<!-- AVATAR-FORGE · part 20 -->
) {

					x = 0;
					y = 0.707106781;
					z = 0.707106781;

				} else {

					x = Math.sqrt( xx );
					y = xy / x;
					z = xz / x;

				}

			} else if ( yy > zz ) {

				// m22 is the largest diagonal term

				if ( yy < epsilon ) {

					x = 0.707106781;
					y = 0;
					z = 0.707106781;

				} else {

					y = Math.sqrt( yy );
					x = xy / y;
					z = yz / y;

				}

			} else {

				// m33 is the largest diagonal term so base result on this

				if ( zz < epsilon ) {

					x = 0.707106781;
					y = 0.707106781;
					z = 0;

				} else {

					z = Math.sqrt( zz );
					x = xz / z;
					y = yz / z;

				}

			}

			this.set( x, y, z, angle );

			return this; // return 180 deg rotation

		}

		// as we have reached here there are no singularities so we can handle normally

		let s = Math.sqrt( ( m32 - m23 ) * ( m32 - m23 ) +
			( m13 - m31 ) * ( m13 - m31 ) +
			( m21 - m12 ) * ( m21 - m12 ) ); // used to normalize

		if ( Math.abs( s ) < 0.001 ) s = 1;

		// prevent divide by zero, should not happen if matrix is orthogonal and should be
		// caught by singularity test above, but I've left it in just in case

		this.x = ( m32 - m23 ) / s;
		this.y = ( m13 - m31 ) / s;
		this.z = ( m21 - m12 ) / s;
		this.w = Math.acos( ( m11 + m22 + m33 - 1 ) / 2 );

		return this;

	}

	min( v ) {

		this.x = Math.min( this.x, v.x );
		this.y = Math.min( this.y, v.y );
		this.z = Math.min( this.z, v.z );
		this.w = Math.min( this.w, v.w );

		return this;

	}

	max( v ) {

		this.x = Math.max( this.x, v.x );
		this.y = Math.max( this.y, v.y );
		this.z = Math.max( this.z, v.z );
		this.w = Math.max( this.w, v.w );

		return this;

	}

	clamp( min, max ) {

		// assumes min < max, componentwise

		this.x = Math.max( min.x, Math.min( max.x, this.x ) );
		this.y = Math.max( min.y, Math.min( max.y, this.y ) );
		this.z = Math.max( min.z, Math.min( max.z, this.z ) );
		this.w = Math.max( min.w, Math.min( max.w, this.w ) );

		return this;

	}

	clampScalar( minVal, maxVal ) {

		this.x = Math.max( minVal, Math.min( maxVal, this.x ) );
		this.y = Math.max( minVal, Math.min( maxVal, this.y ) );
		this.z = Math.max( minVal, Math.min( maxVal, this.z ) );
		this.w = Math.max( minVal, Math.min( maxVal, this.w ) );

		return this;

	}

	clampLength( min, max ) {

		const length = this.length();

		return this.divideScalar( length || 1 ).multiplyScalar( Math.max( min, Math.min( max, length ) ) );

	}

	floor() {

		this.x = Math.floor( this.x );
		this.y = Math.floor( this.y );
		this.z = Math.floor( this.z );
		this.w = Math.floor( this.w );

		return this;

	}

	ceil() {

		this.x = Math.ceil( this.x );
		this.y = Math.ceil( this.y );
		this.z = Math.ceil( this.z );
		this.w = Math.ceil( this.w );

		return this;

	}

	round() {

		this.x = Math.round( this.x );
		this.y = Math.round( this.y );
		this.z = Math.round( this.z );
		this.w = Math.round( this.w );

		return this;

	}

	roundToZero() {

		this.x = Math.trunc( this.x );
		this.y = Math.trunc( this.y );
		this.z = Math.trunc( this.z );
		this.w = Math.trunc( this.w );

		return this;

	}

	negate() {

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

		return this;

	}

	dot( v ) {

		return this.x * v.x + this.y * v.y + this.z * v.z + this.w * v.w;

	}

	lengthSq() {

		return this.x * this.x + this.y * this.y + this.z * this.z + this.w * this.w;

	}

	length() {

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

	}

	manhattanLength() {

		return Math.abs( this.x ) + Math.abs( this.y ) + Math.abs( this.z ) + Math.abs( this.w );

	}

	normalize() {

		return this.divideScalar( this.length() || 1 );

	}

	setLength( length ) {

		return this.normalize().multiplyScalar( length );

	}

	lerp( v, alpha ) {

		this.x += ( v.x - this.x ) * alpha;
		this.y += ( v.y - this.y ) * alpha;
		this.z += ( v.z - this.z ) * alpha;
		this.w += ( v.w - this.w ) * alpha;

		return this;

	}

	lerpVectors( v1, v2, alpha ) {

		this.x = v1.x + ( v2.x - v1.x ) * alpha;
		this.y = v1.y + ( v2.y - v1.y ) * alpha;
		this.z = v1.z + ( v2.z - v1.z ) * alpha;
		this.w = v1.w + ( v2.w - v1.w ) * alpha;

		return this;

	}

	equals( v ) {

		return ( ( v.x === this.x ) && ( v.y === this.y ) && ( v.z === this.z ) && ( v.w === this.w ) );

	}

	fromArray( array, offset = 0 ) {

		this.x = array[ offset ];
		this.y = array[ offset + 1 ];
		this.z = array[ offset + 2 ];
		this.w = array[ offset + 3 ];

		return this;

	}

	toArray( array = [], offset = 0 ) {

		array[ offset ] = this.x;
		array[ offset + 1 ] = this.y;
		array[ offset + 2 ] = this.z;
		array[ offset + 3 ] = this.w;

		return array;

	}

	fromBufferAttribute( attribute, index ) {

		this.x = attribute.getX( index );
		this.y = attribute.getY( index );
		this.z = attribute.getZ( index );
		this.w = attribute.getW( index );

		return this;

	}

	random() {

		this.x = Math.random();
		this.y = Math.random();
		this.z = Math.