Run Detail

completedclaude-opus-5.5

95excellent

Every model's answer from this round

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Provider

openrouter

Challenge Version

v1.1

Turns

Duration

Batched — not timed

Total Tokens

68,865

Input Tokens

708

Output Tokens

68,157

Reasoning Tokens

47,721

Reasoning Effort

default

Est. Cost

$0.6830

Started

10/26/2026, 1:23:31 PM

OR Provider

Anthropic

Finish Reason

stop

Generation ID

gen-batch-1793021010-f5b36056796517bbda01

Turns (1)

Turn #1

708 in68,157 out47,721 reasoning68,865 total

user

You build physics toys, and you have watched someone try the tablecloth trick at a family dinner.

Build me a single HTML page: a table set for dinner, and a tablecloth I can yank out from under it.

The build

A table with a cloth and at least six objects on it: plates, glasses, a candlestick, a bowl. They differ in mass and contact area with the cloth.
A pull-speed control shown on screen in feet per second, with a button to yank the cloth.
Motion comes from friction and inertia, not a scripted rule keyed to pull speed. A slow pull drags the setting along with the cloth and off the edge. A fast pull leaves the objects standing. Between those speeds, some objects slide, some tip, and some fall.
Objects can slide, tip over, collide with each other, fall off the table, and hit the floor.
Keep simulating until everything has stopped moving. Then show a count: how many objects remain on the table, and how many remain upright.
A reset control restores the starting layout.
Loading the page as #speed=12 sets the pull speed to 12 ft/s and pulls one second after load. Any number works.
The art is yours.

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 prediction

One paragraph, before the file: the lowest pull speed at which every object stays on the table, and the speed below which no object stays on the table, as two numbers in ft/s. State the arithmetic using your masses, friction coefficients, and cloth length.

The page

The single fenced html block.

What it actually does

Where it behaves like the physical trick and where it does not. Name any special cases, scripted wobbles, or fall thresholds. Everyone has seen this trick fail; say how yours fails before I find out.

assistant

The prediction

Everything should stay on the table at about 17.3 ft/s and above. Nothing should stay below about 4.6 ft/s.

These numbers come from a single-body Coulomb analysis that uses the page's own parameters:

Geometry. g = 32.2 ft/s². The table is W = 6 ft long. The cloth hangs O = 0.5 ft over the trailing (left) edge and is yanked to the right. An object whose base centre sits at x has L = x + 0.5 ft of cloth behind it and D = 6 − x ft to the edge it falls over.
Riding. Cloth friction accelerates the object at a = μc·g. If v < √(2aL), the object reaches cloth speed before the cloth's tail passes under it. It then rides the cloth off the edge.
Slipping. Otherwise it leaves the cloth at u = v − √(v² − 2aL). It slides a total of d = (u²/2g)(1/μc + 1/μt), where μt is its friction on the bare table.
Stay condition. Setting d = D gives u* = √(2gD/(1/μc + 1/μt)) and v = aL/u* + u*/2. If u* ≥ √(2aL), the threshold is simply the riding speed √(2aL).

The binding objects:

Water glass (x = 4.8, μc 0.30, μt 0.26, L = 5.3, D = 1.2):
- u* = √(77.28/7.179) = 3.28 ft/s
- aL = 51.2
- v = 51.2/3.28 + 1.64 = 17.25 ft/s
Candlestick (x = 0.6, μc 0.30, μt 0.28, L = 1.1, D = 5.4):
- Riding threshold √(2·9.66·1.1) = 4.61 ft/s.
- At that speed it slides only 21.25/64.4 × 6.905 = 2.28 ft, well short of 5.4 ft.

The others fall between those two:

Object	x	μc	μt	Threshold
Plate	1.4	0.22	0.20	5.19 ft/s (riding threshold)
Bowl	3.1	0.25	0.22	8.54 ft/s
Wine glass	2.2	0.42	0.22	9.11 ft/s
Second plate	4.0	0.22	0.20	10.52 ft/s

The wine glass's centre of mass is at 0.336 ft with a 0.11 ft half-base, so its tip threshold is μ ≈ 0.33. Under cloth friction of 0.42 it should also topple during the pull, by a rough energy estimate, somewhere up to about 11–12 ft/s.

The page

<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width,initial-scale=1">
<title>The Tablecloth Trick</title>
<style>
:root{--bg:#17130f;--panel:#241d17;--ink:#f3e9da;--dim:#b4a48e;--acc:#e3a54c;--line:#3b3129}
*{box-sizing:border-box}
body{margin:0;background:var(--bg);color:var(--ink);font:14px/1.45 Georgia,"Times New Roman",serif}
header{padding:12px 16px 6px;display:flex;align-items:baseline;gap:14px;flex-wrap:wrap}
h1{margin:0;font-size:21px;font-weight:normal;letter-spacing:.04em}
header span{color:var(--dim);font-style:italic}
.bar{display:flex;flex-wrap:wrap;gap:10px 18px;align-items:center;padding:9px 16px;background:var(--panel);border-top:1px solid var(--line);border-bottom:1px solid var(--line);font-family:system-ui,sans-serif;font-size:13px}
.bar label{display:flex;align-items:center;gap:8px}
#spd{width:220px;accent-color:var(--acc)}
#spdNum{width:72px;background:#120f0c;color:var(--ink);border:1px solid var(--line);padding:3px 5px;font:inherit}
#spdLbl{font:600 18px/1 ui-monospace,Menlo,monospace;color:var(--acc);min-width:150px}
button{font:600 13px system-ui,sans-serif;padding:7px 16px;border-radius:4px;border:1px solid #7a5a2a;background:#3a2a17;color:var(--ink);cursor:pointer}
button#yank{background:#8c2f22;border-color:#c0503c}
button:disabled{opacity:.45;cursor:default}
select{background:#120f0c;color:var(--ink);border:1px solid var(--line);font:inherit;padding:2px}
#wrap{width:100%;max-width:1280px;margin:0 auto}
canvas{display:block;width:100%}
#status{padding:8px 16px;font:13px ui-monospace,Menlo,monospace;color:var(--dim);min-height:2.6em}
#result{padding:4px 16px 10px;font-size:17px;color:var(--acc);min-height:1.6em}
table{border-collapse:collapse;font:12.5px system-ui,sans-serif;margin:0 16px 22px;color:var(--ink)}
th,td{padding:4px 9px;border-bottom:1px solid var(--line);text-align:right;white-space:nowrap}
th{color:var(--dim);font-weight:600}
td:first-child,th:first-child,td:last-child,th:last-child{text-align:left}
.ok{color:#9fd28b}.bad{color:#f08a74}
.note{color:var(--dim);font:12px system-ui,sans-serif;padding:0 16px 24px;max-width:900px}
</style>
</head>
<body>
<div id="wrap">
<header><h1>The Tablecloth Trick</h1><span>friction, inertia, and a little nerve</span></header>
<div class="bar">
  <label>Pull speed <input id="spd" type="range" min="0.5" max="40" step="0.5" value="12"></label>
  <input id="spdNum" type="number" step="0.1" value="12" title="any number, ft/s">
  <span id="spdLbl">12.0 ft/s</span>
  <button id="yank">Yank the cloth</button>
  <button id="reset">Reset table</button>
  <label>Sim speed <select id="tscale"><option value="0.1">0.1×</option><option value="0.25">0.25×</option><option value="1" selected>1×</option><option value="4">4×</option></select></label>
  <label><input id="hulls" type="checkbox"> show collision hulls</label>
</div>
<canvas id="c"></canvas>
<div id="status"></div>
<div id="result"></div>
<table>
  <thead><tr><th>Object</th><th>mass (lb)</th><th>base (in)</th><th>μ cloth</th><th>μ table</th><th>cloth behind (ft)</th><th>to edge (ft)</th><th>single-body: stays if v ≥</th><th>what happened</th></tr></thead>
  <tbody id="tb"></tbody>
</table>
<p class="note" id="pred"></p>
</div>
<script>
(function(){
'use strict';
const G=32.2, TOP=2.5, W=6, O=0.5;
const VIEW={x0:-1.8,x1:9.2,y0:-0.45,y1:4.55};
const UPRIGHT=0.30;      // rad (~17°)
const SLOP=0.002;

function rect(x0,y0,x1,y1){return [[x0,y0],[x1,y0],[x1,y1],[x0,y1]];}
function trap(y0,w0,y1,w1){return [[-w0/2,y0],[w0/2,y0],[w1/2,y1],[-w1/2,y1]];}
const PLATE_HULL=[[-0.25,0],[0.25,0],[0.425,0.055],[0.425,0.07],[-0.425,0.07],[-0.425,0.055]];
const BOWL_HULL=[[-0.15,0],[0.15,0],[0.29,0.17],[0.31,0.26],[-0.31,0.26],[-0.29,0.17]];

const DEFS=[
 {id:'candle',name:'Brass candlestick',x:0.6,m:2.2,muC:0.30,muT:0.28,base:0.30,
  hull:[[-0.15,0],[0.15,0],[0.15,0.06],[0.035,1.15],[-0.035,1.15],[-0.15,0.06]],
  parts:[{p:rect(-0.15,0,0.15,0.06),d:6},{p:trap(0.06,0.06,0.85,0.04),d:3},{p:rect(-0.035,0.85,0.035,1.15),d:1}],draw:drawCandle},
 {id:'plate1',name:'Dinner plate',x:1.4,m:1.4,muC:0.22,muT:0.20,base:0.5,hull:PLATE_HULL,parts:[{p:PLATE_HULL,d:1}],draw:drawPlate},
 {id:'wine',name:'Wine glass',x:2.2,m:0.45,muC:0.42,muT:0.22,base:0.22,
  hull:[[-0.11,0],[0.11,0],[0.135,0.5],[0.125,0.72],[-0.125,0.72],[-0.135,0.5]],
  parts:[{p:rect(-0.11,0,0.11,0.015),d:4},{p:rect(-0.01,0.015,0.01,0.32),d:4},{p:trap(0.32,0.2,0.72,0.25),d:0.5}],draw:drawWine},
 {id:'bowl',name:'Serving bowl',x:3.1,m:1.1,muC:0.25,muT:0.22,base:0.30,hull:BOWL_HULL,parts:[{p:BOWL_HULL,d:1}],draw:drawBowl},
 {id:'plate2',name:'Dinner plate',x:4.0,m:1.4,muC:0.22,muT:0.20,base:0.5,hull:PLATE_HULL,parts:[{p:PLATE_HULL,d:1}],draw:drawPlate},
 {id:'water',name:'Water glass',x:4.8,m:0.7,muC:0.30,muT:0.26,base:0.20,hull:trap(0,0.2,0.55,0.25),
  parts:[{p:rect(-0.1,0,0.1,0.05),d:5},{p:trap(0.05,0.19,0.38,0.22),d:1},{p:trap(0.38,0.22,0.55,0.25),d:0.15}],draw:drawWater}
];

// ---------- single-body prediction (same parameters the sim uses) ----------
function predict(d){
  const a=d.muC*G, L=d.x+O, D=W-d.x, vr=Math.sqrt(2*a*L);
  const um=Math.sqrt(2*G*D/(1/d.muC+1/d.muT));
  return um>=vr? vr : a*L/um+um/2;
}

// ---------- mass properties ----------
function polyMP(v){
  let A=0,cx=0,cy=0,I=0;const n=v.length;
  for(let i=0;i<n;i++){const x0=v[i][0],y0=v[i][1],x1=v[(i+1)%n][0],y1=v[(i+1)%n][1];
    const c=x0*y1-x1*y0;A+=c;cx+=(x0+x1)*c;cy+=(y0+y1)*c;I+=c*(x0*x0+x0*x1+x1*x1+y0*y0+y0*y1+y1*y1);}
  A/=2;cx/=(6*A);cy/=(6*A);I/=12;return {A,cx,cy,I};
}
function makeBody(def){
  let M=0,mx=0,my=0,Io=0;
  for(const p of def.parts){const q=polyMP(p.p);const mm=q.A*p.d;M+=mm;mx+=mm*q.cx;my+=mm*q.cy;Io+=q.I*p.d;}
  const cx=mx/M,cy=my/M;let Ic=(Io-M*(cx*cx+cy*cy))*(def.m/M);
  const verts=def.hull.map(([x,y])=>[x-cx,y-cy]);
  return {def,name:def.name,verts,wv:verts.map(v=>v.slice()),com:[cx,cy],m:def.m,im:1/def.m,iI:1/Ic,I:Ic,
    muC:def.muC,muT:def.muT,x:def.x+cx,y:TOP+cy,a:0,vx:0,vy:0,w:0,x0:def.x+cx,
    lit:true,spilled:false,cracked:false,cracks:null,static:false};
}
function makeStatic(kind,verts){
  const s={static:true,kind,verts,wv:verts.map(v=>v.slice()),im:0,iI:0,vx:0,vy:0,w:0,x:0,y:0};
  s.minx=Math.min(...verts.map(v=>v[0]));s.maxx=Math.max(...verts.map(v=>v[0]));
  s.miny=Math.min(...verts.map(v=>v[1]));s.maxy=Math.max(...verts.map(v=>v[1]));return s;
}
const statics=[
  makeStatic('table',rect(0,2.2,W,TOP)),
  makeStatic('floor',rect(-30,-3,40,0)),
  makeStatic('wall',rect(-8,-3,VIEW.x0,14)),
  makeStatic('wall',rect(VIEW.x1,-3,16,14))
];

// ---------- state ----------
let bodies=[],speed=12,vPull=12,pulling=false,tPull=0,done=false,still=0,acc=0,simT=0,timeScale=1,showHulls=false;
let lastFrame=performance.now(),settleT=0;

function clothTrail(){return -O+(pulling?vPull*tPull:0);}

function upd(b){
  const c=Math.cos(b.a),s=Math.sin(b.a);let a=1e9,bb=1e9,cc=-1e9,dd=-1e9;
  for(let i=0;i<b.verts.length;i++){const lx=b.verts[i][0],ly=b.verts[i][1];
    const x=b.x+c*lx-s*ly,y=b.y+s*lx+c*ly;b.wv[i][0]=x;b.wv[i][1]=y;
    if(x<a)a=x;if(x>cc)cc=x;if(y<bb)bb=y;if(y>dd)dd=y;}
  b.minx=a-0.01;b.miny=bb-0.01;b.maxx=cc+0.01;b.maxy=dd+0.01;
}
function inside(P,Q,out){
  const q=Q.wv,n=q.length;
  for(const p of P.wv){
    let best=-1e9,bnx=0,bny=0,ok=true;
    for(let i=0;i<n;i++){const a=q[i],b=q[(i+1)%n];const ex=b[0]-a[0],ey=b[1]-a[1];const L=Math.hypot(ex,ey);
      const nx=ey/L,ny=-ex/L;const d=(p[0]-a[0])*nx+(p[1]-a[1])*ny;
      if(d>=0){ok=false;break;} if(d>best){best=d;bnx=nx;bny=ny;}}
    if(ok) out.push({A:P,B:Q,px:p[0],py:p[1],nx:bnx,ny:bny,depth:-best});
  }
}
function pair(A,B,out){
  if(A.maxx<B.minx||B.maxx<A.minx||A.maxy<B.miny||B.maxy<A.miny)return;
  inside(A,B,out);inside(B,A,out);
}
function gather(out){
  out.length=0;const n=bodies.length;
  for(let i=0;i<n;i++)for(let j=i+1;j<n;j++)pair(bodies[i],bodies[j],out);
  for(let i=0;i<n;i++)for(const s of statics)pair(bodies[i],s,out);
}
const C=[],C2=[];
function relv(c){
  const A=c.A,B=c.B;
  return [ (A.vx-A.w*c.ray+c.sAx)-(B.vx-B.w*c.rby+c.sBx),
           (A.vy+A.w*c.rax+c.sAy)-(B.vy+B.w*c.rbx+c.sBy) ];
}
function imp(c,px,py){
  const A=c.A,B=c.B;
  A.vx+=px*A.im;A.vy+=py*A.im;A.w+=A.iI*(c.rax*py-c.ray*px);
  B.vx-=px*B.im;B.vy-=py*B.im;B.w-=B.iI*(c.rbx*py-c.rby*px);
}
function makeCracks(b){
  const xs=b.verts.map(v=>v[0]+b.com[0]),ys=b.verts.map(v=>v[1]+b.com[1]);
  const x0=Math.min(...xs),x1=Math.max(...xs),y0=Math.min(...ys),y1=Math.max(...ys);
  const cx=x0+(x1-x0)*(0.3+0.4*Math.random()),cy=y0+(y1-y0)*(0.3+0.4*Math.random());const lines=[];
  for(let k=0;k<5;k++){const ang=Math.random()*6.283;let px=cx,py=cy;const l=[[px,py]];
    for(let s=0;s<4;s++){px+=Math.cos(ang+(Math.random()-0.5))*(x1-x0)*0.12;py+=Math.sin(ang+(Math.random()-0.5))*(y1-y0)*0.18;l.push([px,py]);}
    lines.push(l);}
  return lines;
}

function step(h){
  for(const b of bodies)upd(b);
  gather(C);
  const trail=clothTrail(), vc=pulling?vPull:0, clothOn=trail<W;
  for(const c of C){
    const A=c.A,B=c.B,S=A.static?A:(B.static?B:null);
    c.sAx=c.sAy=c.sBx=c.sBy=0;
    if(!S){c.mu=0.3;c.e=0.1;}
    else{
      const D=S===A?B:A;
      if(S.kind==='table'){
        const onCloth=clothOn&&c.py>TOP-0.04&&c.px>=trail&&c.px<=W+0.03;
        c.mu=onCloth?D.muC:D.muT;c.e=0.1;
        const sv=onCloth?vc:0;if(S===A)c.sAx=sv;else c.sBx=sv;
      }else if(S.kind==='floor'){c.mu=0.45;c.e=0.25;}
      else {c.mu=0.3;c.e=0.2;}
      c.S=S;c.D=D;
    }
    c.rax=c.px-A.x;c.ray=c.py-A.y;c.rbx=c.px-B.x;c.rby=c.py-B.y;
    const rnA=c.rax*c.ny-c.ray*c.nx,rnB=c.rbx*c.ny-c.rby*c.nx;
    c.kn=A.im+B.im+A.iI*rnA*rnA+B.iI*rnB*rnB;
    c.tx=-c.ny;c.ty=c.nx;
    const rtA=c.rax*c.ty-c.ray*c.tx,rtB=c.rbx*c.ty-c.rby*c.tx;
    c.kt=A.im+B.im+A.iI*rtA*rtA+B.iI*rtB*rtB;
    c.jn=0;c.jt=0;
  }
  for(const b of bodies)b.vy-=G*h;
  for(const c of C){
    const r=relv(c),vn=r[0]*c.nx+r[1]*c.ny;
    c.bias=vn<-1.5?-c.e*vn:0;
    if(c.S&&c.S.kind==='floor'&&vn<-9&&!c.D.cracked&&c.D.def.id!=='candle'){c.D.cracked=true;c.D.cracks=makeCracks(c.D);}
  }
  for(let it=0;it<12;it++){
    for(const c of C){
      if(c.kn<=0)continue;
      let r=relv(c);const vn=r[0]*c.nx+r[1]*c.ny;
      let dj=(c.bias-vn)/c.kn;const nj=Math.max(c.jn+dj,0);dj=nj-c.jn;c.jn=nj;
      imp(c,dj*c.nx,dj*c.ny);
      r=relv(c);const vt=r[0]*c.tx+r[1]*c.ty;
      let dt=-vt/c.kt;const mx=c.mu*c.jn;const nt=Math.max(-mx,Math.min(mx,c.jt+dt));dt=nt-c.jt;c.jt=nt;
      imp(c,dt*c.tx,dt*c.ty);
    }
  }
  for(const b of bodies){
    b.x+=b.vx*h;b.y+=b.vy*h;b.a+=b.w*h;b.w*=(1-0.02*h);
  }
  for(const b of bodies)upd(b);
  gather(C2);
  for(const c of C2){
    if(c.depth>SLOP){const k=c.A.im+c.B.im;if(k>0){const m=(c.depth-SLOP)*0.4/k;
      c.A.x+=c.nx*m*c.A.im;c.A.y+=c.ny*m*c.A.im;c.B.x-=c.nx*m*c.B.im;c.B.y-=c.ny*m*c.B.im;}}
  }
  // cosmetic flags only (no effect on motion)
  for(const b of bodies){
    const na=Math.abs(norm(b.a));
    if(b.def.id==='candle'&&b.lit&&na>0.7)b.lit=false;
    if((b.def.id==='wine'||b.def.id==='water')&&!b.spilled&&na>1.0)b.spilled=true;
  }
  if(pulling){
    tPull+=h;simT+=h;
    const gone=clothTrail()>=W||vPull===0;
    let moving=false;
    for(const b of bodies)if(Math.hypot(b.vx,b.vy)>0.05||Math.abs(b.w)>0.15){moving=true;break;}
    if(gone&&!moving)still+=h;else still=0;
    const timeout=vPull>0?(W+O)/vPull+30:5;
    if(still>0.5||tPull>timeout)finish(still>0.5);
  }
}
function norm(a){return Math.atan2(Math.sin(a),Math.cos(a));}
function onTable(b){return b.y>TOP&&b.x>0&&b.x<W;}
function isUp(b){return Math.abs(norm(b.a))<UPRIGHT;}
function curH(){return (pulling&&vPull>0&&clothTrail()<W)?Math.min(1/1000,0.01/vPull):1/1000;}

// ---------- control ----------
function reset(){
  bodies=DEFS.map(makeBody);pulling=false;tPull=0;done=false;still=0;acc=0;simT=0;
  for(let i=0;i<300;i++)step(1/1000);
  for(const b of bodies){b.x0=b.x;}
  document.getElementById('yank').disabled=false;
  document.getElementById('result').textContent='';
  fillTable(false);
}
function yank(){
  if(pulling)return;
  vPull=speed;pulling=true;tPull=0;still=0;acc=0;done=false;
  document.getElementById('yank').disabled=true;
  document.getElementById('result').textContent='';
}
function finish(settled){
  done=true;settleT=tPull;
  let on=0,up=0,upOn=0;
  for(const b of bodies){const o=onTable(b),u=isUp(b);if(o)on++;if(u)up++;if(o&&u)upOn++;}
  const n=bodies.length;
  document.getElementById('result').textContent=
    (settled?`Everything stopped at t = ${tPull.toFixed(2)} s. `:`Gave up waiting at t = ${tPull.toFixed(1)} s. `)+
    `On the table: ${on} of ${n}. Upright: ${up} of ${n} (${upOn} on the table, ${up-upOn} on the floor).`;
  fillTable(true);
}
function fate(b){
  const na=Math.abs(norm(b.a));let s=onTable(b)?'on table':'on floor';
  if(na<UPRIGHT)s+=', upright';else if(na>Math.PI-0.45)s+=', upside down';else s+=', on its side';
  if(onTable(b))s+=`, moved ${(b.x-b.x0).toFixed(2)} ft`;
  if(b.cracked)s+=' (cracked)';
  return s;
}
function fillTable(withFate){
  const tb=document.getElementById('tb');tb.innerHTML='';
  bodies.forEach(b=>{const d=b.def,thr=predict(d);
    let f='—';
    if(withFate){const predStay=vPull>=thr,st=onTable(b);
      f=`<span class="${predStay===st?'ok':'bad'}">${fate(b)}${predStay===st?'':' — prediction said '+(predStay?'stay':'fall')}</span>`;}
    const tr=document.createElement('tr');
    tr.innerHTML=`<td>${d.name}</td><td>${d.m.toFixed(2)}</td><td>${(d.base*12).toFixed(1)}</td><td>${d.muC.toFixed(2)}</td><td>${d.muT.toFixed(2)}</td><td>${(d.x+O).toFixed(1)}</td><td>${(W-d.x).toFixed(1)}</td><td>${thr.toFixed(2)} ft/s</td><td>${f}</td>`;
    tb.appendChild(tr);});
}
function setSpeed(v){
  if(!isFinite(v))v=(v===Infinity||v===-Infinity)?1e9:12;
  v=Math.min(Math.abs(v),1e9);speed=v;
  const s=document.getElementById('spd'),nb=document.getElementById('spdNum');
  s.value=Math.max(0.5,Math.min(40,v));
  if(document.activeElement!==nb)nb.value=+v.toFixed(3);
  document.getElementById('spdLbl').textContent=`${v<1000?v.toFixed(1):v.toExponential(2)} ft/s (${(v*0.6818).toFixed(1)} mph)`;
}
document.getElementById('spd').addEventListener('input',e=>setSpeed(parseFloat(e.target.value)));
document.getElementById('spdNum').addEventListener('change',e=>{const v=parseFloat(e.target.value);if(!isNaN(v))setSpeed(v);});
document.getElementById('yank').addEventListener('click',yank);
document.getElementById('reset').addEventListener('click',reset);
document.getElementById('tscale').addEventListener('change',e=>{timeScale=parseFloat(e.target.value);});
document.getElementById('hulls').addEventListener('change',e=>{showHulls=e.target.checked;});

function readHash(){
  const m=/speed=([^&]*)/i.exec(location.hash);if(!m)return null;
  const v=parseFloat(decodeURIComponent(m[1]));return isNaN(v)?null:v;
}
let hashTimer=null;
function fromHash(){const v=readHash();if(v===null)return;reset();setSpeed(v);clearTimeout(hashTimer);hashTimer=setTimeout(yank,1000);}
window.addEventListener('hashchange',fromHash);

// ---------- rendering ----------
const cv=document.getElementById('c'),ctx=cv.getContext('2d');
let S=100,CW=1000,CH=450,dpr=1;
function resize(){
  dpr=window.devicePixelRatio||1;CW=cv.parentElement.clientWidth;S=CW/(VIEW.x1-VIEW.x0);
  CH=Math.round(S*(VIEW.y1-VIEW.y0));cv.width=Math.round(CW*dpr);cv.height=Math.round(CH*dpr);cv.style.height=CH+'px';
}
window.addEventListener('resize',resize);
let now=0;

function drawRoom(){
  // wall
  ctx.fillStyle='#2b3a31';ctx.fillRect(VIEW.x0,0,VIEW.x1-VIEW.x0,VIEW.y1);
  ctx.fillStyle='#31433a';
  for(let x=Math.floor(VIEW.x0);x<VIEW.x1;x+=0.5)ctx.fillRect(x,1.25,0.22,VIEW.y1);
  ctx.fillStyle='rgba(212,180,110,0.07)';
  for(let x=Math.floor(VIEW.x0)+0.25;x<VIEW.x1;x+=0.5)for(let y=1.6;y<VIEW.y1;y+=0.5){ctx.beginPath();ctx.arc(x,y,0.035,0,6.283);ctx.fill();}
  // wainscot
  const wg=ctx.createLinearGradient(0,0,0,1.25);wg.addColorStop(0,'#3a2417');wg.addColorStop(1,'#56361f');
  ctx.fillStyle=wg;ctx.fillRect(VIEW.x0,0,VIEW.x1-VIEW.x0,1.25);
  ctx.strokeStyle='rgba(0,0,0,0.35)';ctx.lineWidth=0.02;
  for(let x=VIEW.x0+0.15;x<VIEW.x1;x+=1.1)ctx.strokeRect(x,0.3,0.9,0.8);
  ctx.fillStyle='#6b4527';ctx.fillRect(VIEW.x0,1.22,VIEW.x1-VIEW.x0,0.06);
  ctx.fillStyle='#24160d';ctx.fillRect(VIEW.x0,0,VIEW.x1-VIEW.x0,0.22);
  // window
  const wx0=6.9,wx1=8.7,wy0=2.35,wy1=4.25;
  const sky=ctx.createLinearGradient(0,wy0,0,wy1);sky.addColorStop(0,'#1b2a4a');sky.addColorStop(1,'#0a1022');
  ctx.fillStyle=sky;ctx.fillRect(wx0,wy0,wx1-wx0,wy1-wy0);
  ctx.fillStyle='#f4ecc8';ctx.beginPath();ctx.arc(8.15,3.85,0.16,0,6.283);ctx.fill();
  ctx.fillStyle='#1b2a4a';ctx.beginPath();ctx.arc(8.22,3.9,0.14,0,6.283);ctx.fill();
  ctx.fillStyle='rgba(255,255,230,0.8)';
  [[7.2,4.0],[7.5,3.6],[7.9,4.1],[8.5,3.4],[7.3,3.0],[8.3,2.9]].forEach(p=>ctx.fillRect(p[0],p[1],0.025,0.025));
  ctx.strokeStyle='#d8cdb5';ctx.lineWidth=0.06;ctx.strokeRect(wx0,wy0,wx1-wx0,wy1-wy0);
  ctx.lineWidth=0.035;ctx.beginPath();ctx.moveTo((wx0+wx1)/2,wy0);ctx.lineTo((wx0+wx1)/2,wy1);ctx.moveTo(wx0,(wy0+wy1)/2);ctx.lineTo(wx1,(wy0+wy1)/2);ctx.stroke();
  ctx.fillStyle='#cfc2a6';ctx.fillRect(wx0-0.1,wy0-0.09,wx1-wx0+0.2,0.06);
  // painting
  ctx.fillStyle='#b08a3e';ctx.fillRect(0.9,3.1,1.5,1.05);
  const pg=ctx.createLinearGradient(1,3.2,2.3,4.05);pg.addColorStop(0,'#5c3a2a');pg.addColorStop(1,'#a8683a');
  ctx.fillStyle=pg;ctx.fillRect(1.0,3.2,1.3,0.85);
  ctx.fillStyle='#e7cf8e';ctx.beginPath();ctx.ellipse(1.65,3.55,0.28,0.12,0,0,6.283);ctx.fill();
  ctx.fillStyle='#7a2b22';ctx.beginPath();ctx.arc(1.55,3.62,0.07,0,6.283);ctx.arc(1.75,3.6,0.06,0,6.283);ctx.fill();
  // floor
  const fg=ctx.createLinearGradient(0,VIEW.y0,0,0);fg.addColorStop(0,'#3a2414');fg.addColorStop(1,'#6a4426');
  ctx.fillStyle=fg;ctx.fillRect(VIEW.x0,VIEW.y0,VIEW.x1-VIEW.x0,-VIEW.y0);
  ctx.strokeStyle='rgba(0,0,0,0.3)';ctx.lineWidth=0.012;
  for(let y=-0.12;y>VIEW.y0;y-=0.13){ctx.beginPath();ctx.moveTo(VIEW.x0,y);ctx.lineTo(VIEW.x1,y);ctx.stroke();}
  // table shadow
  ctx.fillStyle='rgba(0,0,0,0.35)';ctx.beginPath();ctx.ellipse(3,-0.03,3.4,0.07,0,0,6.283);ctx.fill();
}
function drawTable(){
  const lg=ctx.createLinearGradient(0,0,0.3,0);lg.addColorStop(0,'#3d220f');lg.addColorStop(0.5,'#6e4220');lg.addColorStop(1,'#3d220f');
  ctx.fillStyle=lg;
  [[0.22,0.5],[5.5,5.78]].forEach(([a,b])=>{
    ctx.beginPath();ctx.moveTo(a,2.0);ctx.lineTo(b,2.0);ctx.lineTo(b-0.05,0.15);ctx.lineTo(b-0.02,0);ctx.lineTo(a+0.02,0);ctx.lineTo(a+0.05,0.15);ctx.closePath();ctx.fill();
  });
  ctx.fillStyle='#4a2a13';ctx.fillRect(0.15,1.98,W-0.3,0.24);
  ctx.fillStyle='rgba(0,0,0,0.25)';ctx.fillRect(0.15,1.98,W-0.3,0.03);
  const tg=ctx.createLinearGradient(0,2.2,0,TOP);tg.addColorStop(0,'#4f2d14');tg.addColorStop(0.6,'#7c4b24');tg.addColorStop(1,'#9a6233');
  ctx.fillStyle=tg;ctx.fillRect(0,2.2,W,TOP-2.2);
  ctx.strokeStyle='rgba(30,15,5,0.35)';ctx.lineWidth=0.008;
  for(let i=0;i<4;i++){ctx.beginPath();ctx.moveTo(0,2.25+i*0.06);for(let x=0;x<=W;x+=0.5)ctx.lineTo(x,2.25+i*0.06+Math.sin(x*1.7+i)*0.008);ctx.stroke();}
}
const CLOTH='#f2ece0',HEM='#a8322a';
function handPos(){
  if(!pulling)return [W+0.28,TOP-0.95];
  const d=vPull*tPull,k=Math.min(d,0.6);return [W+0.28+d,TOP-0.95+k*0.7];
}
function drawCloth(){
  const tr=clothTrail();const [hx,hy]=handPos();
  ctx.lineCap='round';ctx.lineJoin='round';
  if(tr<W){
    const x0=Math.max(tr,0);
    ctx.fillStyle=CLOTH;ctx.fillRect(x0,TOP-0.035,W-x0,0.035);
    ctx.fillStyle='rgba(0,0,0,0.12)';ctx.fillRect(x0,TOP-0.035,W-x0,0.008);
    if(tr<0){
      const L=-tr;ctx.fillStyle=CLOTH;ctx.fillRect(-0.035,TOP-L,0.035,L);
      ctx.fillStyle=HEM;ctx.fillRect(-0.035,TOP-L,0.035,Math.min(0.05,L));
    }else{ctx.fillStyle=HEM;ctx.fillRect(x0,TOP-0.035,0.04,0.035);}
    ctx.strokeStyle=CLOTH;ctx.lineWidth=0.05;
    ctx.beginPath();ctx.moveTo(W+0.015,TOP-0.02);
    const cxp=pulling?W+0.05+(hx-W)*0.3:W+0.035,cyp=pulling?TOP-0.08:TOP-0.5;
    ctx.quadraticCurveTo(cxp,cyp,hx,hy);ctx.stroke();
    ctx.strokeStyle='rgba(150,140,120,0.5)';ctx.lineWidth=0.012;ctx.stroke();
  }else{
    ctx.strokeStyle=CLOTH;ctx.lineWidth=0.06;ctx.beginPath();ctx.moveTo(hx,hy);
    for(let i=1;i<=12;i++){ctx.lineTo(hx-i*0.11,hy-i*0.035+Math.sin(i*0.9-now*0.02)*0.035*i/12);}
    ctx.stroke();
    ctx.strokeStyle=HEM;ctx.lineWidth=0.02;ctx.stroke();
  }
  // arm and hand
  ctx.strokeStyle='#4f2328';ctx.lineWidth=0.17;
  ctx.beginPath();ctx.moveTo(hx+0.14,hy+0.06);ctx.lineTo(hx+1.4,hy+0.75);ctx.stroke();
  ctx.strokeStyle='#efe9df';ctx.lineWidth=0.18;ctx.beginPath();ctx.moveTo(hx+0.12,hy+0.05);ctx.lineTo(hx+0.17,hy+0.08);ctx.stroke();
  ctx.fillStyle='#e6b48f';ctx.beginPath();ctx.ellipse(hx+0.02,hy,0.095,0.075,0.5,0,6.283);ctx.fill();
}

// ----- object art, drawn in each body's base frame (y up, ft) -----
function drawCandle(c,b){
  if(b.lit){
    const fl=1+0.08*Math.sin(now*0.021)+0.06*Math.sin(now*0.053);
    const g=c.createRadialGradient(0,1.24,0,0,1.24,0.4);g.addColorStop(0,'rgba(255,205,110,0.35)');g.addColorStop(1,'rgba(255,205,110,0)');
    c.fillStyle=g;c.beginPath();c.arc(0,1.24,0.4,0,6.283);c.fill();
    c.fillStyle='#ffd46b';c.beginPath();c.moveTo(0,1.165);c.quadraticCurveTo(0.045,1.21,0,1.165+0.13*fl);c.quadraticCurveTo(-0.045,1.21,0,1.165);c.fill();
    c.fillStyle='#fff6d8';c.beginPath();c.moveTo(0,1.17);c.quadraticCurveTo(0.018,1.2,0,1.17+0.06*fl);c.quadraticCurveTo(-0.018,1.2,0,1.17);c.fill();
  }
  c.strokeStyle='#222';c.lineWidth=0.008;c.beginPath();c.moveTo(0,1.15);c.lineTo(0,1.175);c.stroke();
  c.fillStyle='#efe5cc';c.fillRect(-0.035,0.85,0.07,0.3);
  c.fillStyle='#e3d6b6';c.fillRect(0.015,0.85,0.02,0.3);
  c.fillStyle='#f6efdc';c.beginPath();c.ellipse(-0.035,1.06,0.008,0.04,0,0,6.283);c.fill();
  const g=c.createLinearGradient(-0.15,0,0.15,0);
  g.addColorStop(0,'#6e4f18');g.addColorStop(0.35,'#d7b25a');g.addColorStop(0.5,'#fff0b0');g.addColorStop(0.7,'#b88a2e');g.addColorStop(1,'#5e4313');
  c.fillStyle=g;c.beginPath();
  c.moveTo(-0.15,0);c.lineTo(0.15,0);c.lineTo(0.15,0.03);c.quadraticCurveTo(0.13,0.06,0.05,0.075);c.lineTo(0.025,0.1);
  c.lineTo(0.02,0.3);c.quadraticCurveTo(0.065,0.34,0.02,0.38);c.lineTo(0.02,0.78);c.lineTo(0.06,0.82);c.lineTo(0.06,0.85);
  c.lineTo(-0.06,0.85);c.lineTo(-0.06,0.82);c.lineTo(-0.02,0.78);c.lineTo(-0.02,0.38);c.quadraticCurveTo(-0.065,0.34,-0.02,0.3);
  c.lineTo(-0.025,0.1);c.lineTo(-0.05,0.075);c.quadraticCurveTo(-0.13,0.06,-0.15,0.03);c.closePath();c.fill();
  c.strokeStyle='rgba(60,40,10,0.6)';c.lineWidth=0.006;c.stroke();
}
function drawPlate(c,b){
  const g=c.createLinearGradient(0,0,0,0.07);g.addColorStop(0,'#bdb8ae');g.addColorStop(1,'#fbf9f4');
  c.fillStyle=g;c.beginPath();c.moveTo(-0.25,0);c.lineTo(0.25,0);c.lineTo(0.27,0.015);c.quadraticCurveTo(0.35,0.045,0.425,0.056);
  c.lineTo(0.425,0.07);c.lineTo(-0.425,0.07);c.lineTo(-0.425,0.056);c.quadraticCurveTo(-0.35,0.045,-0.27,0.015);c.closePath();c.fill();
  c.strokeStyle='#8f8a80';c.lineWidth=0.005;c.stroke();
  c.strokeStyle='#2f5d8a';c.lineWidth=0.009;c.beginPath();c.moveTo(-0.415,0.064);c.lineTo(0.415,0.064);c.stroke();
  c.fillStyle='#9c978c';c.fillRect(-0.25,0,0.5,0.008);
  if(b.cracked)drawCracks(c,b,'rgba(80,80,80,0.9)');
}
function wineBowlPath(c){
  c.beginPath();c.moveTo(-0.01,0.32);c.quadraticCurveTo(-0.14,0.36,-0.135,0.5);c.quadraticCurveTo(-0.132,0.62,-0.125,0.72);
  c.lineTo(0.125,0.72);c.quadraticCurveTo(0.132,0.62,0.135,0.5);c.quadraticCurveTo(0.14,0.36,0.01,0.32);c.closePath();
}
function drawWine(c,b){
  if(!b.spilled){c.save();wineBowlPath(c);c.clip();c.fillStyle='#6a0e1d';c.fillRect(-0.2,0.3,0.4,0.22);
    c.fillStyle='#8f2233';c.fillRect(-0.2,0.505,0.4,0.015);c.restore();}
  wineBowlPath(c);c.fillStyle='rgba(215,238,255,0.16)';c.fill();
  c.strokeStyle='rgba(235,248,255,0.75)';c.lineWidth=0.006;c.stroke();
  c.fillStyle='rgba(225,242,255,0.55)';
  c.beginPath();c.moveTo(-0.11,0);c.lineTo(0.11,0);c.lineTo(0.1,0.014);c.quadraticCurveTo(0.02,0.02,0.011,0.045);
  c.lineTo(0.009,0.32);c.lineTo(-0.009,0.32);c.lineTo(-0.011,0.045);c.quadraticCurveTo(-0.02,0.02,-0.1,0.014);c.closePath();c.fill();
  c.strokeStyle='rgba(255,255,255,0.6)';c.lineWidth=0.008;c.beginPath();c.moveTo(-0.09,0.45);c.quadraticCurveTo(-0.1,0.58,-0.09,0.66);c.stroke();
  if(b.cracked)drawCracks(c,b,'rgba(255,255,255,0.9)');
}
function drawBowl(c,b){
  const g=c.createLinearGradient(-0.3,0,0.3,0.2);g.addColorStop(0,'#174a52');g.addColorStop(0.5,'#2f8790');g.addColorStop(1,'#123a40');
  c.fillStyle=g;c.beginPath();c.moveTo(-0.15,0);c.lineTo(0.15,0);c.lineTo(0.16,0.025);c.quadraticCurveTo(0.3,0.07,0.31,0.26);
  c.lineTo(-0.31,0.26);c.quadraticCurveTo(-0.3,0.07,-0.16,0.025);c.closePath();c.fill();
  c.strokeStyle='#f2ead6';c.lineWidth=0.012;c.beginPath();
  for(let x=-0.27;x<=0.27;x+=0.01){const y=0.17+Math.sin(x*60)*0.012;x===-0.27?c.moveTo(x,y):c.lineTo(x,y);}c.stroke();
  c.fillStyle='#e8dcc0';c.fillRect(-0.31,0.245,0.62,0.015);
  c.fillStyle='#0d2a2e';c.fillRect(-0.15,0,0.3,0.012);
  if(b.cracked)drawCracks(c,b,'rgba(240,230,210,0.9)');
}
function drawWater(c,b){
  if(!b.spilled){c.fillStyle='rgba(140,195,235,0.42)';c.beginPath();c.moveTo(-0.093,0.05);c.lineTo(0.093,0.05);c.lineTo(0.11,0.38);c.lineTo(-0.11,0.38);c.closePath();c.fill();
    c.fillStyle='rgba(235,248,255,0.7)';c.save();c.translate(-0.03,0.33);c.rotate(0.3);c.fillRect(-0.035,-0.035,0.07,0.07);c.restore();
    c.save();c.translate(0.045,0.3);c.rotate(-0.4);c.fillRect(-0.03,-0.03,0.06,0.06);c.restore();
    c.fillStyle='rgba(200,230,250,0.8)';c.fillRect(-0.11,0.372,0.22,0.01);}
  c.fillStyle='rgba(220,240,255,0.14)';c.beginPath();c.moveTo(-0.1,0);c.lineTo(0.1,0);c.lineTo(0.125,0.55);c.lineTo(-0.125,0.55);c.closePath();c.fill();
  c.strokeStyle='rgba(235,248,255,0.75)';c.lineWidth=0.007;c.stroke();
  c.fillStyle='rgba(230,245,255,0.35)';c.fillRect(-0.1,0,0.2,0.05);
  c.strokeStyle='rgba(255,255,255,0.55)';c.lineWidth=0.01;c.beginPath();c.moveTo(-0.08,0.1);c.lineTo(-0.098,0.48);c.stroke();
  if(b.cracked)drawCracks(c,b,'rgba(255,255,255,0.9)');
}
function drawCracks(c,b,col){
  if(!b.cracks)return;c.strokeStyle=col;c.lineWidth=0.006;
  for(const l of b.cracks){c.beginPath();c.moveTo(l[0][0],l[0][1]);for(let i=1;i<l.length;i++)c.lineTo(l[i][0],l[i][1]);c.stroke();}
}
function drawBody(b){
  ctx.save();ctx.translate(b.x,b.y);ctx.rotate(b.a);ctx.translate(-b.com[0],-b.com[1]);
  b.def.draw(ctx,b);ctx.restore();
  if(showHulls){
    ctx.strokeStyle='#ff3df0';ctx.lineWidth=0.008;ctx.beginPath();
    b.wv.forEach((p,i)=>i?ctx.lineTo(p[0],p[1]):ctx.moveTo(p[0],p[1]));ctx.closePath();ctx.stroke();
    ctx.fillStyle='#ff3df0';ctx.beginPath();ctx.arc(b.x,b.y,0.02,0,6.283);ctx.fill();
  }
}
function draw(){
  ctx.setTransform(1,0,0,1,0,0);ctx.clearRect(0,0,cv.width,cv.height);
  ctx.setTransform(S*dpr,0,0,-S*dpr,-VIEW.x0*S*dpr,(CH+VIEW.y0*S)*dpr);
  drawRoom();drawTable();drawCloth();
  for(const b of bodies)drawBody(b);
  if(showHulls){ctx.strokeStyle='#3df0ff';ctx.lineWidth=0.01;const tr=Math.max(0,clothTrail());
    if(tr<W){ctx.beginPath();ctx.moveTo(tr,TOP+0.01);ctx.lineTo(W,TOP+0.01);ctx.stroke();}}
}
function status(){
  const el=document.getElementById('status');
  if(!pulling){el.textContent=`Ready. Cloth: ${(W+2*O).toFixed(1)} ft over a ${W} ft table, ${O} ft hanging off the far end. Press "Yank" (or load with #speed=N).`;return;}
  const tr=clothTrail(),d=vPull*tPull;
  const cl=tr>=W?`cloth clear of the table (took ${((W+O)/vPull).toFixed(3)} s)`:`cloth pulled ${d.toFixed(2)} ft of ${(W+O).toFixed(1)}`;
  let mv=0;for(const b of bodies)if(Math.hypot(b.vx,b.vy)>0.05||Math.abs(b.w)>0.15)mv++;
  el.textContent=`t = ${tPull.toFixed(3)} s · pull ${vPull<1000?vPull.toFixed(1):vPull.toExponential(2)} ft/s · ${cl} · ${done?'settled':mv+' object(s) moving'}`;
}
function frame(ts){
  now=ts;const rdt=Math.min((ts-lastFrame)/1000,0.05);lastFrame=ts;
  if(pulling&&!done){
    acc+=rdt*timeScale;let n=0;
    while(acc>0&&n<1500&&!done){const h=curH();step(h);acc-=h;n++;}
    if(n>=1500)acc=0;
  }
  draw();status();requestAnimationFrame(frame);
}

// prediction note
(function(){
  const th=DEFS.map(predict);const hi=Math.max(...th),lo=Math.min(...th);
  document.getElementById('pred').textContent=
    `Single-body prediction from these parameters (g = ${G} ft/s², Coulomb friction, cloth snapped to full speed instantly, object falls when its centre of mass passes the edge): `+
    `everything stays at ≥ ${hi.toFixed(2)} ft/s; nothing stays below ${lo.toFixed(2)} ft/s. `+
    `Tipping and collisions are not in that formula — the simulation includes them, so the "what happened" column can disagree, and it says so in red.`;
})();

resize();setSpeed(12);reset();
fromHash();
requestAnimationFrame(frame);
})();
</script>
</body>
</html>

What it actually does

I have not run this file. What follows describes how it is built and where I expect it to diverge. The table under the canvas puts each object's single-body threshold next to its actual outcome, and turns red when they disagree, so you can check me.

Where it behaves like the physical trick:

Nothing is keyed to pull speed. The page is a 2D side-view rigid-body simulator using sequential-impulse contacts and Coulomb friction. The cloth is a region of the tabletop that has its own friction coefficient per object. While pulling, it carries a surface velocity of v.
Slow pulls: objects reach cloth speed and stick (static friction emerges from the impulse clamp). They ride to the edge, pivot over the table corner, and fall.
Fast pulls: contact lasts only (6.5 ft)/v seconds. Objects pick up little speed and coast to a stop on bare wood.
Order of failure: objects near the pulled edge fail first. They have the most cloth behind them and the least table in front of them.
Tipping: this comes only from friction at the base corners against the centre of mass. The wine glass (centre of mass 0.34 ft, half-base 0.11 ft) leans backward under cloth friction of 0.42. A short pull's angular impulse lets it rock back; a moderate pull topples it. I expect a band of roughly 9–12 ft/s where it stays on the table but ends on its side. A toppling glass can strike its neighbours, and objects landing at the table's foot pile on each other.

Where it does not behave like the physical trick:

One friction coefficient, no static/kinetic split. Under Coulomb friction, mass and contact area cancel out of sliding acceleration. So in this model they matter only through tipping (base width against centre-of-mass height) and through collisions. Real felt and linen are not this tidy.
The cloth is idealised.
- It jumps instantly to full speed; no hand acceleration ramp.
- It has zero thickness, so objects don't drop when it leaves.
- It is perfectly flat and has no hem.
- It is never pulled downward over the edge.
- It never bunches, lifts, or drags.
Real attempts usually fail because a hem or wrinkle snags a plate, or because the pull angle lifts the cloth. This version cannot fail that way. Above the threshold it is more forgiving than reality: a clean, fast pull always succeeds.
Single-body arithmetic. The prediction treats each base as a point at its centre. The sim spreads friction over two base corners, and tipping moves load onto the rear corner, which leaves the cloth earlier. Expect real thresholds to differ from the printed ones by a few tenths of a ft/s, more for the wine glass.
It is 2D. Glasses can't roll sideways, and plates are profile polygons. Contacts are found by vertex-in-polygon tests, so two thin bodies crossing edge-to-edge (an X with no vertex inside the other) are missed. Penetration is fixed by a linear position nudge (40%, 0.002 ft slop). Restitution switches on only above 1.5 ft/s approach speed.
Materials and timestep:
- Floor friction is 0.45, object-on-object 0.3, and there is a small angular damping of 2% per second.
- The timestep shrinks during the cloth phase so the cloth moves at most 0.01 ft per step.
- Speeds above roughly 1000 ft/s therefore play in slow motion.

Thresholds and special cases you would otherwise discover:

"Upright" means within 0.30 rad (about 17°) of the starting orientation. "On the table" means the centre of mass is above the tabletop and between its ends.
"Stopped" means the cloth is gone and every object stays below 0.05 ft/s and 0.15 rad/s for 0.5 s. A timeout ends the run at (cloth time + 30 s) if something keeps creeping, and the result line says it gave up.
Mass properties come from weighted sub-polygons: a heavy brass base, wine in the glass, a thick tumbler bottom. The wine is rigid and never sloshes.
Purely cosmetic effects, which do not change the motion:
- The candle flame flickers, and goes out past 0.7 rad of tilt.
- Drinks "spill" (vanish) past 1.0 rad of tilt.
- Crack lines appear on a floor impact faster than 9 ft/s. Nothing actually shatters.
There are no scripted wobbles and no fall rules: falling off happens geometrically, when support disappears.
The speed hash:
- #speed=N accepts any number and pulls one second after load.
- Negative values use their magnitude, so direction is ignored.
- Infinity is clamped to 1e9 ft/s.
- 0 leaves the cloth still; the run "settles" with everything in place.
- Very slow pulls take real time to watch (6.5 s per ft/s of slowness); use the 4× sim speed.

Attachments

anthropic/claude-opus-5.5 — page