three.js/src/math/Quaternion.js

/**
 * @author mikael emtinger / http://gomo.se/
 * @author alteredq / http://alteredqualia.com/
 * @author WestLangley / http://github.com/WestLangley
 * @author bhouston / http://clara.io
 */

import { MathUtils } from './MathUtils.js';

function Quaternion( x = 0, y = 0, z = 0, w = 1 ) {

	this._x = x;
	this._y = y;
	this._z = z;
	this._w = w;

}

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

		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 ( w0 !== w1 || x0 !== x1 || y0 !== y1 || z0 !== z1 ) {

			let 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 ) {

				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;

	},

	multiplyQuaternionsFlat: function ( 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;

	}

} );

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, {

	isQuaternion: true,

	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.' );

		}

		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: function ( 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: 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)

		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: function ( vFrom, vTo ) {

		// assumes direction vectors vFrom and vTo are normalized

		const EPS = 0.000001;

		let r = vFrom.dot( vTo ) + 1;

		if ( r < EPS ) {

			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: function ( q ) {

		return 2 * Math.acos( Math.abs( MathUtils.clamp( this.dot( q ), - 1, 1 ) ) );

	},

	rotateTowards: function ( 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;

	},

	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 () {

		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: 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

		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: function ( 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;

	},

	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;

	},

	fromBufferAttribute: function ( 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: function ( callback ) {

		this._onChangeCallback = callback;

		return this;

	},

	_onChangeCallback: function () {}

} );


export { Quaternion };