);elG.textContent='gust at the canopy: '+Math.hypot(WX,WY).toFixed(1)+' m/s ('+Math.round(Math.hypot(WX,WY)*3.6)+' km/h)';
  elM.textContent=(auto?'wind rising on its own':'manual wind')+' · rain on you: '+P.hitRate.toFixed(0)+' drops/s';
  const lines=[];let grip=0,frame=0;
  if(umb){
    if(umb.gone)lines.push('Umbrella #'+umbCount+' is gone — '+umb.why+'.\nFetching another…');
    else if(!umb.held)lines.push('Umbrella #'+umbCount+' '+umb.why+'.\nIt is tumbling away.');
    else{
      lines.push(P.two>0.5?'Two hands, leaning in, braced':'One hand, relaxed');
      grip=Math.hypot(P.Fsx,P.Fsy)/umb.fGrip;
      for(const sd of umb.sides){
        frame=Math.max(frame,sd.load/STRUT_BREAK);
        const where=sd.n[4].x<sd.n[0].x?'upwind':'downwind';
        if(sd.broken)lines.push(where+' rib snapped');
        else if(sd.state)lines.push(where+' half inside out'+(sd.inv>1?' (×'+sd.inv+')':''));
        else if(sd.inv>0)lines.push(where+' rib bent from '+sd.inv+' inversion'+(sd.inv>1?'s':''));
      }
      if(umb.sat)lines.push('being wrenched sideways — wrist at its limit');
      if(umb.slip>0.05)lines.push('handle slipping…');
      if(P.fix)lines.push('reaching up to pull it back the right way');
    }
  }
  elSt.textContent=lines.join('\n');
  bGrip.style.width=Math.min(100,grip*100)+'%';bGrip.style.background=grip>1?'#ff6a5a':grip>0.75?'#ffb35a':'#7fc4ff';
  bFrame.style.width=Math.min(100,frame*100)+'%';bFrame.style.background=frame>0.8?'#ff6a5a':frame>0.55?'#ffb35a':'#7fc4ff';
}

/* ---------------- loop ---------------- */
let last=performance.now(),acc=0,hudT=0;
personPrep(0);newUmb();rainInit();
function frame(now){
  let dt=(now-last)/1000;last=now;if(!(dt>0))dt=1/60;if(dt>1/30)dt=1/30;
  if(auto){windSet=Math.min(WMAX,windSet+RAMP*dt);sl.value=windSet;}
  Umean+=(windSet-Umean)*Math.min(1,dt/1.5);
  LULL=1+0.06*Math.sin(0.05*T+1);
  personPrep(dt);
  acc+=dt;let n=Math.floor(acc/HSTEP);if(n>40){n=40;acc=0;}else acc-=n*HSTEP;
  const H0x=P.Hx,H0y=P.Hy,H1x=P.Hnx,H1y=P.Hny,hvx=(H1x-H0x)/dt,hvy=(H1y-H0y)/dt;
  umb.accFx=umb.accFy=0;umb.accN=0;
  for(let k=0;k<n;k++){T+=HSTEP;Dadv+=Umean*HSTEP;const f=(k+1)/n;
    if(!umb.gone)stepUmb(umb,HSTEP,H0x+(H1x-H0x)*f,H0y+(H1y-H0y)*f,hvx,hvy);}
  P.Hx=H1x;P.Hy=H1y;
  if(umb.held&&umb.accN>0){P.Fax=umb.accFx/umb.accN;P.Fay=umb.accFy/umb.accN;}else{P.Fax=0;P.Fay=0;}
  P.Fsx+=(P.Fax-P.Fsx)*Math.min(1,dt/0.08);P.Fsy+=(P.Fay-P.Fsy)*Math.min(1,dt/0.08);
  personDyn(dt);
  if(!umb.held){
    umb.freeT+=dt;
    if(!umb.gone&&(umb.cx>viewR()+1.5||umb.cx<viewL()-2||umb.cy>viewT()+3))umb.gone=true;
    if(umb.gone){umb.goneT+=dt;if(umb.goneT>2.5)newUmb();}
    else if(umb.freeT>8)newUmb();
  }
  rainStep(dt);
  draw();
  hudT-=dt;if(hudT<=0){hud();hudT=0.12;}
  requestAnimationFrame(frame);
}
requestAnimationFrame(frame);
</script>
</body>
</html>

What it actually does

These notes describe what the model is built to produce. I have not watched it run, and I cannot test it here. The thresholds (knuckle stiffness, grip limits, stretcher break load) are estimates from rough force arithmetic, not values tuned on screen. The timings below are where I expect things to land, not where I saw them land.

Where it should look right

Inversion snaps. The knuckle has two wells, so the rim visibly strains upward and then flips. It does not fade from one state to the other.
Inversion sticks. At low wind, the person reaches up and pulls the inverted half back.
Damage accumulates. Each flip bends the rib a little, so a battered umbrella inverts sooner.
Gusts sway the person. The person leans by balancing at the ankles, with a lagging feedforward. A gust rocks them before they settle. When the umbrella is ripped away mid-gust, they lurch forward into the wind, because they were leaning on a force that has vanished. That is what a person really does.
The person adapts as wind rises. They widen their stance, crouch, switch to two hands, and point the crown into the wind like a shield.
The failure order is roughly right. Expect flex first, then flips of the downwind rim on updrafts, then wrenching as the wrist hits its torque limit, then the handle slipping and the umbrella tumbling off.
Rain angle and speed follow the local gust field. The streak length shows speed. The canopy and the person intercept drops, and a counter reports how many hit the person.

Where it is wrong or simplified

Two ribs, not eight. A real umbrella inverts as a ring: one panel goes, the neighbours get dragged with it, and it often ends up half-inside-out and lopsided. Here each half flips independently, and the 3D fabric between ribs is reduced to a hoop limit.
No fabric flutter or luffing. The real hallmark of a gale is the cloth slapping and the rim buzzing just before failure. My canopy is a set of springy rods with smooth pressure on them, so it bends cleanly instead of shuddering.
Inversion may come too late. Cheap umbrellas flip around 10–13 m/s gusts. With my numbers it probably needs a strong updraft at that speed, or more like 16–20 m/s mean. Lowering K_KN makes it fold earlier.
Pointing into the wind does not pop it back. In reality, pointing an inverted umbrella into the wind often fixes it. Here the flow on the inverted rim is too weak against the knuckle spring. Recovery is mostly the scripted hand pull.
The hand pull is a cheat. The free hand reaches toward the inverted rim, often from beyond arm's length, and a spring force does the work. The arm never actually has to get there.
The person is a controller with a script. Tilt, grip and stance follow rules from the smoothed wind. The person never steps, slides, turns their back to the wind, or lowers the umbrella to their side. The umbrella is never closed. The arm compliance is a single spring.
Coupling is quasi-static. Canopy forces go straight to the shaft as if the ribs were massless when transmitting load. Fast whipping of the ribs therefore does not kick the handle the way a real one does.
Free flight is crude. The escaped umbrella is a rigid stick with floppy rib tips, and ground contact is a two-point bounce. It skates and tumbles plausibly but not accurately, and it never cartwheels on its rim.
The wind field is fake turbulence. It is a handful of sines advected downstream: the pattern repeats over long times and has no eddies shed by the umbrella or the person. Shielding and wake are absent, so rain falls straight through the "lee" of the canopy.

Attachments

anthropic/claude-opus-5.5 — page