three.js/src/math/Quaternion.js

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

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,

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

		this.x = x;
		this.y = y;
		this.z = z;
		this.w = w;

		return this;

	},

	copy: function ( q ) {

		this.x = q.x;
		this.y = q.y;
		this.z = q.z;
		this.w = q.w;

		return this;

	},

	setFromEuler: function ( v, order ) {

		// 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( v.x / 2 );
		var c2 = Math.cos( v.y / 2 );
		var c3 = Math.cos( v.z / 2 );
		var s1 = Math.sin( v.x / 2 );
		var s2 = Math.sin( v.y / 2 );
		var s3 = Math.sin( v.z / 2 );

		if ( order === undefined || 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;
				
		}
		
		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 );

		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;
		
		}
	
		return this;

	},

	inverse: function () {

		this.conjugate().normalize();

		return this;

	},

	conjugate: function () {

		this.x *= -1;
		this.y *= -1;
		this.z *= -1;

		return this;

	},

	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 = Math.sqrt( this.x * this.x + this.y * this.y + this.z * this.z + this.w * this.w );

		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 ( 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,
		qbx = b.x, qby = b.y, qbz = b.z, qbw = b.w;

		this.x =  qax * qbw + qay * qbz - qaz * qby + qaw * qbx;
		this.y = -qax * qbz + qay * qbw + qaz * qbx + qaw * qby;
		this.z =  qax * qby - qay * qbx + qaz * qbw + qaw * qbz;
		this.w = -qax * qbx - qay * qby - qaz * qbz + qaw * qbw;

		return this;

	},

	multiplySelf: function ( b ) {

		var qax = this.x, qay = this.y, qaz = this.z, qaw = this.w,
		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;

		return this;

	},

	multiplyVector3: function ( vector, dest ) {

		if ( !dest ) { dest = vector; }

		var x    = vector.x,  y  = vector.y,  z  = vector.z,
			qx   = this.x, qy = this.y, qz = this.z, qw = this.w;

		// calculate quat * vector

		var ix =  qw * x + qy * z - qz * y,
			iy =  qw * y + qz * x - qx * z,
			iz =  qw * z + qx * y - qy * x,
			iw = -qx * x - qy * y - qz * z;

		// calculate result * inverse quat

		dest.x = ix * qw + iw * -qx + iy * -qz - iz * -qy;
		dest.y = iy * qw + iw * -qy + iz * -qx - ix * -qz;
		dest.z = iz * qw + iw * -qz + ix * -qy - iy * -qx;

		return dest;

	},

	slerpSelf: 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 );

		return this;

	},

	clone: function () {

		return new THREE.Quaternion( this.x, this.y, this.z, this.w );

	}

}

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

	// http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/slerp/

	var cosHalfTheta = qa.w * qb.w + qa.x * qb.x + qa.y * qb.y + qa.z * qb.z;

	if ( cosHalfTheta < 0 ) {

		qm.w = -qb.w;
		qm.x = -qb.x;
		qm.y = -qb.y;
		qm.z = -qb.z;

		cosHalfTheta = -cosHalfTheta;

	} else {

		qm.copy( qb );

	}

	if ( Math.abs( cosHalfTheta ) >= 1.0 ) {

		qm.w = qa.w;
		qm.x = qa.x;
		qm.y = qa.y;
		qm.z = qa.z;

		return qm;

	}

	var halfTheta = Math.acos( cosHalfTheta );
	var sinHalfTheta = Math.sqrt( 1.0 - cosHalfTheta * cosHalfTheta );

	if ( Math.abs( sinHalfTheta ) < 0.001 ) {

		qm.w = 0.5 * ( qa.w + qm.w );
		qm.x = 0.5 * ( qa.x + qm.x );
		qm.y = 0.5 * ( qa.y + qm.y );
		qm.z = 0.5 * ( qa.z + qm.z );

		return qm;

	}

	var ratioA = Math.sin( ( 1 - t ) * halfTheta ) / sinHalfTheta;
	var ratioB = Math.sin( t * halfTheta ) / sinHalfTheta;

	qm.w = ( qa.w * ratioA + qm.w * ratioB );
	qm.x = ( qa.x * ratioA + qm.x * ratioB );
	qm.y = ( qa.y * ratioA + qm.y * ratioB );
	qm.z = ( qa.z * ratioA + qm.z * ratioB );

	return qm;

}