import * as MathUtils from './MathUtils.js';
class Quaternion {
constructor( x = 0, y = 0, z = 0, w = 1 ) {
this.isQuaternion = true;
this._x = x;
this._y = y;
this._z = z;
this._w = w;
}
static slerpFlat( dst, dstOffset, src0, srcOffset0, src1, srcOffset1, t ) {
// fuzz-free, array-based Quaternion SLERP operation
let x0 = src0[ srcOffset0 + 0 ],
y0 = src0[ srcOffset0 + 1 ],
z0 = src0[ srcOffset0 + 2 ],
w0 = src0[ srcOffset0 + 3 ];
const x1 = src1[ srcOffset1 + 0 ],
y1 = src1[ srcOffset1 + 1 ],
z1 = src1[ srcOffset1 + 2 ],
w1 = src1[ srcOffset1 + 3 ];
if ( t === 0 ) {
dst[ dstOffset + 0 ] = x0;
dst[ dstOffset + 1 ] = y0;
dst[ dstOffset + 2 ] = z0;
dst[ dstOffset + 3 ] = w0;
return;
}
if ( t === 1 ) {
dst[ dstOffset + 0 ] = x1;
dst[ dstOffset + 1 ] = y1;
dst[ dstOffset + 2 ] = z1;
dst[ dstOffset + 3 ] = w1;
return;
}
if ( w0 !== w1 || x0 !== x1 || y0 !== y1 || z0 !== z1 ) {
let s = 1 - t;
const 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 ) {
const sin = Math.sqrt( sqrSin ),
len = Math.atan2( sin, cos * dir );
s = Math.sin( s * len ) / sin;
t = Math.sin( t * len ) / sin;
}
const 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 ) {
const 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;
}
static multiplyQuaternionsFlat( dst, dstOffset, src0, srcOffset0, src1, srcOffset1 ) {
const x0 = src0[ srcOffset0 ];
const y0 = src0[ srcOffset0 + 1 ];
const z0 = src0[ srcOffset0 + 2 ];
const w0 = src0[ srcOffset0 + 3 ];
const x1 = src1[ srcOffset1 ];
const y1 = src1[ srcOffset1 + 1 ];
const z1 = src1[ srcOffset1 + 2 ];
const w1 = src1[ srcOffset1 + 3 ];
dst[ dstOffset ] = x0 * w1 + w0 * x1 + y0 * z1 - z0 * y1;
dst[ dstOffset + 1 ] = y0 * w1 + w0 * y1 + z0 * x1 - x0 * z1;
dst[ dstOffset + 2 ] = z0 * w1 + w0 * z1 + x0 * y1 - y0 * x1;
dst[ dstOffset + 3 ] = w0 * w1 - x0 * x1 - y0 * y1 - z0 * z1;
return dst;
}
get x() {
return this._x;
}
set x( value ) {
this._x = value;
this._onChangeCallback();
}
get y() {
return this._y;
}
set y( value ) {
this._y = value;
this._onChangeCallback();
}
get z() {
return this._z;
}
set z( value ) {
this._z = value;
this._onChangeCallback();
}
get w() {
return this._w;
}
set w( value ) {
this._w = value;
this._onChangeCallback();
}
set( x, y, z, w ) {
this._x = x;
this._y = y;
this._z = z;
this._w = w;
this._onChangeCallback();
return this;
}
clone() {
return new this.constructor( this._x, this._y, this._z, this._w );
}
copy( quaternion ) {
this._x = quaternion.x;
this._y = quaternion.y;
this._z = quaternion.z;
this._w = quaternion.w;
this._onChangeCallback();
return this;
}
setFromEuler( euler, update ) {
const 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
const cos = Math.cos;
const sin = Math.sin;
const c1 = cos( x / 2 );
const c2 = cos( y / 2 );
const c3 = cos( z / 2 );
const s1 = sin( x / 2 );
const s2 = sin( y / 2 );
const s3 = sin( z / 2 );
switch ( order ) {
case '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;
break;
case '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;
break;
case '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;
break;
case '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;
break;
case '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;
break;
case '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;
break;
default:
console.warn( 'THREE.Quaternion: .setFromEuler() encountered an unknown order: ' + order );
}
if ( update !== false ) this._onChangeCallback();
return this;
}
setFromAxisAngle( axis, angle ) {
// http://www.euclideanspace.com/maths/geometry/rotations/conversions/angleToQuaternion/index.htm
// assumes axis is normalized
const 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( 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)
const 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;
if ( trace > 0 ) {
const 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 ) {
const 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 ) {
const 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 {
const 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( vFrom, vTo ) {
// assumes direction vectors vFrom and vTo are normalized
let r = vFrom.dot( vTo ) + 1;
if ( r < Number.EPSILON ) {
// vFrom and vTo point in opposite directions
r = 0;
if ( Math.abs( vFrom.x ) > Math.abs( vFrom.z ) ) {
this._x = - vFrom.y;
this._y = vFrom.x;
this._z = 0;
this._w = r;
} else {
this._x = 0;
this._y = - vFrom.z;
this._z = vFrom.y;
this._w = r;
}
} else {
// crossVectors( vFrom, vTo ); // inlined to avoid cyclic dependency on Vector3
this._x = vFrom.y * vTo.z - vFrom.z * vTo.y;
this._y = vFrom.z * vTo.x - vFrom.x * vTo.z;
this._z = vFrom.x * vTo.y - vFrom.y * vTo.x;
this._w = r;
}
return this.normalize();
}
angleTo( q ) {
return 2 * Math.acos( Math.abs( MathUtils.clamp( this.dot( q ), - 1, 1 ) ) );
}
rotateTowards( q, step ) {
const angle = this.angleTo( q );
if ( angle === 0 ) return this;
const t = Math.min( 1, step / angle );
this.slerp( q, t );
return this;
}
identity() {
return this.set( 0, 0, 0, 1 );
}
invert() {
// quaternion is assumed to have unit length
return this.conjugate();
}
conjugate() {
this._x *= - 1;
this._y *= - 1;
this._z *= - 1;
this._onChangeCallback();
return this;
}
dot( v ) {
return this._x * v._x + this._y * v._y + this._z * v._z + this._w * v._w;
}
lengthSq() {
return this._x * this._x + this._y * this._y + this._z * this._z + this._w * this._w;
}
length() {
return Math.sqrt( this._x * this._x + this._y * this._y + this._z * this._z + this._w * this._w );
}
normalize() {
let 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( q ) {
return this.multiplyQuaternions( this, q );
}
premultiply( q ) {
return this.multiplyQuaternions( q, this );
}
multiplyQuaternions( a, b ) {
// from http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/code/index.htm
const qax = a._x, qay = a._y, qaz = a._z, qaw = a._w;
const 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( qb, t ) {
if ( t === 0 ) return this;
if ( t === 1 ) return this.copy( qb );
const x = this._x, y = this._y, z = this._z, w = this._w;
// http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/slerp/
let 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;
}
const sqrSinHalfTheta = 1.0 - cosHalfTheta * cosHalfTheta;
if ( sqrSinHalfTheta <= Number.EPSILON ) {
const s = 1 - t;
this._w = s * w + t * this._w;
this._x = s * x + t * this._x;
this._y = s * y + t * this._y;
this._z = s * z + t * this._z;
this.normalize();
this._onChangeCallback();
return this;
}
const sinHalfTheta = Math.sqrt( sqrSinHalfTheta );
const halfTheta = Math.atan2( sinHalfTheta, cosHalfTheta );
const 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;
}
slerpQuaternions( qa, qb, t ) {
return this.copy( qa ).slerp( qb, t );
}
random() {
// Derived from http://planning.cs.uiuc.edu/node198.html
// Note, this source uses w, x, y, z ordering,
// so we swap the order below.
const u1 = Math.random();
const sqrt1u1 = Math.sqrt( 1 - u1 );
const sqrtu1 = Math.sqrt( u1 );
const u2 = 2 * Math.PI * Math.random();
const u3 = 2 * Math.PI * Math.random();
return this.set(
sqrt1u1 * Math.cos( u2 ),
sqrtu1 * Math.sin( u3 ),
sqrtu1 * Math.cos( u3 ),
sqrt1u1 * Math.sin( u2 ),
);
}
equals( quaternion ) {
return ( quaternion._x === this._x ) && ( quaternion._y === this._y ) && ( quaternion._z === this._z ) && ( quaternion._w === this._w );
}
fromArray( array, 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( array = [], offset = 0 ) {
array[ offset ] = this._x;
array[ offset + 1 ] = this._y;
array[ offset + 2 ] = this._z;
array[ offset + 3 ] = this._w;
return array;
}
fromBufferAttribute( attribute, index ) {
this._x = attribute.getX( index );
this._y = attribute.getY( index );
this._z = attribute.getZ( index );
this._w = attribute.getW( index );
return this;
}
_onChange( callback ) {
this._onChangeCallback = callback;
return this;
}
_onChangeCallback() {}
*[ Symbol.iterator ]() {
yield this._x;
yield this._y;
yield this._z;
yield this._w;
}
}
export { Quaternion };
