<!-- AVATAR-FORGE · part 33 -->
ossVectors( up, _z );

		}

		_x.normalize();
		_y.crossVectors( _z, _x );

		te[ 0 ] = _x.x; te[ 4 ] = _y.x; te[ 8 ] = _z.x;
		te[ 1 ] = _x.y; te[ 5 ] = _y.y; te[ 9 ] = _z.y;
		te[ 2 ] = _x.z; te[ 6 ] = _y.z; te[ 10 ] = _z.z;

		return this;

	}

	multiply( m ) {

		return this.multiplyMatrices( this, m );

	}

	premultiply( m ) {

		return this.multiplyMatrices( m, this );

	}

	multiplyMatrices( a, b ) {

		const ae = a.elements;
		const be = b.elements;
		const te = this.elements;

		const a11 = ae[ 0 ], a12 = ae[ 4 ], a13 = ae[ 8 ], a14 = ae[ 12 ];
		const a21 = ae[ 1 ], a22 = ae[ 5 ], a23 = ae[ 9 ], a24 = ae[ 13 ];
		const a31 = ae[ 2 ], a32 = ae[ 6 ], a33 = ae[ 10 ], a34 = ae[ 14 ];
		const a41 = ae[ 3 ], a42 = ae[ 7 ], a43 = ae[ 11 ], a44 = ae[ 15 ];

		const b11 = be[ 0 ], b12 = be[ 4 ], b13 = be[ 8 ], b14 = be[ 12 ];
		const b21 = be[ 1 ], b22 = be[ 5 ], b23 = be[ 9 ], b24 = be[ 13 ];
		const b31 = be[ 2 ], b32 = be[ 6 ], b33 = be[ 10 ], b34 = be[ 14 ];
		const b41 = be[ 3 ], b42 = be[ 7 ], b43 = be[ 11 ], b44 = be[ 15 ];

		te[ 0 ] = a11 * b11 + a12 * b21 + a13 * b31 + a14 * b41;
		te[ 4 ] = a11 * b12 + a12 * b22 + a13 * b32 + a14 * b42;
		te[ 8 ] = a11 * b13 + a12 * b23 + a13 * b33 + a14 * b43;
		te[ 12 ] = a11 * b14 + a12 * b24 + a13 * b34 + a14 * b44;

		te[ 1 ] = a21 * b11 + a22 * b21 + a23 * b31 + a24 * b41;
		te[ 5 ] = a21 * b12 + a22 * b22 + a23 * b32 + a24 * b42;
		te[ 9 ] = a21 * b13 + a22 * b23 + a23 * b33 + a24 * b43;
		te[ 13 ] = a21 * b14 + a22 * b24 + a23 * b34 + a24 * b44;

		te[ 2 ] = a31 * b11 + a32 * b21 + a33 * b31 + a34 * b41;
		te[ 6 ] = a31 * b12 + a32 * b22 + a33 * b32 + a34 * b42;
		te[ 10 ] = a31 * b13 + a32 * b23 + a33 * b33 + a34 * b43;
		te[ 14 ] = a31 * b14 + a32 * b24 + a33 * b34 + a34 * b44;

		te[ 3 ] = a41 * b11 + a42 * b21 + a43 * b31 + a44 * b41;
		te[ 7 ] = a41 * b12 + a42 * b22 + a43 * b32 + a44 * b42;
		te[ 11 ] = a41 * b13 + a42 * b23 + a43 * b33 + a44 * b43;
		te[ 15 ] = a41 * b14 + a42 * b24 + a43 * b34 + a44 * b44;

		return this;

	}

	multiplyScalar( s ) {

		const te = this.elements;

		te[ 0 ] *= s; te[ 4 ] *= s; te[ 8 ] *= s; te[ 12 ] *= s;
		te[ 1 ] *= s; te[ 5 ] *= s; te[ 9 ] *= s; te[ 13 ] *= s;
		te[ 2 ] *= s; te[ 6 ] *= s; te[ 10 ] *= s; te[ 14 ] *= s;
		te[ 3 ] *= s; te[ 7 ] *= s; te[ 11 ] *= s; te[ 15 ] *= s;

		return this;

	}

	determinant() {

		const te = this.elements;

		const n11 = te[ 0 ], n12 = te[ 4 ], n13 = te[ 8 ], n14 = te[ 12 ];
		const n21 = te[ 1 ], n22 = te[ 5 ], n23 = te[ 9 ], n24 = te[ 13 ];
		const n31 = te[ 2 ], n32 = te[ 6 ], n33 = te[ 10 ], n34 = te[ 14 ];
		const n41 = te[ 3 ], n42 = te[ 7 ], n43 = te[ 11 ], n44 = te[ 15 ];

		//TODO: make this more efficient
		//( based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm )

		return (
			n41 * (
				+ n14 * n23 * n32
				 - n13 * n24 * n32
				 - n14 * n22 * n33
				 + n12 * n24 * n33
				 + n13 * n22 * n34
				 - n12 * n23 * n34
			) +
			n42 * (
				+ n11 * n23 * n34
				 - n11 * n24 * n33
				 + n14 * n21 * n33
				 - n13 * n21 * n34
				 + n13 * n24 * n31
				 - n14 * n23 * n31
			) +
			n43 * (
				+ n11 * n24 * n32
				 - n11 * n22 * n34
				 - n14 * n21 * n32
				 + n12 * n21 * n34
				 + n14 * n22 * n31
				 - n12 * n24 * n31
			) +
			n44 * (
				- n13 * n22 * n31
				 - n11 * n23 * n32
				 + n11 * n22 * n33
				 + n13 * n21 * n32
				 - n12 * n21 * n33
				 + n12 * n23 * n31
			)

		);

	}

	transpose() {

		const te = this.elements;
		let tmp;

		tmp = te[ 1 ]; te[ 1 ] = te[ 4 ]; te[ 4 ] = tmp;
		tmp = te[ 2 ]; te[ 2 ] = te[ 8 ]; te[ 8 ] = tmp;
		tmp = te[ 6 ]; te[ 6 ] = te[ 9 ]; te[ 9 ] = tmp;

		tmp = te[ 3 ]; te[ 3 ] = te[ 12 ]; te[ 12 ] = tmp;
		tmp = te[ 7 ]; te[ 7 ] = te[ 13 ]; te[ 13 ] = tmp;
		tmp = te[ 11 ]; te[ 11 ] = te[ 14 ]; te[ 14 ] = tmp;

		return this;

	}

	setPosition( x, y, z ) {

		const te = this.elements;

		if ( x.isVector3 ) {

			te[ 12 ] = x.x;
			te[ 13 ] = x.y;
			te[ 14 ] = x.z;

		} else {

			te[ 12 ] = x;
			te[ 13 ] = y;
			te[ 14 ] = z;

		}

		return this;

	}

	invert() {

		// based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm
		const te = this.elements,

			n11 = te[ 0 ], n21 = te[ 1 ], n31 = te[ 2 ], n41 = te[ 3 ],
			n12 = te[ 4 ], n22 = te[ 5 ], n32 = te[ 6 ], n42 = te[ 7 ],
			n13 = te[ 8 ], n23 = te[ 9 ], n33 = te[ 10 ], n43 = te[ 11 ],
			n14 = te[ 12 ], n24 = te[ 13 ], n34 = te[ 14 ], n44 = te[ 15 ],

			t11 = n23 * n34 * n42 - n24 * n33 * n42 + n24 * n32 * n43 - n22 * n34 * n43 - n23 * n32 * n44 + n22 * n33 * n44,
			t12 = n14 * n33 * n42 - n13 * n34 * n42 - n14 * n32 * n43 + n12 * n34 * n43 + n13 * n32 * n44 - n12 * n33 * n44,
			t13 = n13 * n24 * n42 - n14 * n23 * n42 + n14 * n22 * n43 - n12 * n24 * n43 - n13 * n22 * n44 + n12 * n23 * n44,
			t14 = n14 * n23 * n32 - n13 * n24 * n32 - n14 * n22 * n33 + n12 * n24 * n33 + n13 * n22 * n34 - n12 * n23 * n34;

		const det = n11 * t11 + n21 * t12 + n31