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birds-on-a-line.html
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birds-on-a-line.html
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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
"http://www.w3.org/TR/html4/loose.dtd">
<html lang="en">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<title>Birds on a Power Line</title>
<style type="text/css" media="screen">
body { background-color: #e6e2df; }
#boids { display:block; margin: 0px auto; }
#credits {margin: 10px; font-size: 10pt; text-align: right; width: 600px; margin: 0 auto;}
#credits a, #credits a:visited {color: #777; text-decoration: none;}
#credits a:hover, #credits a:hover { text-decoration: underline; color: #333;}
</style>
<script type="text/javascript" charset="utf-8">
var FLOCK_SIZE = 100, NUM_POWER_LINES = 3, POWER_LINES_Z = 20.0, POWER_LINES_Y = 5.0, POWER_LINES_SPACING = 3.0,
COLLISION_DISTANCE = 1.0, WALL_COLLISION_DISTANCE = 4.0, CENTER_ATTRACTION_WEIGHT = 0.01,
VELOCITY_ATTRACTION_WEIGHT = 0.125, COLLISION_AVOIDANCE_WEIGHT = 0.2, POWER_LINE_ATTRACTION_WEIGHT = 0.2,
MAXIMUM_VELOCITY = 1.0, POWER_LINE_ATTRACT_DISTANCE = 3.0, MESMARIZE_DISTANCE = 2.0, POWER_LINE_SIT_DISTANCE = 0.4,
MINIMUM_SIT_VELOCITY = 0.5, SITTING_INFLUENCE_DISTANCE = 3.5, LAUNCH_INFLUENCE = 3.0, STEP_DISTANCE = 0.2,
STEP_TIMING = 10, IDEAL_LINE_DISTANCE = 1.0, TOLERABLE_LINE_DISTANCE = .5, MINIMUM_LINE_DISTANCE = 0.4,
LAUNCH_VELOCITY = 1.0, PYRAMID_BASE = 5.0, PYRAMID_TOP = 50.0, PYRAMID_HALFWIDTH_AT_BASE = PYRAMID_BASE,
PYRAMID_HALFWIDTH_AT_TOP = PYRAMID_TOP,
WALL_SLOPE = (PYRAMID_HALFWIDTH_AT_TOP - PYRAMID_HALFWIDTH_AT_BASE) / ( PYRAMID_TOP - PYRAMID_BASE ),
WIDTH_AT_BASE = PYRAMID_HALFWIDTH_AT_BASE - PYRAMID_BASE * WALL_SLOPE;
var timer, flock=[], lines=[];
function el(id) { return document.getElementById(id); }
function each(a,f) { for (var i=0,l=a.length; i<l; i++) f(a[i],i); }
function padd(p1,p2) { return {x:p1.x+p2.x, y:p1.y+p2.y, z:p1.z+p2.z} }
function paddto(p1,p2) { p1.x+=p2.x; p1.y+=p2.y; p1.z+=p2.z; }
function psub(p1,p2) { return {x:p1.x-p2.x, y:p1.y-p2.y, z:p1.z-p2.z} }
function psubfrom(p1,p2) { p1.x-=p2.x; p1.y-=p2.y; p1.z-=p2.z; }
function pmul(p,c) { return {x:p.x*c, y:p.y*c, z:p.z*c}; }
function pmulby(p,c) { p.x*=c; p.y*=c; p.z*=c; }
function metric(p1,p2) { var dx=p1.x-p2.x, dy=p1.y-p2.y, dz=p1.z-p2.z; return Math.sqrt(dx*dx+dy*dy+dz*dz); }
function magnitude(p) { return metric(p,{x:0,y:0,z:0}); }
function near(p1,p2,r) { return metric(p1,p2) <= r; }
function yz(p) { return {x:0, y:p.y, z:p.z}; }
function Boid( x, y, z ) {
var boid = {p:{x:x, y:y, z:z}, powerLine:-1, v:{x:0,y:0,z:0}};
var lastStep=0;
function stepSitting() {
var i, b;
var rightNeighbor = boid.p.z * WALL_SLOPE + WIDTH_AT_BASE,
leftNeighbor = -rightNeighbor,
difference = 0.0, flockInfluence = {x:0,y:0,z:0}, influence = 0.0, distance = 0.0;
for (i=0; b=flock[i]; i++) {
if (b === boid) continue;
if (b.powerLine==boid.powerLine) {
if (b.p.x<boid.p.x && b.p.x>leftNeighbor) leftNeighbor = b.p.x;
if (b.p.x>boid.p.x && b.p.x<rightNeighbor) rightNeighbor = b.p.x;
} else if (( b.powerLine < 0 ) && ( near( boid.p, b.p, SITTING_INFLUENCE_DISTANCE ) )) {
flockInfluence = padd(flockInfluence, b.v);
}
}
leftNeighbor = boid.p.x - leftNeighbor;
rightNeighbor -= boid.p.x;
// if nearest neighbor is below minimum distance, launch
if (( leftNeighbor < MINIMUM_LINE_DISTANCE ) || ( rightNeighbor < MINIMUM_LINE_DISTANCE )) {
return launch();
}
// determine if the flock has influenced this boid to launch
influence = magnitude(flockInfluence);
if ( influence > LAUNCH_INFLUENCE )
return launch( pmul(flockInfluence, 1/influence) );
if ( ++lastStep >= STEP_TIMING ) {
if ( leftNeighbor < IDEAL_LINE_DISTANCE ) {
if ( rightNeighbor < IDEAL_LINE_DISTANCE ) {
difference = rightNeighbor - leftNeighbor;
if ( difference < -STEP_DISTANCE ) {
boid.p.x -= STEP_DISTANCE; lastStep = 0;
} else if ( difference > STEP_DISTANCE ) {
boid.p.x += STEP_DISTANCE; lastStep = 0;
} else if (( rightNeighbor < TOLERABLE_LINE_DISTANCE ) || ( leftNeighbor < TOLERABLE_LINE_DISTANCE )) {
return launch();
}
} else if ( leftNeighbor < IDEAL_LINE_DISTANCE - STEP_DISTANCE ) {
boid.p.x += STEP_DISTANCE; lastStep = 0;
}
} else if ( rightNeighbor < IDEAL_LINE_DISTANCE - STEP_DISTANCE ) {
boid.p.x -= STEP_DISTANCE; lastStep = 0;
}
}
}
function stepFlying() {
var centerOfFlock = {x:0,y:0,z:0}, averageVelocity = {x:0,y:0,z:0}, collisionAvoidance = {x:0,y:0,z:0},
powerLineAttraction = {x:0,y:0,z:0}, powerLineAdjustment = 1.0, tmpPowerLineAdj = 1.0, distance = 0.0,
vBar = 0.0, widthAtZ = 0.0, flying = 0, mesmarized = false;
// perform power line calculations
for (var i=0,line; line=lines[i]; i++) {
distance = metric(yz(boid.p),line);
if ( distance <= POWER_LINE_ATTRACT_DISTANCE ) {
vBar = line.directionalVelocity( boid.p, boid.v );
if ( vBar >= 0 ) {
powerLineAttraction.y += line.y - boid.p.y;
powerLineAttraction.z += line.z - boid.p.z;
tmpPowerLineAdj = distance / POWER_LINE_ATTRACT_DISTANCE;
if ( tmpPowerLineAdj < powerLineAdjustment ) powerLineAdjustment = tmpPowerLineAdj;
if (( distance < POWER_LINE_SIT_DISTANCE ) && ( vBar < MINIMUM_SIT_VELOCITY )) {
// bird is now sitting, discontinue calculations
boid.v.x=boid.v.y=boid.v.z=0;
boid.p.y = line.y; boid.p.z = line.z; boid.powerLine = i;
return;
}
if ( distance < MESMARIZE_DISTANCE ) mesmarized = true;
}
}
}
// iterate through all boids calculating new velocity
for (var i=0,b; b=flock[i]; i++) {
if ((b === boid) || (b.powerLine>=0)) continue;
if ( ! mesmarized ) {
centerOfFlock = padd(centerOfFlock,b.p);
averageVelocity = padd(averageVelocity, b.v);
}
if ( near(b.p,boid.p, COLLISION_DISTANCE) )
psubfrom(collisionAvoidance, psub(b.p,boid.p) );
flying++
}
if ( ! mesmarized ) centerOfFlock = psub(pmul( centerOfFlock, 1.0 / flying ), boid.p);
// perform collision avoidance on area boundries
if ( boid.p.z > PYRAMID_TOP - WALL_COLLISION_DISTANCE )
collisionAvoidance.z += PYRAMID_TOP - WALL_COLLISION_DISTANCE - boid.p.z;
if ( boid.p.z < PYRAMID_BASE + WALL_COLLISION_DISTANCE )
collisionAvoidance.z += PYRAMID_BASE + WALL_COLLISION_DISTANCE - boid.p.z;
widthAtZ = boid.p.z * WALL_SLOPE + WIDTH_AT_BASE;
if ( boid.p.x > widthAtZ - WALL_COLLISION_DISTANCE )
collisionAvoidance.x += widthAtZ - WALL_COLLISION_DISTANCE - boid.p.x;
if ( boid.p.x < -widthAtZ + WALL_COLLISION_DISTANCE )
collisionAvoidance.x += -widthAtZ + WALL_COLLISION_DISTANCE - boid.p.x;
if ( boid.p.y > widthAtZ - WALL_COLLISION_DISTANCE )
collisionAvoidance.y += widthAtZ - WALL_COLLISION_DISTANCE - boid.p.y;
if ( boid.p.y < -widthAtZ + WALL_COLLISION_DISTANCE )
collisionAvoidance.y += -widthAtZ + WALL_COLLISION_DISTANCE - boid.p.y;
// scale velocity modifiers
if ( ! mesmarized ) {
pmulby(centerOfFlock, CENTER_ATTRACTION_WEIGHT );
pmulby( averageVelocity, VELOCITY_ATTRACTION_WEIGHT / flying );
}
pmulby(collisionAvoidance, COLLISION_AVOIDANCE_WEIGHT );
pmulby( powerLineAttraction, POWER_LINE_ATTRACTION_WEIGHT );
// use calculations to compute new velocity
paddto(boid.v,padd(padd(centerOfFlock,averageVelocity),padd(collisionAvoidance,powerLineAttraction)));
vBar = magnitude(boid.v);
if (( powerLineAdjustment < 1.0 ) && ( vBar > 0.2 )) pmulby( boid.v, powerLineAdjustment );
// do not let velocity exceed a maximum
if ( vBar > MAXIMUM_VELOCITY ) pmulby( boid.v, MAXIMUM_VELOCITY / vBar );
paddto( boid.p, boid.v );
}
function launch(direction) {
if ( ! direction ) {
var theta = 2.0 * Math.PI * Math.random();
direction = {x:0, y:Math.sin(theta), z:Math.cos(theta)};
}
lastStep = 0;
boid.powerLine = -1;
boid.v.x = LAUNCH_VELOCITY * direction.x;
boid.v.y = LAUNCH_VELOCITY * direction.y;
boid.v.z = LAUNCH_VELOCITY * direction.z;
return 0;
}
boid.step = function() {
var pl = boid.powerLine;
if (boid.powerLine >= 0) stepSitting();
else stepFlying();
}
return boid;
}
function PowerLine(y,z) {
var line = {x:0,y:y,z:z};
line.directionalVelocity = function(p,v) {
var distance = metric(yz(p),line);
return distance > 0.0 ? (( line.y - p.y ) * v.y + ( line.z - p.z ) * v.z ) / distance : -magnitude( yz(v) );
}
return line;
}
function init() {
// place all boids on side edge of world
for ( var i=0; i < FLOCK_SIZE; i++ ) {
var z = (PYRAMID_TOP - PYRAMID_BASE) * Math.random() + PYRAMID_BASE, w = (z - PYRAMID_BASE) * (PYRAMID_HALFWIDTH_AT_TOP
- PYRAMID_HALFWIDTH_AT_BASE) / (PYRAMID_TOP - PYRAMID_BASE) - PYRAMID_HALFWIDTH_AT_BASE, w2 = 2 * w * Math.random() - w;
var xy = [{x:w2,y:w},{x:w2,y:-w},{y:w2,x:w},{y:w2,x:-w}][parseInt( Math.random() * 3.99999 )];
flock.push( Boid(xy.x, xy.y, z) );
}
// create power lines
for ( var i=0; i < NUM_POWER_LINES; i++ )
lines.push( PowerLine( POWER_LINES_Y + i*POWER_LINES_SPACING, POWER_LINES_Z ) );
var timer = setInterval( step, 50 );
}
function step() {
each(flock,function(b) { b.step(); })
draw();
}
function fog(ctx,z) {
var c=Math.max(0,parseInt( -50+284*(z/PYRAMID_TOP)));
ctx.fillStyle='rgb('+c+','+c+','+c+')';
}
function draw() {
var ctx = el('boids').getContext('2d');
ctx.clearRect(0,0,ctx.canvas.width,ctx.canvas.height);
ctx.fillStyle = '#000';
ctx.strokeStyle = '#000';
ctx.lineWidth = .5;
flock.sort(function(a,b) { return b.p.z - a.p.z; });
each(flock,function(b) { fog(ctx,b.p.z); circle( ctx, 225*b.p.x/b.p.z+300, 225*b.p.y/b.p.z+225, 62.5/b.p.z); })
each(lines,function(l) { var v=parseInt(225*l.y/l.z+225); line( ctx, 0, v, ctx.canvas.width, v); })
}
function circle( ctx, x, y, r ) {
ctx.beginPath();
ctx.arc(x, y, r, 0, Math.PI*2, true);
ctx.closePath();
ctx.fill();
}
function line( ctx, x1, y1, x2, y2 ) {
ctx.beginPath();
ctx.moveTo( x1, y1 );
ctx.lineTo( x2, y2 );
ctx.closePath();
ctx.stroke();
}
</script>
</head>
<body onload="init()">
<canvas id="boids" width="600" height="450"></canvas>
<div id="credits">
<a href="http://blog.carbonfive.com/2011/02/13/a-3d-flocking-simulation-using-html5-canvas/">about this simulation »</a>
</div>
</body>
</html>