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://exocortex.com
 */

THREE.Quaternion = function ( x, y, z, w ) {

	this._x = x || 0;
	this._y = y || 0;
	this._z = z || 0;
	this._w = ( w !== undefined ) ? w : 1;

};

THREE.Quaternion.prototype = {

	constructor: THREE.Quaternion,

	_x: 0,_y: 0, _z: 0, _w: 0,

	_euler: undefined,

	_updateEuler: function ( callback ) {

		if ( this._euler !== undefined ) {

			this._euler.setFromQuaternion( this, undefined, false );

		}

	},

	get x () {

		return this._x;

	},

	set x ( value ) {

		this._x = value;
		this._updateEuler();

	},

	get y () {

		return this._y;

	},

	set y ( value ) {

		this._y = value;
		this._updateEuler();

	},

	get z () {

		return this._z;

	},

	set z ( value ) {

		this._z = value;
		this._updateEuler();

	},

	get w () {

		return this._w;

	},

	set w ( value ) {

		this._w = value;
		this._updateEuler();

	},

	set: function ( x, y, z, w ) {

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

		this._updateEuler();

		return this;

	},

	copy: function ( quaternion ) {

		this._x = quaternion._x;
		this._y = quaternion._y;
		this._z = quaternion._z;
		this._w = quaternion._w;

		this._updateEuler();

		return this;

	},

	setFromEuler: function ( euler, update ) {

		if ( euler instanceof THREE.Euler === false ) {

			throw new Error( 'ERROR: Quaternion\'s .setFromEuler() now expects a Euler rotation rather than a Vector3 and order.  Please update your code.' );
		}

		// http://www.mathworks.com/matlabcentral/fileexchange/
		// 	20696-function-to-convert-between-dcm-euler-angles-quaternions-and-euler-vectors/
		//	content/SpinCalc.m

		var c1 = Math.cos( euler._x / 2 );
		var c2 = Math.cos( euler._y / 2 );
		var c3 = Math.cos( euler._z / 2 );
		var s1 = Math.sin( euler._x / 2 );
		var s2 = Math.sin( euler._y / 2 );
		var s3 = Math.sin( euler._z / 2 );

		if ( euler.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 ( euler.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 ( euler.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 ( euler.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 ( euler.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 ( euler.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._updateEuler();

		return this;

	},

	setFromAxisAngle: function ( axis, angle ) {

		// from http://www.euclideanspace.com/maths/geometry/rotations/conversions/angleToQuaternion/index.htm
		// axis have to be 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._updateEuler();

		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._updateEuler();

		return this;

	},

	inverse: function () {

		this.conjugate().normalize();

		return this;

	},

	conjugate: function () {

		this._x *= -1;
		this._y *= -1;
		this._z *= -1;

		this._updateEuler();

		return this;

	},

	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;

		}

		return this;

	},

	multiply: function ( q, p ) {

		if ( p !== undefined ) {

			console.warn( 'DEPRECATED: Quaternion\'s .multiply() now only accepts one argument. Use .multiplyQuaternions( a, b ) instead.' );
			return this.multiplyQuaternions( q, p );

		}

		return this.multiplyQuaternions( this, q );

	},

	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._updateEuler();

		return this;

	},

	multiplyVector3: function ( vector ) {

		console.warn( 'DEPRECATED: Quaternion\'s .multiplyVector3() has been removed. Use is now vector.applyQuaternion( quaternion ) instead.' );
		return vector.applyQuaternion( this );

	},

	slerp: function ( qb, t ) {

		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 halfTheta = Math.acos( cosHalfTheta );
		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 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._updateEuler();

		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 ) {

		this._x = array[ 0 ];
		this._y = array[ 1 ];
		this._z = array[ 2 ];
		this._w = array[ 3 ];

		this._updateEuler();

		return this;

	},

	toArray: function () {

		return [ this._x, this._y, this._z, this._w ];

	},

	clone: function () {

		return new THREE.Quaternion( this._x, this._y, this._z, this._w );

	}

};

THREE.Quaternion.slerp = function ( qa, qb, qm, t ) {

	return qm.copy( qa ).slerp( qb, t );

}