three
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JavaScript 3D library
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JavaScript
/*
* Cloth Simulation using a relaxed constraints solver
*/
// Suggested Readings
// Advanced Character Physics by Thomas Jakobsen Character
// http://freespace.virgin.net/hugo.elias/models/m_cloth.htm
// http://en.wikipedia.org/wiki/Cloth_modeling
// http://cg.alexandra.dk/tag/spring-mass-system/
// Real-time Cloth Animation http://www.darwin3d.com/gamedev/articles/col0599.pdf
var DAMPING = 0.03;
var DRAG = 1 - DAMPING;
var MASS = 0.1;
var restDistance = 25;
var xSegs = 10;
var ySegs = 10;
var clothFunction = plane( restDistance * xSegs, restDistance * ySegs );
var cloth = new Cloth( xSegs, ySegs );
var GRAVITY = 981 * 1.4;
var gravity = new THREE.Vector3( 0, - GRAVITY, 0 ).multiplyScalar( MASS );
var TIMESTEP = 18 / 1000;
var TIMESTEP_SQ = TIMESTEP * TIMESTEP;
var pins = [];
var wind = true;
var windStrength = 2;
var windForce = new THREE.Vector3( 0, 0, 0 );
var ballPosition = new THREE.Vector3( 0, - 45, 0 );
var ballSize = 60; //40
var tmpForce = new THREE.Vector3();
var lastTime;
function plane( width, height ) {
return function ( u, v, target ) {
var x = ( u - 0.5 ) * width;
var y = ( v + 0.5 ) * height;
var z = 0;
target.set( x, y, z );
};
}
function Particle( x, y, z, mass ) {
this.position = new THREE.Vector3();
this.previous = new THREE.Vector3();
this.original = new THREE.Vector3();
this.a = new THREE.Vector3( 0, 0, 0 ); // acceleration
this.mass = mass;
this.invMass = 1 / mass;
this.tmp = new THREE.Vector3();
this.tmp2 = new THREE.Vector3();
// init
clothFunction( x, y, this.position ); // position
clothFunction( x, y, this.previous ); // previous
clothFunction( x, y, this.original );
}
// Force -> Acceleration
Particle.prototype.addForce = function ( force ) {
this.a.add(
this.tmp2.copy( force ).multiplyScalar( this.invMass )
);
};
// Performs Verlet integration
Particle.prototype.integrate = function ( timesq ) {
var newPos = this.tmp.subVectors( this.position, this.previous );
newPos.multiplyScalar( DRAG ).add( this.position );
newPos.add( this.a.multiplyScalar( timesq ) );
this.tmp = this.previous;
this.previous = this.position;
this.position = newPos;
this.a.set( 0, 0, 0 );
};
var diff = new THREE.Vector3();
function satisfyConstraints( p1, p2, distance ) {
diff.subVectors( p2.position, p1.position );
var currentDist = diff.length();
if ( currentDist === 0 ) return; // prevents division by 0
var correction = diff.multiplyScalar( 1 - distance / currentDist );
var correctionHalf = correction.multiplyScalar( 0.5 );
p1.position.add( correctionHalf );
p2.position.sub( correctionHalf );
}
function Cloth( w, h ) {
w = w || 10;
h = h || 10;
this.w = w;
this.h = h;
var particles = [];
var constraints = [];
var u, v;
// Create particles
for ( v = 0; v <= h; v ++ ) {
for ( u = 0; u <= w; u ++ ) {
particles.push(
new Particle( u / w, v / h, 0, MASS )
);
}
}
// Structural
for ( v = 0; v < h; v ++ ) {
for ( u = 0; u < w; u ++ ) {
constraints.push( [
particles[ index( u, v ) ],
particles[ index( u, v + 1 ) ],
restDistance
] );
constraints.push( [
particles[ index( u, v ) ],
particles[ index( u + 1, v ) ],
restDistance
] );
}
}
for ( u = w, v = 0; v < h; v ++ ) {
constraints.push( [
particles[ index( u, v ) ],
particles[ index( u, v + 1 ) ],
restDistance
] );
}
for ( v = h, u = 0; u < w; u ++ ) {
constraints.push( [
particles[ index( u, v ) ],
particles[ index( u + 1, v ) ],
restDistance
] );
}
// While many systems use shear and bend springs,
// the relaxed constraints model seems to be just fine
// using structural springs.
// Shear
// var diagonalDist = Math.sqrt(restDistance * restDistance * 2);
// for (v=0;v<h;v++) {
// for (u=0;u<w;u++) {
// constraints.push([
// particles[index(u, v)],
// particles[index(u+1, v+1)],
// diagonalDist
// ]);
// constraints.push([
// particles[index(u+1, v)],
// particles[index(u, v+1)],
// diagonalDist
// ]);
// }
// }
this.particles = particles;
this.constraints = constraints;
function index( u, v ) {
return u + v * ( w + 1 );
}
this.index = index;
}
function simulate( time ) {
if ( ! lastTime ) {
lastTime = time;
return;
}
var i, il, particles, particle, pt, constraints, constraint;
// Aerodynamics forces
if ( wind ) {
var face, faces = clothGeometry.faces, normal;
particles = cloth.particles;
for ( i = 0, il = faces.length; i < il; i ++ ) {
face = faces[ i ];
normal = face.normal;
tmpForce.copy( normal ).normalize().multiplyScalar( normal.dot( windForce ) );
particles[ face.a ].addForce( tmpForce );
particles[ face.b ].addForce( tmpForce );
particles[ face.c ].addForce( tmpForce );
}
}
for ( particles = cloth.particles, i = 0, il = particles.length; i < il; i ++ ) {
particle = particles[ i ];
particle.addForce( gravity );
particle.integrate( TIMESTEP_SQ );
}
// Start Constraints
constraints = cloth.constraints;
il = constraints.length;
for ( i = 0; i < il; i ++ ) {
constraint = constraints[ i ];
satisfyConstraints( constraint[ 0 ], constraint[ 1 ], constraint[ 2 ] );
}
// Ball Constraints
ballPosition.z = - Math.sin( Date.now() / 600 ) * 90; //+ 40;
ballPosition.x = Math.cos( Date.now() / 400 ) * 70;
if ( sphere.visible ) {
for ( particles = cloth.particles, i = 0, il = particles.length; i < il; i ++ ) {
particle = particles[ i ];
var pos = particle.position;
diff.subVectors( pos, ballPosition );
if ( diff.length() < ballSize ) {
// collided
diff.normalize().multiplyScalar( ballSize );
pos.copy( ballPosition ).add( diff );
}
}
}
// Floor Constraints
for ( particles = cloth.particles, i = 0, il = particles.length; i < il; i ++ ) {
particle = particles[ i ];
pos = particle.position;
if ( pos.y < - 250 ) {
pos.y = - 250;
}
}
// Pin Constraints
for ( i = 0, il = pins.length; i < il; i ++ ) {
var xy = pins[ i ];
var p = particles[ xy ];
p.position.copy( p.original );
p.previous.copy( p.original );
}
}