1 files changed, 414 insertions, 0 deletions
diff --git a/client/assets/javascripts/mx/mx.quaternion.js b/client/assets/javascripts/mx/mx.quaternion.js
new file mode 100644
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+++ b/client/assets/javascripts/mx/mx.quaternion.js
@@ -0,0 +1,414 @@
+/**
+ * quaternion taken from three.js
+ * @author mikael emtinger / http://gomo.se/
+ * @author alteredq / http://alteredqualia.com/
+ * @author WestLangley / http://github.com/WestLangley
+ * @author bhouston / http://exocortex.com
+ */
+
+MX.Quaternion = function ( x, y, z, w ) {
+
+	this._x = x || 0;
+	this._y = y || 0;
+	this._z = z || 0;
+	this._w = ( w !== undefined ) ? w : 1;
+
+};
+
+MX.Quaternion.prototype = {
+
+	constructor: MX.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 MX.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 );
+
+		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 MX.Quaternion( this._x, this._y, this._z, this._w );
+
+	}
+
+};
+
+MX.Quaternion.slerp = function ( qa, qb, qm, t ) {
+
+	return qm.copy( qa ).slerp( qb, t );
+
+}