/**
* @author alteredq / http://alteredqualia.com/
* @author mrdoob / http://mrdoob.com/
*/
var _Math = {
DEG2RAD: Math.PI / 180,
RAD2DEG: 180 / Math.PI,
generateUUID: ( function () {
// http://stackoverflow.com/questions/105034/how-to-create-a-guid-uuid-in-javascript/21963136#21963136
var lut = [];
for ( var i = 0; i < 256; i ++ ) {
lut[ i ] = ( i < 16 ? '0' : '' ) + ( i ).toString( 16 ).toUpperCase();
}
return function generateUUID() {
var d0 = Math.random() * 0xffffffff | 0;
var d1 = Math.random() * 0xffffffff | 0;
var d2 = Math.random() * 0xffffffff | 0;
var d3 = Math.random() * 0xffffffff | 0;
return lut[ d0 & 0xff ] + lut[ d0 >> 8 & 0xff ] + lut[ d0 >> 16 & 0xff ] + lut[ d0 >> 24 & 0xff ] + '-' +
lut[ d1 & 0xff ] + lut[ d1 >> 8 & 0xff ] + '-' + lut[ d1 >> 16 & 0x0f | 0x40 ] + lut[ d1 >> 24 & 0xff ] + '-' +
lut[ d2 & 0x3f | 0x80 ] + lut[ d2 >> 8 & 0xff ] + '-' + lut[ d2 >> 16 & 0xff ] + lut[ d2 >> 24 & 0xff ] +
lut[ d3 & 0xff ] + lut[ d3 >> 8 & 0xff ] + lut[ d3 >> 16 & 0xff ] + lut[ d3 >> 24 & 0xff ];
};
} )(),
clamp: function ( value, min, max ) {
return Math.max( min, Math.min( max, value ) );
},
// compute euclidian modulo of m % n
// https://en.wikipedia.org/wiki/Modulo_operation
euclideanModulo: function ( n, m ) {
return ( ( n % m ) + m ) % m;
},
// Linear mapping from range <a1, a2> to range <b1, b2>
mapLinear: function ( x, a1, a2, b1, b2 ) {
return b1 + ( x - a1 ) * ( b2 - b1 ) / ( a2 - a1 );
},
// https://en.wikipedia.org/wiki/Linear_interpolation
lerp: function ( x, y, t ) {
return ( 1 - t ) * x + t * y;
},
// http://en.wikipedia.org/wiki/Smoothstep
smoothstep: function ( x, min, max ) {
if ( x <= min ) return 0;
if ( x >= max ) return 1;
x = ( x - min ) / ( max - min );
return x * x * ( 3 - 2 * x );
},
smootherstep: function ( x, min, max ) {
if ( x <= min ) return 0;
if ( x >= max ) return 1;
x = ( x - min ) / ( max - min );
return x * x * x * ( x * ( x * 6 - 15 ) + 10 );
},
// Random integer from <low, high> interval
randInt: function ( low, high ) {
return low + Math.floor( Math.random() * ( high - low + 1 ) );
},
// Random float from <low, high> interval
randFloat: function ( low, high ) {
return low + Math.random() * ( high - low );
},
// Random float from <-range/2, range/2> interval
randFloatSpread: function ( range ) {
return range * ( 0.5 - Math.random() );
},
degToRad: function ( degrees ) {
return degrees * _Math.DEG2RAD;
},
radToDeg: function ( radians ) {
return radians * _Math.RAD2DEG;
},
isPowerOfTwo: function ( value ) {
return ( value & ( value - 1 ) ) === 0 && value !== 0;
},
ceilPowerOfTwo: function ( value ) {
return Math.pow( 2, Math.ceil( Math.log( value ) / Math.LN2 ) );
},
floorPowerOfTwo: function ( value ) {
return Math.pow( 2, Math.floor( Math.log( value ) / Math.LN2 ) );
}
};
/**
* @author mrdoob / http://mrdoob.com/
* @author philogb / http://blog.thejit.org/
* @author egraether / http://egraether.com/
* @author zz85 / http://www.lab4games.net/zz85/blog
*/
function Vector2( x, y ) {
this.x = x || 0;
this.y = y || 0;
}
Object.defineProperties( Vector2.prototype, {
"width": {
get: function () {
return this.x;
},
set: function ( value ) {
this.x = value;
}
},
"height": {
get: function () {
return this.y;
},
set: function ( value ) {
this.y = value;
}
}
} );
Object.assign( Vector2.prototype, {
isVector2: true,
set: function ( x, y ) {
this.x = x;
this.y = y;
return this;
},
setScalar: function ( scalar ) {
this.x = scalar;
this.y = scalar;
return this;
},
setX: function ( x ) {
this.x = x;
return this;
},
setY: function ( y ) {
this.y = y;
return this;
},
setComponent: function ( index, value ) {
switch ( index ) {
case 0: this.x = value; break;
case 1: this.y = value; break;
default: throw new Error( 'index is out of range: ' + index );
}
return this;
},
getComponent: function ( index ) {
switch ( index ) {
case 0: return this.x;
case 1: return this.y;
default: throw new Error( 'index is out of range: ' + index );
}
},
clone: function () {
return new this.constructor( this.x, this.y );
},
copy: function ( v ) {
this.x = v.x;
this.y = v.y;
return this;
},
add: function ( v, w ) {
if ( w !== undefined ) {
console.warn( 'THREE.Vector2: .add() now only accepts one argument. Use .addVectors( a, b ) instead.' );
return this.addVectors( v, w );
}
this.x += v.x;
this.y += v.y;
return this;
},
addScalar: function ( s ) {
this.x += s;
this.y += s;
return this;
},
addVectors: function ( a, b ) {
this.x = a.x + b.x;
this.y = a.y + b.y;
return this;
},
addScaledVector: function ( v, s ) {
this.x += v.x * s;
this.y += v.y * s;
return this;
},
sub: function ( v, w ) {
if ( w !== undefined ) {
console.warn( 'THREE.Vector2: .sub() now only accepts one argument. Use .subVectors( a, b ) instead.' );
return this.subVectors( v, w );
}
this.x -= v.x;
this.y -= v.y;
return this;
},
subScalar: function ( s ) {
this.x -= s;
this.y -= s;
return this;
},
subVectors: function ( a, b ) {
this.x = a.x - b.x;
this.y = a.y - b.y;
return this;
},
multiply: function ( v ) {
this.x *= v.x;
this.y *= v.y;
return this;
},
multiplyScalar: function ( scalar ) {
this.x *= scalar;
this.y *= scalar;
return this;
},
divide: function ( v ) {
this.x /= v.x;
this.y /= v.y;
return this;
},
divideScalar: function ( scalar ) {
return this.multiplyScalar( 1 / scalar );
},
applyMatrix3: function ( m ) {
var x = this.x, y = this.y;
var e = m.elements;
this.x = e[ 0 ] * x + e[ 3 ] * y + e[ 6 ];
this.y = e[ 1 ] * x + e[ 4 ] * y + e[ 7 ];
return this;
},
min: function ( v ) {
this.x = Math.min( this.x, v.x );
this.y = Math.min( this.y, v.y );
return this;
},
max: function ( v ) {
this.x = Math.max( this.x, v.x );
this.y = Math.max( this.y, v.y );
return this;
},
clamp: function ( min, max ) {
// assumes min < max, componentwise
this.x = Math.max( min.x, Math.min( max.x, this.x ) );
this.y = Math.max( min.y, Math.min( max.y, this.y ) );
return this;
},
clampScalar: function () {
var min = new Vector2();
var max = new Vector2();
return function clampScalar( minVal, maxVal ) {
min.set( minVal, minVal );
max.set( maxVal, maxVal );
return this.clamp( min, max );
};
}(),
clampLength: function ( min, max ) {
var length = this.length();
return this.divideScalar( length || 1 ).multiplyScalar( Math.max( min, Math.min( max, length ) ) );
},
floor: function () {
this.x = Math.floor( this.x );
this.y = Math.floor( this.y );
return this;
},
ceil: function () {
this.x = Math.ceil( this.x );
this.y = Math.ceil( this.y );
return this;
},
round: function () {
this.x = Math.round( this.x );
this.y = Math.round( this.y );
return this;
},
roundToZero: function () {
this.x = ( this.x < 0 ) ? Math.ceil( this.x ) : Math.floor( this.x );
this.y = ( this.y < 0 ) ? Math.ceil( this.y ) : Math.floor( this.y );
return this;
},
negate: function () {
this.x = - this.x;
this.y = - this.y;
return this;
},
dot: function ( v ) {
return this.x * v.x + this.y * v.y;
},
lengthSq: function () {
return this.x * this.x + this.y * this.y;
},
length: function () {
return Math.sqrt( this.x * this.x + this.y * this.y );
},
manhattanLength: function () {
return Math.abs( this.x ) + Math.abs( this.y );
},
normalize: function () {
return this.divideScalar( this.length() || 1 );
},
angle: function () {
// computes the angle in radians with respect to the positive x-axis
var angle = Math.atan2( this.y, this.x );
if ( angle < 0 ) angle += 2 * Math.PI;
return angle;
},
distanceTo: function ( v ) {
return Math.sqrt( this.distanceToSquared( v ) );
},
distanceToSquared: function ( v ) {
var dx = this.x - v.x, dy = this.y - v.y;
return dx * dx + dy * dy;
},
manhattanDistanceTo: function ( v ) {
return Math.abs( this.x - v.x ) + Math.abs( this.y - v.y );
},
setLength: function ( length ) {
return this.normalize().multiplyScalar( length );
},
lerp: function ( v, alpha ) {
this.x += ( v.x - this.x ) * alpha;
this.y += ( v.y - this.y ) * alpha;
return this;
},
lerpVectors: function ( v1, v2, alpha ) {
return this.subVectors( v2, v1 ).multiplyScalar( alpha ).add( v1 );
},
equals: function ( v ) {
return ( ( v.x === this.x ) && ( v.y === this.y ) );
},
fromArray: function ( array, offset ) {
if ( offset === undefined ) offset = 0;
this.x = array[ offset ];
this.y = array[ offset + 1 ];
return this;
},
toArray: function ( array, offset ) {
if ( array === undefined ) array = [];
if ( offset === undefined ) offset = 0;
array[ offset ] = this.x;
array[ offset + 1 ] = this.y;
return array;
},
fromBufferAttribute: function ( attribute, index, offset ) {
if ( offset !== undefined ) {
console.warn( 'THREE.Vector2: offset has been removed from .fromBufferAttribute().' );
}
this.x = attribute.getX( index );
this.y = attribute.getY( index );
return this;
},
rotateAround: function ( center, angle ) {
var c = Math.cos( angle ), s = Math.sin( angle );
var x = this.x - center.x;
var y = this.y - center.y;
this.x = x * c - y * s + center.x;
this.y = x * s + y * c + center.y;
return this;
}
} );
/**
* @author mrdoob / http://mrdoob.com/
* @author kile / http://kile.stravaganza.org/
* @author philogb / http://blog.thejit.org/
* @author mikael emtinger / http://gomo.se/
* @author egraether / http://egraether.com/
* @author WestLangley / http://github.com/WestLangley
*/
function Vector3( x, y, z ) {
this.x = x || 0;
this.y = y || 0;
this.z = z || 0;
}
Object.assign( Vector3.prototype, {
isVector3: true,
set: function ( x, y, z ) {
this.x = x;
this.y = y;
this.z = z;
return this;
},
setScalar: function ( scalar ) {
this.x = scalar;
this.y = scalar;
this.z = scalar;
return this;
},
setX: function ( x ) {
this.x = x;
return this;
},
setY: function ( y ) {
this.y = y;
return this;
},
setZ: function ( z ) {
this.z = z;
return this;
},
setComponent: function ( index, value ) {
switch ( index ) {
case 0: this.x = value; break;
case 1: this.y = value; break;
case 2: this.z = value; break;
default: throw new Error( 'index is out of range: ' + index );
}
return this;
},
getComponent: function ( index ) {
switch ( index ) {
case 0: return this.x;
case 1: return this.y;
case 2: return this.z;
default: throw new Error( 'index is out of range: ' + index );
}
},
clone: function () {
return new this.constructor( this.x, this.y, this.z );
},
copy: function ( v ) {
this.x = v.x;
this.y = v.y;
this.z = v.z;
return this;
},
add: function ( v, w ) {
if ( w !== undefined ) {
console.warn( 'THREE.Vector3: .add() now only accepts one argument. Use .addVectors( a, b ) instead.' );
return this.addVectors( v, w );
}
this.x += v.x;
this.y += v.y;
this.z += v.z;
return this;
},
addScalar: function ( s ) {
this.x += s;
this.y += s;
this.z += s;
return this;
},
addVectors: function ( a, b ) {
this.x = a.x + b.x;
this.y = a.y + b.y;
this.z = a.z + b.z;
return this;
},
addScaledVector: function ( v, s ) {
this.x += v.x * s;
this.y += v.y * s;
this.z += v.z * s;
return this;
},
sub: function ( v, w ) {
if ( w !== undefined ) {
console.warn( 'THREE.Vector3: .sub() now only accepts one argument. Use .subVectors( a, b ) instead.' );
return this.subVectors( v, w );
}
this.x -= v.x;
this.y -= v.y;
this.z -= v.z;
return this;
},
subScalar: function ( s ) {
this.x -= s;
this.y -= s;
this.z -= s;
return this;
},
subVectors: function ( a, b ) {
this.x = a.x - b.x;
this.y = a.y - b.y;
this.z = a.z - b.z;
return this;
},
multiply: function ( v, w ) {
if ( w !== undefined ) {
console.warn( 'THREE.Vector3: .multiply() now only accepts one argument. Use .multiplyVectors( a, b ) instead.' );
return this.multiplyVectors( v, w );
}
this.x *= v.x;
this.y *= v.y;
this.z *= v.z;
return this;
},
multiplyScalar: function ( scalar ) {
this.x *= scalar;
this.y *= scalar;
this.z *= scalar;
return this;
},
multiplyVectors: function ( a, b ) {
this.x = a.x * b.x;
this.y = a.y * b.y;
this.z = a.z * b.z;
return this;
},
applyEuler: function () {
var quaternion = new Quaternion();
return function applyEuler( euler ) {
if ( ! ( euler && euler.isEuler ) ) {
console.error( 'THREE.Vector3: .applyEuler() now expects an Euler rotation rather than a Vector3 and order.' );
}
return this.applyQuaternion( quaternion.setFromEuler( euler ) );
};
}(),
applyAxisAngle: function () {
var quaternion = new Quaternion();
return function applyAxisAngle( axis, angle ) {
return this.applyQuaternion( quaternion.setFromAxisAngle( axis, angle ) );
};
}(),
applyMatrix3: function ( m ) {
var x = this.x, y = this.y, z = this.z;
var e = m.elements;
this.x = e[ 0 ] * x + e[ 3 ] * y + e[ 6 ] * z;
this.y = e[ 1 ] * x + e[ 4 ] * y + e[ 7 ] * z;
this.z = e[ 2 ] * x + e[ 5 ] * y + e[ 8 ] * z;
return this;
},
applyMatrix4: function ( m ) {
var x = this.x, y = this.y, z = this.z;
var e = m.elements;
var w = 1 / ( e[ 3 ] * x + e[ 7 ] * y + e[ 11 ] * z + e[ 15 ] );
this.x = ( e[ 0 ] * x + e[ 4 ] * y + e[ 8 ] * z + e[ 12 ] ) * w;
this.y = ( e[ 1 ] * x + e[ 5 ] * y + e[ 9 ] * z + e[ 13 ] ) * w;
this.z = ( e[ 2 ] * x + e[ 6 ] * y + e[ 10 ] * z + e[ 14 ] ) * w;
return this;
},
applyQuaternion: function ( q ) {
var x = this.x, y = this.y, z = this.z;
var qx = q.x, qy = q.y, qz = q.z, qw = q.w;
// calculate quat * vector
var ix = qw * x + qy * z - qz * y;
var iy = qw * y + qz * x - qx * z;
var iz = qw * z + qx * y - qy * x;
var iw = - qx * x - qy * y - qz * z;
// calculate result * inverse quat
this.x = ix * qw + iw * - qx + iy * - qz - iz * - qy;
this.y = iy * qw + iw * - qy + iz * - qx - ix * - qz;
this.z = iz * qw + iw * - qz + ix * - qy - iy * - qx;
return this;
},
project: function () {
var matrix = new Matrix4();
return function project( camera ) {
matrix.multiplyMatrices( camera.projectionMatrix, matrix.getInverse( camera.matrixWorld ) );
return this.applyMatrix4( matrix );
};
}(),
unproject: function () {
var matrix = new Matrix4();
return function unproject( camera ) {
matrix.multiplyMatrices( camera.matrixWorld, matrix.getInverse( camera.projectionMatrix ) );
return this.applyMatrix4( matrix );
};
}(),
transformDirection: function ( m ) {
// input: THREE.Matrix4 affine matrix
// vector interpreted as a direction
var x = this.x, y = this.y, z = this.z;
var e = m.elements;
this.x = e[ 0 ] * x + e[ 4 ] * y + e[ 8 ] * z;
this.y = e[ 1 ] * x + e[ 5 ] * y + e[ 9 ] * z;
this.z = e[ 2 ] * x + e[ 6 ] * y + e[ 10 ] * z;
return this.normalize();
},
divide: function ( v ) {
this.x /= v.x;
this.y /= v.y;
this.z /= v.z;
return this;
},
divideScalar: function ( scalar ) {
return this.multiplyScalar( 1 / scalar );
},
min: function ( v ) {
this.x = Math.min( this.x, v.x );
this.y = Math.min( this.y, v.y );
this.z = Math.min( this.z, v.z );
return this;
},
max: function ( v ) {
this.x = Math.max( this.x, v.x );
this.y = Math.max( this.y, v.y );
this.z = Math.max( this.z, v.z );
return this;
},
clamp: function ( min, max ) {
// assumes min < max, componentwise
this.x = Math.max( min.x, Math.min( max.x, this.x ) );
this.y = Math.max( min.y, Math.min( max.y, this.y ) );
this.z = Math.max( min.z, Math.min( max.z, this.z ) );
return this;
},
clampScalar: function () {
var min = new Vector3();
var max = new Vector3();
return function clampScalar( minVal, maxVal ) {
min.set( minVal, minVal, minVal );
max.set( maxVal, maxVal, maxVal );
return this.clamp( min, max );
};
}(),
clampLength: function ( min, max ) {
var length = this.length();
return this.divideScalar( length || 1 ).multiplyScalar( Math.max( min, Math.min( max, length ) ) );
},
floor: function () {
this.x = Math.floor( this.x );
this.y = Math.floor( this.y );
this.z = Math.floor( this.z );
return this;
},
ceil: function () {
this.x = Math.ceil( this.x );
this.y = Math.ceil( this.y );
this.z = Math.ceil( this.z );
return this;
},
round: function () {
this.x = Math.round( this.x );
this.y = Math.round( this.y );
this.z = Math.round( this.z );
return this;
},
roundToZero: function () {
this.x = ( this.x < 0 ) ? Math.ceil( this.x ) : Math.floor( this.x );
this.y = ( this.y < 0 ) ? Math.ceil( this.y ) : Math.floor( this.y );
this.z = ( this.z < 0 ) ? Math.ceil( this.z ) : Math.floor( this.z );
return this;
},
negate: function () {
this.x = - this.x;
this.y = - this.y;
this.z = - this.z;
return this;
},
dot: function ( v ) {
return this.x * v.x + this.y * v.y + this.z * v.z;
},
// TODO lengthSquared?
lengthSq: function () {
return this.x * this.x + this.y * this.y + this.z * this.z;
},
length: function () {
return Math.sqrt( this.x * this.x + this.y * this.y + this.z * this.z );
},
manhattanLength: function () {
return Math.abs( this.x ) + Math.abs( this.y ) + Math.abs( this.z );
},
normalize: function () {
return this.divideScalar( this.length() || 1 );
},
setLength: function ( length ) {
return this.normalize().multiplyScalar( length );
},
lerp: function ( v, alpha ) {
this.x += ( v.x - this.x ) * alpha;
this.y += ( v.y - this.y ) * alpha;
this.z += ( v.z - this.z ) * alpha;
return this;
},
lerpVectors: function ( v1, v2, alpha ) {
return this.subVectors( v2, v1 ).multiplyScalar( alpha ).add( v1 );
},
cross: function ( v, w ) {
if ( w !== undefined ) {
console.warn( 'THREE.Vector3: .cross() now only accepts one argument. Use .crossVectors( a, b ) instead.' );
return this.crossVectors( v, w );
}
return this.crossVectors( this, v );
},
crossVectors: function ( a, b ) {
var ax = a.x, ay = a.y, az = a.z;
var bx = b.x, by = b.y, bz = b.z;
this.x = ay * bz - az * by;
this.y = az * bx - ax * bz;
this.z = ax * by - ay * bx;
return this;
},
projectOnVector: function ( vector ) {
var scalar = vector.dot( this ) / vector.lengthSq();
return this.copy( vector ).multiplyScalar( scalar );
},
projectOnPlane: function () {
var v1 = new Vector3();
return function projectOnPlane( planeNormal ) {
v1.copy( this ).projectOnVector( planeNormal );
return this.sub( v1 );
};
}(),
reflect: function () {
// reflect incident vector off plane orthogonal to normal
// normal is assumed to have unit length
var v1 = new Vector3();
return function reflect( normal ) {
return this.sub( v1.copy( normal ).multiplyScalar( 2 * this.dot( normal ) ) );
};
}(),
angleTo: function ( v ) {
var theta = this.dot( v ) / ( Math.sqrt( this.lengthSq() * v.lengthSq() ) );
// clamp, to handle numerical problems
return Math.acos( _Math.clamp( theta, - 1, 1 ) );
},
distanceTo: function ( v ) {
return Math.sqrt( this.distanceToSquared( v ) );
},
distanceToSquared: function ( v ) {
var dx = this.x - v.x, dy = this.y - v.y, dz = this.z - v.z;
return dx * dx + dy * dy + dz * dz;
},
manhattanDistanceTo: function ( v ) {
return Math.abs( this.x - v.x ) + Math.abs( this.y - v.y ) + Math.abs( this.z - v.z );
},
setFromSpherical: function ( s ) {
var sinPhiRadius = Math.sin( s.phi ) * s.radius;
this.x = sinPhiRadius * Math.sin( s.theta );
this.y = Math.cos( s.phi ) * s.radius;
this.z = sinPhiRadius * Math.cos( s.theta );
return this;
},
setFromCylindrical: function ( c ) {
this.x = c.radius * Math.sin( c.theta );
this.y = c.y;
this.z = c.radius * Math.cos( c.theta );
return this;
},
setFromMatrixPosition: function ( m ) {
var e = m.elements;
this.x = e[ 12 ];
this.y = e[ 13 ];
this.z = e[ 14 ];
return this;
},
setFromMatrixScale: function ( m ) {
var sx = this.setFromMatrixColumn( m, 0 ).length();
var sy = this.setFromMatrixColumn( m, 1 ).length();
var sz = this.setFromMatrixColumn( m, 2 ).length();
this.x = sx;
this.y = sy;
this.z = sz;
return this;
},
setFromMatrixColumn: function ( m, index ) {
return this.fromArray( m.elements, index * 4 );
},
equals: function ( v ) {
return ( ( v.x === this.x ) && ( v.y === this.y ) && ( v.z === this.z ) );
},
fromArray: function ( array, offset ) {
if ( offset === undefined ) offset = 0;
this.x = array[ offset ];
this.y = array[ offset + 1 ];
this.z = array[ offset + 2 ];
return this;
},
toArray: function ( array, offset ) {
if ( array === undefined ) array = [];
if ( offset === undefined ) offset = 0;
array[ offset ] = this.x;
array[ offset + 1 ] = this.y;
array[ offset + 2 ] = this.z;
return array;
},
fromBufferAttribute: function ( attribute, index, offset ) {
if ( offset !== undefined ) {
console.warn( 'THREE.Vector3: offset has been removed from .fromBufferAttribute().' );
}
this.x = attribute.getX( index );
this.y = attribute.getY( index );
this.z = attribute.getZ( index );
return this;
}
} );
/**
* @author mikael emtinger / http://gomo.se/
* @author alteredq / http://alteredqualia.com/
* @author WestLangley / http://github.com/WestLangley
* @author bhouston / http://clara.io
*/
function Quaternion( x, y, z, w ) {
this._x = x || 0;
this._y = y || 0;
this._z = z || 0;
this._w = ( w !== undefined ) ? w : 1;
}
Object.assign( Quaternion, {
slerp: function ( qa, qb, qm, t ) {
return qm.copy( qa ).slerp( qb, t );
},
slerpFlat: function ( dst, dstOffset, src0, srcOffset0, src1, srcOffset1, t ) {
// fuzz-free, array-based Quaternion SLERP operation
var x0 = src0[ srcOffset0 + 0 ],
y0 = src0[ srcOffset0 + 1 ],
z0 = src0[ srcOffset0 + 2 ],
w0 = src0[ srcOffset0 + 3 ],
x1 = src1[ srcOffset1 + 0 ],
y1 = src1[ srcOffset1 + 1 ],
z1 = src1[ srcOffset1 + 2 ],
w1 = src1[ srcOffset1 + 3 ];
if ( w0 !== w1 || x0 !== x1 || y0 !== y1 || z0 !== z1 ) {
var s = 1 - t,
cos = x0 * x1 + y0 * y1 + z0 * z1 + w0 * w1,
dir = ( cos >= 0 ? 1 : - 1 ),
sqrSin = 1 - cos * cos;
// Skip the Slerp for tiny steps to avoid numeric problems:
if ( sqrSin > Number.EPSILON ) {
var sin = Math.sqrt( sqrSin ),
len = Math.atan2( sin, cos * dir );
s = Math.sin( s * len ) / sin;
t = Math.sin( t * len ) / sin;
}
var tDir = t * dir;
x0 = x0 * s + x1 * tDir;
y0 = y0 * s + y1 * tDir;
z0 = z0 * s + z1 * tDir;
w0 = w0 * s + w1 * tDir;
// Normalize in case we just did a lerp:
if ( s === 1 - t ) {
var f = 1 / Math.sqrt( x0 * x0 + y0 * y0 + z0 * z0 + w0 * w0 );
x0 *= f;
y0 *= f;
z0 *= f;
w0 *= f;
}
}
dst[ dstOffset ] = x0;
dst[ dstOffset + 1 ] = y0;
dst[ dstOffset + 2 ] = z0;
dst[ dstOffset + 3 ] = w0;
}
} );
Object.defineProperties( Quaternion.prototype, {
x: {
get: function () {
return this._x;
},
set: function ( value ) {
this._x = value;
this.onChangeCallback();
}
},
y: {
get: function () {
return this._y;
},
set: function ( value ) {
this._y = value;
this.onChangeCallback();
}
},
z: {
get: function () {
return this._z;
},
set: function ( value ) {
this._z = value;
this.onChangeCallback();
}
},
w: {
get: function () {
return this._w;
},
set: function ( value ) {
this._w = value;
this.onChangeCallback();
}
}
} );
Object.assign( Quaternion.prototype, {
set: function ( x, y, z, w ) {
this._x = x;
this._y = y;
this._z = z;
this._w = w;
this.onChangeCallback();
return this;
},
clone: function () {
return new this.constructor( this._x, this._y, this._z, this._w );
},
copy: function ( quaternion ) {
this._x = quaternion.x;
this._y = quaternion.y;
this._z = quaternion.z;
this._w = quaternion.w;
this.onChangeCallback();
return this;
},
setFromEuler: function ( euler, update ) {
if ( ! ( euler && euler.isEuler ) ) {
throw new Error( 'THREE.Quaternion: .setFromEuler() now expects an Euler rotation rather than a Vector3 and order.' );
}
var x = euler._x, y = euler._y, z = euler._z, order = euler.order;
// http://www.mathworks.com/matlabcentral/fileexchange/
// 20696-function-to-convert-between-dcm-euler-angles-quaternions-and-euler-vectors/
// content/SpinCalc.m
var cos = Math.cos;
var sin = Math.sin;
var c1 = cos( x / 2 );
var c2 = cos( y / 2 );
var c3 = cos( z / 2 );
var s1 = sin( x / 2 );
var s2 = sin( y / 2 );
var s3 = sin( z / 2 );
if ( order === 'XYZ' ) {
this._x = s1 * c2 * c3 + c1 * s2 * s3;
this._y = c1 * s2 * c3 - s1 * c2 * s3;
this._z = c1 * c2 * s3 + s1 * s2 * c3;
this._w = c1 * c2 * c3 - s1 * s2 * s3;
} else if ( order === 'YXZ' ) {
this._x = s1 * c2 * c3 + c1 * s2 * s3;
this._y = c1 * s2 * c3 - s1 * c2 * s3;
this._z = c1 * c2 * s3 - s1 * s2 * c3;
this._w = c1 * c2 * c3 + s1 * s2 * s3;
} else if ( order === 'ZXY' ) {
this._x = s1 * c2 * c3 - c1 * s2 * s3;
this._y = c1 * s2 * c3 + s1 * c2 * s3;
this._z = c1 * c2 * s3 + s1 * s2 * c3;
this._w = c1 * c2 * c3 - s1 * s2 * s3;
} else if ( order === 'ZYX' ) {
this._x = s1 * c2 * c3 - c1 * s2 * s3;
this._y = c1 * s2 * c3 + s1 * c2 * s3;
this._z = c1 * c2 * s3 - s1 * s2 * c3;
this._w = c1 * c2 * c3 + s1 * s2 * s3;
} else if ( order === 'YZX' ) {
this._x = s1 * c2 * c3 + c1 * s2 * s3;
this._y = c1 * s2 * c3 + s1 * c2 * s3;
this._z = c1 * c2 * s3 - s1 * s2 * c3;
this._w = c1 * c2 * c3 - s1 * s2 * s3;
} else if ( order === 'XZY' ) {
this._x = s1 * c2 * c3 - c1 * s2 * s3;
this._y = c1 * s2 * c3 - s1 * c2 * s3;
this._z = c1 * c2 * s3 + s1 * s2 * c3;
this._w = c1 * c2 * c3 + s1 * s2 * s3;
}
if ( update !== false ) this.onChangeCallback();
return this;
},
setFromAxisAngle: function ( axis, angle ) {
// http://www.euclideanspace.com/maths/geometry/rotations/conversions/angleToQuaternion/index.htm
// assumes axis is normalized
var halfAngle = angle / 2, s = Math.sin( halfAngle );
this._x = axis.x * s;
this._y = axis.y * s;
this._z = axis.z * s;
this._w = Math.cos( halfAngle );
this.onChangeCallback();
return this;
},
setFromRotationMatrix: function ( m ) {
// http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm
// assumes the upper 3x3 of m is a pure rotation matrix (i.e, unscaled)
var te = m.elements,
m11 = te[ 0 ], m12 = te[ 4 ], m13 = te[ 8 ],
m21 = te[ 1 ], m22 = te[ 5 ], m23 = te[ 9 ],
m31 = te[ 2 ], m32 = te[ 6 ], m33 = te[ 10 ],
trace = m11 + m22 + m33,
s;
if ( trace > 0 ) {
s = 0.5 / Math.sqrt( trace + 1.0 );
this._w = 0.25 / s;
this._x = ( m32 - m23 ) * s;
this._y = ( m13 - m31 ) * s;
this._z = ( m21 - m12 ) * s;
} else if ( m11 > m22 && m11 > m33 ) {
s = 2.0 * Math.sqrt( 1.0 + m11 - m22 - m33 );
this._w = ( m32 - m23 ) / s;
this._x = 0.25 * s;
this._y = ( m12 + m21 ) / s;
this._z = ( m13 + m31 ) / s;
} else if ( m22 > m33 ) {
s = 2.0 * Math.sqrt( 1.0 + m22 - m11 - m33 );
this._w = ( m13 - m31 ) / s;
this._x = ( m12 + m21 ) / s;
this._y = 0.25 * s;
this._z = ( m23 + m32 ) / s;
} else {
s = 2.0 * Math.sqrt( 1.0 + m33 - m11 - m22 );
this._w = ( m21 - m12 ) / s;
this._x = ( m13 + m31 ) / s;
this._y = ( m23 + m32 ) / s;
this._z = 0.25 * s;
}
this.onChangeCallback();
return this;
},
setFromUnitVectors: function () {
// assumes direction vectors vFrom and vTo are normalized
var v1 = new Vector3();
var r;
var EPS = 0.000001;
return function setFromUnitVectors( vFrom, vTo ) {
if ( v1 === undefined ) v1 = new Vector3();
r = vFrom.dot( vTo ) + 1;
if ( r < EPS ) {
r = 0;
if ( Math.abs( vFrom.x ) > Math.abs( vFrom.z ) ) {
v1.set( - vFrom.y, vFrom.x, 0 );
} else {
v1.set( 0, - vFrom.z, vFrom.y );
}
} else {
v1.crossVectors( vFrom, vTo );
}
this._x = v1.x;
this._y = v1.y;
this._z = v1.z;
this._w = r;
return this.normalize();
};
}(),
inverse: function () {
// quaternion is assumed to have unit length
return this.conjugate();
},
conjugate: function () {
this._x *= - 1;
this._y *= - 1;
this._z *= - 1;
this.onChangeCallback();
return this;
},
dot: function ( v ) {
return this._x * v._x + this._y * v._y + this._z * v._z + this._w * v._w;
},
lengthSq: function () {
return this._x * this._x + this._y * this._y + this._z * this._z + this._w * this._w;
},
length: function () {
return Math.sqrt( this._x * this._x + this._y * this._y + this._z * this._z + this._w * this._w );
},
normalize: function () {
var l = this.length();
if ( l === 0 ) {
this._x = 0;
this._y = 0;
this._z = 0;
this._w = 1;
} else {
l = 1 / l;
this._x = this._x * l;
this._y = this._y * l;
this._z = this._z * l;
this._w = this._w * l;
}
this.onChangeCallback();
return this;
},
multiply: function ( q, p ) {
if ( p !== undefined ) {
console.warn( 'THREE.Quaternion: .multiply() now only accepts one argument. Use .multiplyQuaternions( a, b ) instead.' );
return this.multiplyQuaternions( q, p );
}
return this.multiplyQuaternions( this, q );
},
premultiply: function ( q ) {
return this.multiplyQuaternions( q, this );
},
multiplyQuaternions: function ( a, b ) {
// from http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/code/index.htm
var qax = a._x, qay = a._y, qaz = a._z, qaw = a._w;
var qbx = b._x, qby = b._y, qbz = b._z, qbw = b._w;
this._x = qax * qbw + qaw * qbx + qay * qbz - qaz * qby;
this._y = qay * qbw + qaw * qby + qaz * qbx - qax * qbz;
this._z = qaz * qbw + qaw * qbz + qax * qby - qay * qbx;
this._w = qaw * qbw - qax * qbx - qay * qby - qaz * qbz;
this.onChangeCallback();
return this;
},
slerp: function ( qb, t ) {
if ( t === 0 ) return this;
if ( t === 1 ) return this.copy( qb );
var x = this._x, y = this._y, z = this._z, w = this._w;
// http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/slerp/
var cosHalfTheta = w * qb._w + x * qb._x + y * qb._y + z * qb._z;
if ( cosHalfTheta < 0 ) {
this._w = - qb._w;
this._x = - qb._x;
this._y = - qb._y;
this._z = - qb._z;
cosHalfTheta = - cosHalfTheta;
} else {
this.copy( qb );
}
if ( cosHalfTheta >= 1.0 ) {
this._w = w;
this._x = x;
this._y = y;
this._z = z;
return this;
}
var sinHalfTheta = Math.sqrt( 1.0 - cosHalfTheta * cosHalfTheta );
if ( Math.abs( sinHalfTheta ) < 0.001 ) {
this._w = 0.5 * ( w + this._w );
this._x = 0.5 * ( x + this._x );
this._y = 0.5 * ( y + this._y );
this._z = 0.5 * ( z + this._z );
return this;
}
var halfTheta = Math.atan2( sinHalfTheta, cosHalfTheta );
var ratioA = Math.sin( ( 1 - t ) * halfTheta ) / sinHalfTheta,
ratioB = Math.sin( t * halfTheta ) / sinHalfTheta;
this._w = ( w * ratioA + this._w * ratioB );
this._x = ( x * ratioA + this._x * ratioB );
this._y = ( y * ratioA + this._y * ratioB );
this._z = ( z * ratioA + this._z * ratioB );
this.onChangeCallback();
return this;
},
equals: function ( quaternion ) {
return ( quaternion._x === this._x ) && ( quaternion._y === this._y ) && ( quaternion._z === this._z ) && ( quaternion._w === this._w );
},
fromArray: function ( array, offset ) {
if ( offset === undefined ) offset = 0;
this._x = array[ offset ];
this._y = array[ offset + 1 ];
this._z = array[ offset + 2 ];
this._w = array[ offset + 3 ];
this.onChangeCallback();
return this;
},
toArray: function ( array, offset ) {
if ( array === undefined ) array = [];
if ( offset === undefined ) offset = 0;
array[ offset ] = this._x;
array[ offset + 1 ] = this._y;
array[ offset + 2 ] = this._z;
array[ offset + 3 ] = this._w;
return array;
},
onChange: function ( callback ) {
this.onChangeCallback = callback;
return this;
},
onChangeCallback: function () {}
} );
/**
* @author mrdoob / http://mrdoob.com/
* @author supereggbert / http://www.paulbrunt.co.uk/
* @author philogb / http://blog.thejit.org/
* @author jordi_ros / http://plattsoft.com
* @author D1plo1d / http://github.com/D1plo1d
* @author alteredq / http://alteredqualia.com/
* @author mikael emtinger / http://gomo.se/
* @author timknip / http://www.floorplanner.com/
* @author bhouston / http://clara.io
* @author WestLangley / http://github.com/WestLangley
*/
function Matrix4() {
this.elements = [
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1
];
if ( arguments.length > 0 ) {
console.error( 'THREE.Matrix4: the constructor no longer reads arguments. use .set() instead.' );
}
}
Object.assign( Matrix4.prototype, {
isMatrix4: true,
set: function ( n11, n12, n13, n14, n21, n22, n23, n24, n31, n32, n33, n34, n41, n42, n43, n44 ) {
var te = this.elements;
te[ 0 ] = n11; te[ 4 ] = n12; te[ 8 ] = n13; te[ 12 ] = n14;
te[ 1 ] = n21; te[ 5 ] = n22; te[ 9 ] = n23; te[ 13 ] = n24;
te[ 2 ] = n31; te[ 6 ] = n32; te[ 10 ] = n33; te[ 14 ] = n34;
te[ 3 ] = n41; te[ 7 ] = n42; te[ 11 ] = n43; te[ 15 ] = n44;
return this;
},
identity: function () {
this.set(
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1
);
return this;
},
clone: function () {
return new Matrix4().fromArray( this.elements );
},
copy: function ( m ) {
var te = this.elements;
var me = m.elements;
te[ 0 ] = me[ 0 ]; te[ 1 ] = me[ 1 ]; te[ 2 ] = me[ 2 ]; te[ 3 ] = me[ 3 ];
te[ 4 ] = me[ 4 ]; te[ 5 ] = me[ 5 ]; te[ 6 ] = me[ 6 ]; te[ 7 ] = me[ 7 ];
te[ 8 ] = me[ 8 ]; te[ 9 ] = me[ 9 ]; te[ 10 ] = me[ 10 ]; te[ 11 ] = me[ 11 ];
te[ 12 ] = me[ 12 ]; te[ 13 ] = me[ 13 ]; te[ 14 ] = me[ 14 ]; te[ 15 ] = me[ 15 ];
return this;
},
copyPosition: function ( m ) {
var te = this.elements, me = m.elements;
te[ 12 ] = me[ 12 ];
te[ 13 ] = me[ 13 ];
te[ 14 ] = me[ 14 ];
return this;
},
extractBasis: function ( xAxis, yAxis, zAxis ) {
xAxis.setFromMatrixColumn( this, 0 );
yAxis.setFromMatrixColumn( this, 1 );
zAxis.setFromMatrixColumn( this, 2 );
return this;
},
makeBasis: function ( xAxis, yAxis, zAxis ) {
this.set(
xAxis.x, yAxis.x, zAxis.x, 0,
xAxis.y, yAxis.y, zAxis.y, 0,
xAxis.z, yAxis.z, zAxis.z, 0,
0, 0, 0, 1
);
return this;
},
extractRotation: function () {
var v1 = new Vector3();
return function extractRotation( m ) {
var te = this.elements;
var me = m.elements;
var scaleX = 1 / v1.setFromMatrixColumn( m, 0 ).length();
var scaleY = 1 / v1.setFromMatrixColumn( m, 1 ).length();
var scaleZ = 1 / v1.setFromMatrixColumn( m, 2 ).length();
te[ 0 ] = me[ 0 ] * scaleX;
te[ 1 ] = me[ 1 ] * scaleX;
te[ 2 ] = me[ 2 ] * scaleX;
te[ 4 ] = me[ 4 ] * scaleY;
te[ 5 ] = me[ 5 ] * scaleY;
te[ 6 ] = me[ 6 ] * scaleY;
te[ 8 ] = me[ 8 ] * scaleZ;
te[ 9 ] = me[ 9 ] * scaleZ;
te[ 10 ] = me[ 10 ] * scaleZ;
return this;
};
}(),
makeRotationFromEuler: function ( euler ) {
if ( ! ( euler && euler.isEuler ) ) {
console.error( 'THREE.Matrix4: .makeRotationFromEuler() now expects a Euler rotation rather than a Vector3 and order.' );
}
var te = this.elements;
var x = euler.x, y = euler.y, z = euler.z;
var a = Math.cos( x ), b = Math.sin( x );
var c = Math.cos( y ), d = Math.sin( y );
var e = Math.cos( z ), f = Math.sin( z );
if ( euler.order === 'XYZ' ) {
var ae = a * e, af = a * f, be = b * e, bf = b * f;
te[ 0 ] = c * e;
te[ 4 ] = - c * f;
te[ 8 ] = d;
te[ 1 ] = af + be * d;
te[ 5 ] = ae - bf * d;
te[ 9 ] = - b * c;
te[ 2 ] = bf - ae * d;
te[ 6 ] = be + af * d;
te[ 10 ] = a * c;
} else if ( euler.order === 'YXZ' ) {
var ce = c * e, cf = c * f, de = d * e, df = d * f;
te[ 0 ] = ce + df * b;
te[ 4 ] = de * b - cf;
te[ 8 ] = a * d;
te[ 1 ] = a * f;
te[ 5 ] = a * e;
te[ 9 ] = - b;
te[ 2 ] = cf * b - de;
te[ 6 ] = df + ce * b;
te[ 10 ] = a * c;
} else if ( euler.order === 'ZXY' ) {
var ce = c * e, cf = c * f, de = d * e, df = d * f;
te[ 0 ] = ce - df * b;
te[ 4 ] = - a * f;
te[ 8 ] = de + cf * b;
te[ 1 ] = cf + de * b;
te[ 5 ] = a * e;
te[ 9 ] = df - ce * b;
te[ 2 ] = - a * d;
te[ 6 ] = b;
te[ 10 ] = a * c;
} else if ( euler.order === 'ZYX' ) {
var ae = a * e, af = a * f, be = b * e, bf = b * f;
te[ 0 ] = c * e;
te[ 4 ] = be * d - af;
te[ 8 ] = ae * d + bf;
te[ 1 ] = c * f;
te[ 5 ] = bf * d + ae;
te[ 9 ] = af * d - be;
te[ 2 ] = - d;
te[ 6 ] = b * c;
te[ 10 ] = a * c;
} else if ( euler.order === 'YZX' ) {
var ac = a * c, ad = a * d, bc = b * c, bd = b * d;
te[ 0 ] = c * e;
te[ 4 ] = bd - ac * f;
te[ 8 ] = bc * f + ad;
te[ 1 ] = f;
te[ 5 ] = a * e;
te[ 9 ] = - b * e;
te[ 2 ] = - d * e;
te[ 6 ] = ad * f + bc;
te[ 10 ] = ac - bd * f;
} else if ( euler.order === 'XZY' ) {
var ac = a * c, ad = a * d, bc = b * c, bd = b * d;
te[ 0 ] = c * e;
te[ 4 ] = - f;
te[ 8 ] = d * e;
te[ 1 ] = ac * f + bd;
te[ 5 ] = a * e;
te[ 9 ] = ad * f - bc;
te[ 2 ] = bc * f - ad;
te[ 6 ] = b * e;
te[ 10 ] = bd * f + ac;
}
// last column
te[ 3 ] = 0;
te[ 7 ] = 0;
te[ 11 ] = 0;
// bottom row
te[ 12 ] = 0;
te[ 13 ] = 0;
te[ 14 ] = 0;
te[ 15 ] = 1;
return this;
},
makeRotationFromQuaternion: function ( q ) {
var te = this.elements;
var x = q._x, y = q._y, z = q._z, w = q._w;
var x2 = x + x, y2 = y + y, z2 = z + z;
var xx = x * x2, xy = x * y2, xz = x * z2;
var yy = y * y2, yz = y * z2, zz = z * z2;
var wx = w * x2, wy = w * y2, wz = w * z2;
te[ 0 ] = 1 - ( yy + zz );
te[ 4 ] = xy - wz;
te[ 8 ] = xz + wy;
te[ 1 ] = xy + wz;
te[ 5 ] = 1 - ( xx + zz );
te[ 9 ] = yz - wx;
te[ 2 ] = xz - wy;
te[ 6 ] = yz + wx;
te[ 10 ] = 1 - ( xx + yy );
// last column
te[ 3 ] = 0;
te[ 7 ] = 0;
te[ 11 ] = 0;
// bottom row
te[ 12 ] = 0;
te[ 13 ] = 0;
te[ 14 ] = 0;
te[ 15 ] = 1;
return this;
},
lookAt: function () {
var x = new Vector3();
var y = new Vector3();
var z = new Vector3();
return function lookAt( eye, target, up ) {
var te = this.elements;
z.subVectors( eye, target );
if ( z.lengthSq() === 0 ) {
// eye and target are in the same position
z.z = 1;
}
z.normalize();
x.crossVectors( up, z );
if ( x.lengthSq() === 0 ) {
// up and z are parallel
if ( Math.abs( up.z ) === 1 ) {
z.x += 0.0001;
} else {
z.z += 0.0001;
}
z.normalize();
x.crossVectors( up, z );
}
x.normalize();
y.crossVectors( z, x );
te[ 0 ] = x.x; te[ 4 ] = y.x; te[ 8 ] = z.x;
te[ 1 ] = x.y; te[ 5 ] = y.y; te[ 9 ] = z.y;
te[ 2 ] = x.z; te[ 6 ] = y.z; te[ 10 ] = z.z;
return this;
};
}(),
multiply: function ( m, n ) {
if ( n !== undefined ) {
console.warn( 'THREE.Matrix4: .multiply() now only accepts one argument. Use .multiplyMatrices( a, b ) instead.' );
return this.multiplyMatrices( m, n );
}
return this.multiplyMatrices( this, m );
},
premultiply: function ( m ) {
return this.multiplyMatrices( m, this );
},
multiplyMatrices: function ( a, b ) {
var ae = a.elements;
var be = b.elements;
var te = this.elements;
var a11 = ae[ 0 ], a12 = ae[ 4 ], a13 = ae[ 8 ], a14 = ae[ 12 ];
var a21 = ae[ 1 ], a22 = ae[ 5 ], a23 = ae[ 9 ], a24 = ae[ 13 ];
var a31 = ae[ 2 ], a32 = ae[ 6 ], a33 = ae[ 10 ], a34 = ae[ 14 ];
var a41 = ae[ 3 ], a42 = ae[ 7 ], a43 = ae[ 11 ], a44 = ae[ 15 ];
var b11 = be[ 0 ], b12 = be[ 4 ], b13 = be[ 8 ], b14 = be[ 12 ];
var b21 = be[ 1 ], b22 = be[ 5 ], b23 = be[ 9 ], b24 = be[ 13 ];
var b31 = be[ 2 ], b32 = be[ 6 ], b33 = be[ 10 ], b34 = be[ 14 ];
var b41 = be[ 3 ], b42 = be[ 7 ], b43 = be[ 11 ], b44 = be[ 15 ];
te[ 0 ] = a11 * b11 + a12 * b21 + a13 * b31 + a14 * b41;
te[ 4 ] = a11 * b12 + a12 * b22 + a13 * b32 + a14 * b42;
te[ 8 ] = a11 * b13 + a12 * b23 + a13 * b33 + a14 * b43;
te[ 12 ] = a11 * b14 + a12 * b24 + a13 * b34 + a14 * b44;
te[ 1 ] = a21 * b11 + a22 * b21 + a23 * b31 + a24 * b41;
te[ 5 ] = a21 * b12 + a22 * b22 + a23 * b32 + a24 * b42;
te[ 9 ] = a21 * b13 + a22 * b23 + a23 * b33 + a24 * b43;
te[ 13 ] = a21 * b14 + a22 * b24 + a23 * b34 + a24 * b44;
te[ 2 ] = a31 * b11 + a32 * b21 + a33 * b31 + a34 * b41;
te[ 6 ] = a31 * b12 + a32 * b22 + a33 * b32 + a34 * b42;
te[ 10 ] = a31 * b13 + a32 * b23 + a33 * b33 + a34 * b43;
te[ 14 ] = a31 * b14 + a32 * b24 + a33 * b34 + a34 * b44;
te[ 3 ] = a41 * b11 + a42 * b21 + a43 * b31 + a44 * b41;
te[ 7 ] = a41 * b12 + a42 * b22 + a43 * b32 + a44 * b42;
te[ 11 ] = a41 * b13 + a42 * b23 + a43 * b33 + a44 * b43;
te[ 15 ] = a41 * b14 + a42 * b24 + a43 * b34 + a44 * b44;
return this;
},
multiplyScalar: function ( s ) {
var te = this.elements;
te[ 0 ] *= s; te[ 4 ] *= s; te[ 8 ] *= s; te[ 12 ] *= s;
te[ 1 ] *= s; te[ 5 ] *= s; te[ 9 ] *= s; te[ 13 ] *= s;
te[ 2 ] *= s; te[ 6 ] *= s; te[ 10 ] *= s; te[ 14 ] *= s;
te[ 3 ] *= s; te[ 7 ] *= s; te[ 11 ] *= s; te[ 15 ] *= s;
return this;
},
applyToBufferAttribute: function () {
var v1 = new Vector3();
return function applyToBufferAttribute( attribute ) {
for ( var i = 0, l = attribute.count; i < l; i ++ ) {
v1.x = attribute.getX( i );
v1.y = attribute.getY( i );
v1.z = attribute.getZ( i );
v1.applyMatrix4( this );
attribute.setXYZ( i, v1.x, v1.y, v1.z );
}
return attribute;
};
}(),
determinant: function () {
var te = this.elements;
var n11 = te[ 0 ], n12 = te[ 4 ], n13 = te[ 8 ], n14 = te[ 12 ];
var n21 = te[ 1 ], n22 = te[ 5 ], n23 = te[ 9 ], n24 = te[ 13 ];
var n31 = te[ 2 ], n32 = te[ 6 ], n33 = te[ 10 ], n34 = te[ 14 ];
var n41 = te[ 3 ], n42 = te[ 7 ], n43 = te[ 11 ], n44 = te[ 15 ];
//TODO: make this more efficient
//( based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm )
return (
n41 * (
+ n14 * n23 * n32
- n13 * n24 * n32
- n14 * n22 * n33
+ n12 * n24 * n33
+ n13 * n22 * n34
- n12 * n23 * n34
) +
n42 * (
+ n11 * n23 * n34
- n11 * n24 * n33
+ n14 * n21 * n33
- n13 * n21 * n34
+ n13 * n24 * n31
- n14 * n23 * n31
) +
n43 * (
+ n11 * n24 * n32
- n11 * n22 * n34
- n14 * n21 * n32
+ n12 * n21 * n34
+ n14 * n22 * n31
- n12 * n24 * n31
) +
n44 * (
- n13 * n22 * n31
- n11 * n23 * n32
+ n11 * n22 * n33
+ n13 * n21 * n32
- n12 * n21 * n33
+ n12 * n23 * n31
)
);
},
transpose: function () {
var te = this.elements;
var tmp;
tmp = te[ 1 ]; te[ 1 ] = te[ 4 ]; te[ 4 ] = tmp;
tmp = te[ 2 ]; te[ 2 ] = te[ 8 ]; te[ 8 ] = tmp;
tmp = te[ 6 ]; te[ 6 ] = te[ 9 ]; te[ 9 ] = tmp;
tmp = te[ 3 ]; te[ 3 ] = te[ 12 ]; te[ 12 ] = tmp;
tmp = te[ 7 ]; te[ 7 ] = te[ 13 ]; te[ 13 ] = tmp;
tmp = te[ 11 ]; te[ 11 ] = te[ 14 ]; te[ 14 ] = tmp;
return this;
},
setPosition: function ( v ) {
var te = this.elements;
te[ 12 ] = v.x;
te[ 13 ] = v.y;
te[ 14 ] = v.z;
return this;
},
getInverse: function ( m, throwOnDegenerate ) {
// based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm
var te = this.elements,
me = m.elements,
n11 = me[ 0 ], n21 = me[ 1 ], n31 = me[ 2 ], n41 = me[ 3 ],
n12 = me[ 4 ], n22 = me[ 5 ], n32 = me[ 6 ], n42 = me[ 7 ],
n13 = me[ 8 ], n23 = me[ 9 ], n33 = me[ 10 ], n43 = me[ 11 ],
n14 = me[ 12 ], n24 = me[ 13 ], n34 = me[ 14 ], n44 = me[ 15 ],
t11 = n23 * n34 * n42 - n24 * n33 * n42 + n24 * n32 * n43 - n22 * n34 * n43 - n23 * n32 * n44 + n22 * n33 * n44,
t12 = n14 * n33 * n42 - n13 * n34 * n42 - n14 * n32 * n43 + n12 * n34 * n43 + n13 * n32 * n44 - n12 * n33 * n44,
t13 = n13 * n24 * n42 - n14 * n23 * n42 + n14 * n22 * n43 - n12 * n24 * n43 - n13 * n22 * n44 + n12 * n23 * n44,
t14 = n14 * n23 * n32 - n13 * n24 * n32 - n14 * n22 * n33 + n12 * n24 * n33 + n13 * n22 * n34 - n12 * n23 * n34;
var det = n11 * t11 + n21 * t12 + n31 * t13 + n41 * t14;
if ( det === 0 ) {
var msg = "THREE.Matrix4: .getInverse() can't invert matrix, determinant is 0";
if ( throwOnDegenerate === true ) {
throw new Error( msg );
} else {
console.warn( msg );
}
return this.identity();
}
var detInv = 1 / det;
te[ 0 ] = t11 * detInv;
te[ 1 ] = ( n24 * n33 * n41 - n23 * n34 * n41 - n24 * n31 * n43 + n21 * n34 * n43 + n23 * n31 * n44 - n21 * n33 * n44 ) * detInv;
te[ 2 ] = ( n22 * n34 * n41 - n24 * n32 * n41 + n24 * n31 * n42 - n21 * n34 * n42 - n22 * n31 * n44 + n21 * n32 * n44 ) * detInv;
te[ 3 ] = ( n23 * n32 * n41 - n22 * n33 * n41 - n23 * n31 * n42 + n21 * n33 * n42 + n22 * n31 * n43 - n21 * n32 * n43 ) * detInv;
te[ 4 ] = t12 * detInv;
te[ 5 ] = ( n13 * n34 * n41 - n14 * n33 * n41 + n14 * n31 * n43 - n11 * n34 * n43 - n13 * n31 * n44 + n11 * n33 * n44 ) * detInv;
te[ 6 ] = ( n14 * n32 * n41 - n12 * n34 * n41 - n14 * n31 * n42 + n11 * n34 * n42 + n12 * n31 * n44 - n11 * n32 * n44 ) * detInv;
te[ 7 ] = ( n12 * n33 * n41 - n13 * n32 * n41 + n13 * n31 * n42 - n11 * n33 * n42 - n12 * n31 * n43 + n11 * n32 * n43 ) * detInv;
te[ 8 ] = t13 * detInv;
te[ 9 ] = ( n14 * n23 * n41 - n13 * n24 * n41 - n14 * n21 * n43 + n11 * n24 * n43 + n13 * n21 * n44 - n11 * n23 * n44 ) * detInv;
te[ 10 ] = ( n12 * n24 * n41 - n14 * n22 * n41 + n14 * n21 * n42 - n11 * n24 * n42 - n12 * n21 * n44 + n11 * n22 * n44 ) * detInv;
te[ 11 ] = ( n13 * n22 * n41 - n12 * n23 * n41 - n13 * n21 * n42 + n11 * n23 * n42 + n12 * n21 * n43 - n11 * n22 * n43 ) * detInv;
te[ 12 ] = t14 * detInv;
te[ 13 ] = ( n13 * n24 * n31 - n14 * n23 * n31 + n14 * n21 * n33 - n11 * n24 * n33 - n13 * n21 * n34 + n11 * n23 * n34 ) * detInv;
te[ 14 ] = ( n14 * n22 * n31 - n12 * n24 * n31 - n14 * n21 * n32 + n11 * n24 * n32 + n12 * n21 * n34 - n11 * n22 * n34 ) * detInv;
te[ 15 ] = ( n12 * n23 * n31 - n13 * n22 * n31 + n13 * n21 * n32 - n11 * n23 * n32 - n12 * n21 * n33 + n11 * n22 * n33 ) * detInv;
return this;
},
scale: function ( v ) {
var te = this.elements;
var x = v.x, y = v.y, z = v.z;
te[ 0 ] *= x; te[ 4 ] *= y; te[ 8 ] *= z;
te[ 1 ] *= x; te[ 5 ] *= y; te[ 9 ] *= z;
te[ 2 ] *= x; te[ 6 ] *= y; te[ 10 ] *= z;
te[ 3 ] *= x; te[ 7 ] *= y; te[ 11 ] *= z;
return this;
},
getMaxScaleOnAxis: function () {
var te = this.elements;
var scaleXSq = te[ 0 ] * te[ 0 ] + te[ 1 ] * te[ 1 ] + te[ 2 ] * te[ 2 ];
var scaleYSq = te[ 4 ] * te[ 4 ] + te[ 5 ] * te[ 5 ] + te[ 6 ] * te[ 6 ];
var scaleZSq = te[ 8 ] * te[ 8 ] + te[ 9 ] * te[ 9 ] + te[ 10 ] * te[ 10 ];
return Math.sqrt( Math.max( scaleXSq, scaleYSq, scaleZSq ) );
},
makeTranslation: function ( x, y, z ) {
this.set(
1, 0, 0, x,
0, 1, 0, y,
0, 0, 1, z,
0, 0, 0, 1
);
return this;
},
makeRotationX: function ( theta ) {
var c = Math.cos( theta ), s = Math.sin( theta );
this.set(
1, 0, 0, 0,
0, c, - s, 0,
0, s, c, 0,
0, 0, 0, 1
);
return this;
},
makeRotationY: function ( theta ) {
var c = Math.cos( theta ), s = Math.sin( theta );
this.set(
c, 0, s, 0,
0, 1, 0, 0,
- s, 0, c, 0,
0, 0, 0, 1
);
return this;
},
makeRotationZ: function ( theta ) {
var c = Math.cos( theta ), s = Math.sin( theta );
this.set(
c, - s, 0, 0,
s, c, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1
);
return this;
},
makeRotationAxis: function ( axis, angle ) {
// Based on http://www.gamedev.net/reference/articles/article1199.asp
var c = Math.cos( angle );
var s = Math.sin( angle );
var t = 1 - c;
var x = axis.x, y = axis.y, z = axis.z;
var tx = t * x, ty = t * y;
this.set(
tx * x + c, tx * y - s * z, tx * z + s * y, 0,
tx * y + s * z, ty * y + c, ty * z - s * x, 0,
tx * z - s * y, ty * z + s * x, t * z * z + c, 0,
0, 0, 0, 1
);
return this;
},
makeScale: function ( x, y, z ) {
this.set(
x, 0, 0, 0,
0, y, 0, 0,
0, 0, z, 0,
0, 0, 0, 1
);
return this;
},
makeShear: function ( x, y, z ) {
this.set(
1, y, z, 0,
x, 1, z, 0,
x, y, 1, 0,
0, 0, 0, 1
);
return this;
},
compose: function ( position, quaternion, scale ) {
this.makeRotationFromQuaternion( quaternion );
this.scale( scale );
this.setPosition( position );
return this;
},
decompose: function () {
var vector = new Vector3();
var matrix = new Matrix4();
return function decompose( position, quaternion, scale ) {
var te = this.elements;
var sx = vector.set( te[ 0 ], te[ 1 ], te[ 2 ] ).length();
var sy = vector.set( te[ 4 ], te[ 5 ], te[ 6 ] ).length();
var sz = vector.set( te[ 8 ], te[ 9 ], te[ 10 ] ).length();
// if determine is negative, we need to invert one scale
var det = this.determinant();
if ( det < 0 ) sx = - sx;
position.x = te[ 12 ];
position.y = te[ 13 ];
position.z = te[ 14 ];
// scale the rotation part
matrix.copy( this );
var invSX = 1 / sx;
var invSY = 1 / sy;
var invSZ = 1 / sz;
matrix.elements[ 0 ] *= invSX;
matrix.elements[ 1 ] *= invSX;
matrix.elements[ 2 ] *= invSX;
matrix.elements[ 4 ] *= invSY;
matrix.elements[ 5 ] *= invSY;
matrix.elements[ 6 ] *= invSY;
matrix.elements[ 8 ] *= invSZ;
matrix.elements[ 9 ] *= invSZ;
matrix.elements[ 10 ] *= invSZ;
quaternion.setFromRotationMatrix( matrix );
scale.x = sx;
scale.y = sy;
scale.z = sz;
return this;
};
}(),
makePerspective: function ( left, right, top, bottom, near, far ) {
if ( far === undefined ) {
console.warn( 'THREE.Matrix4: .makePerspective() has been redefined and has a new signature. Please check the docs.' );
}
var te = this.elements;
var x = 2 * near / ( right - left );
var y = 2 * near / ( top - bottom );
var a = ( right + left ) / ( right - left );
var b = ( top + bottom ) / ( top - bottom );
var c = - ( far + near ) / ( far - near );
var d = - 2 * far * near / ( far - near );
te[ 0 ] = x; te[ 4 ] = 0; te[ 8 ] = a; te[ 12 ] = 0;
te[ 1 ] = 0; te[ 5 ] = y; te[ 9 ] = b; te[ 13 ] = 0;
te[ 2 ] = 0; te[ 6 ] = 0; te[ 10 ] = c; te[ 14 ] = d;
te[ 3 ] = 0; te[ 7 ] = 0; te[ 11 ] = - 1; te[ 15 ] = 0;
return this;
},
makeOrthographic: function ( left, right, top, bottom, near, far ) {
var te = this.elements;
var w = 1.0 / ( right - left );
var h = 1.0 / ( top - bottom );
var p = 1.0 / ( far - near );
var x = ( right + left ) * w;
var y = ( top + bottom ) * h;
var z = ( far + near ) * p;
te[ 0 ] = 2 * w; te[ 4 ] = 0; te[ 8 ] = 0; te[ 12 ] = - x;
te[ 1 ] = 0; te[ 5 ] = 2 * h; te[ 9 ] = 0; te[ 13 ] = - y;
te[ 2 ] = 0; te[ 6 ] = 0; te[ 10 ] = - 2 * p; te[ 14 ] = - z;
te[ 3 ] = 0; te[ 7 ] = 0; te[ 11 ] = 0; te[ 15 ] = 1;
return this;
},
equals: function ( matrix ) {
var te = this.elements;
var me = matrix.elements;
for ( var i = 0; i < 16; i ++ ) {
if ( te[ i ] !== me[ i ] ) return false;
}
return true;
},
fromArray: function ( array, offset ) {
if ( offset === undefined ) offset = 0;
for ( var i = 0; i < 16; i ++ ) {
this.elements[ i ] = array[ i + offset ];
}
return this;
},
toArray: function ( array, offset ) {
if ( array === undefined ) array = [];
if ( offset === undefined ) offset = 0;
var te = this.elements;
array[ offset ] = te[ 0 ];
array[ offset + 1 ] = te[ 1 ];
array[ offset + 2 ] = te[ 2 ];
array[ offset + 3 ] = te[ 3 ];
array[ offset + 4 ] = te[ 4 ];
array[ offset + 5 ] = te[ 5 ];
array[ offset + 6 ] = te[ 6 ];
array[ offset + 7 ] = te[ 7 ];
array[ offset + 8 ] = te[ 8 ];
array[ offset + 9 ] = te[ 9 ];
array[ offset + 10 ] = te[ 10 ];
array[ offset + 11 ] = te[ 11 ];
array[ offset + 12 ] = te[ 12 ];
array[ offset + 13 ] = te[ 13 ];
array[ offset + 14 ] = te[ 14 ];
array[ offset + 15 ] = te[ 15 ];
return array;
}
} );
