ArcballControls.js

import {
	GridHelper,
	EllipseCurve,
	BufferGeometry,
	Line,
	LineBasicMaterial,
	Raycaster,
	Group,
	Box3,
	Sphere,
	Quaternion,
	Vector2,
	Vector3,
	Matrix4,
	MathUtils,
	EventDispatcher
} from './three.js';

//trackball state
const STATE = {

	IDLE: Symbol(),
	ROTATE: Symbol(),
	PAN: Symbol(),
	SCALE: Symbol(),
	FOV: Symbol(),
	FOCUS: Symbol(),
	ZROTATE: Symbol(),
	TOUCH_MULTI: Symbol(),
	ANIMATION_FOCUS: Symbol(),
	ANIMATION_ROTATE: Symbol()

};

const INPUT = {

	NONE: Symbol(),
	ONE_FINGER: Symbol(),
	ONE_FINGER_SWITCHED: Symbol(),
	TWO_FINGER: Symbol(),
	MULT_FINGER: Symbol(),
	CURSOR: Symbol()

};

//cursor center coordinates
const _center = {

	x: 0,
	y: 0

};

//transformation matrices for gizmos and camera
const _transformation = {

	camera: new Matrix4(),
	gizmos: new Matrix4()

};

//events
const _changeEvent = { type: 'change' };
const _startEvent = { type: 'start' };
const _endEvent = { type: 'end' };

const _raycaster = new Raycaster();
const _offset = new Vector3();

const _gizmoMatrixStateTemp = new Matrix4();
const _cameraMatrixStateTemp = new Matrix4();
const _scalePointTemp = new Vector3();
/**
 *
 * @param {Camera} camera Virtual camera used in the scene
 * @param {HTMLElement} domElement Renderer's dom element
 * @param {Scene} scene The scene to be rendered
 */
class ArcballControls extends EventDispatcher {

	constructor( camera, domElement, scene = null ) {

		super();
		this.camera = null;
		this.domElement = domElement;
		this.scene = scene;
		this.target = new Vector3();
		this._currentTarget = new Vector3();
		this.radiusFactor = 0.67;

		this.mouseActions = [];
		this._mouseOp = null;


		//global vectors and matrices that are used in some operations to avoid creating new objects every time (e.g. every time cursor moves)
		this._v2_1 = new Vector2();
		this._v3_1 = new Vector3();
		this._v3_2 = new Vector3();

		this._m4_1 = new Matrix4();
		this._m4_2 = new Matrix4();

		this._quat = new Quaternion();

		//transformation matrices
		this._translationMatrix = new Matrix4(); //matrix for translation operation
		this._rotationMatrix = new Matrix4(); //matrix for rotation operation
		this._scaleMatrix = new Matrix4(); //matrix for scaling operation

		this._rotationAxis = new Vector3(); //axis for rotate operation


		//camera state
		this._cameraMatrixState = new Matrix4();
		this._cameraProjectionState = new Matrix4();

		this._fovState = 1;
		this._upState = new Vector3();
		this._zoomState = 1;
		this._nearPos = 0;
		this._farPos = 0;

		this._gizmoMatrixState = new Matrix4();

		//initial values
		this._up0 = new Vector3();
		this._zoom0 = 1;
		this._fov0 = 0;
		this._initialNear = 0;
		this._nearPos0 = 0;
		this._initialFar = 0;
		this._farPos0 = 0;
		this._cameraMatrixState0 = new Matrix4();
		this._gizmoMatrixState0 = new Matrix4();

		//pointers array
		this._button = - 1;
		this._touchStart = [];
		this._touchCurrent = [];
		this._input = INPUT.NONE;

		//two fingers touch interaction
		this._switchSensibility = 32;	//minimum movement to be performed to fire single pan start after the second finger has been released
		this._startFingerDistance = 0; //distance between two fingers
		this._currentFingerDistance = 0;
		this._startFingerRotation = 0; //amount of rotation performed with two fingers
		this._currentFingerRotation = 0;

		//double tap
		this._devPxRatio = 0;
		this._downValid = true;
		this._nclicks = 0;
		this._downEvents = [];
		this._downStart = 0;	//pointerDown time
		this._clickStart = 0;	//first click time
		this._maxDownTime = 250;
		this._maxInterval = 300;
		this._posThreshold = 24;
		this._movementThreshold = 24;

		//cursor positions
		this._currentCursorPosition = new Vector3();
		this._startCursorPosition = new Vector3();

		//grid
		this._grid = null; //grid to be visualized during pan operation
		this._gridPosition = new Vector3();

		//gizmos
		this._gizmos = new Group();
		this._curvePts = 128;


		//animations
		this._timeStart = - 1; //initial time
		this._animationId = - 1;

		//focus animation
		this.focusAnimationTime = 500; //duration of focus animation in ms

		//rotate animation
		this._timePrev = 0; //time at which previous rotate operation has been detected
		this._timeCurrent = 0; //time at which current rotate operation has been detected
		this._anglePrev = 0; //angle of previous rotation
		this._angleCurrent = 0; //angle of current rotation
		this._cursorPosPrev = new Vector3();	//cursor position when previous rotate operation has been detected
		this._cursorPosCurr = new Vector3();//cursor position when current rotate operation has been detected
		this._wPrev = 0; //angular velocity of the previous rotate operation
		this._wCurr = 0; //angular velocity of the current rotate operation


		//parameters
		this.adjustNearFar = false;
		this.scaleFactor = 1.1;	//zoom/distance multiplier
		this.dampingFactor = 25;
		this.wMax = 20;	//maximum angular velocity allowed
		this.enableAnimations = true; //if animations should be performed
		this.enableGrid = false; //if grid should be showed during pan operation
		this.cursorZoom = false;	//if wheel zoom should be cursor centered
		this.minFov = 5;
		this.maxFov = 90;

		this.enabled = true;
		this.enablePan = true;
		this.enableRotate = true;
		this.enableZoom = true;
		this.enableGizmos = true;

		this.minDistance = 0;
		this.maxDistance = Infinity;
		this.minZoom = 0;
		this.maxZoom = Infinity;

		//trackball parameters
		this._tbRadius = 1;

		//FSA
		this._state = STATE.IDLE;

		this.setCamera( camera );

		if ( this.scene != null ) {

			this.scene.add( this._gizmos );

		}

		this.domElement.style.touchAction = 'none';
		this._devPxRatio = window.devicePixelRatio;

		this.initializeMouseActions();

		this.domElement.addEventListener( 'contextmenu', this.onContextMenu );
		this.domElement.addEventListener( 'wheel', this.onWheel );
		this.domElement.addEventListener( 'pointerdown', this.onPointerDown );
		this.domElement.addEventListener( 'pointercancel', this.onPointerCancel );

		window.addEventListener( 'resize', this.onWindowResize );

	}

	//listeners

	onWindowResize = () => {

		const scale = ( this._gizmos.scale.x + this._gizmos.scale.y + this._gizmos.scale.z ) / 3;
		this._tbRadius = this.calculateTbRadius( this.camera );

		const newRadius = this._tbRadius / scale;
		const curve = new EllipseCurve( 0, 0, newRadius, newRadius );
		const points = curve.getPoints( this._curvePts );
		const curveGeometry = new BufferGeometry().setFromPoints( points );


		for ( const gizmo in this._gizmos.children ) {

			this._gizmos.children[ gizmo ].geometry = curveGeometry;

		}

		this.dispatchEvent( _changeEvent );

	};

	onContextMenu = ( event ) => {

		if ( ! this.enabled ) {

			return;

		}

		for ( let i = 0; i < this.mouseActions.length; i ++ ) {

			if ( this.mouseActions[ i ].mouse == 2 ) {

				//prevent only if button 2 is actually used
				event.preventDefault();
				break;

			}

		}

	};

	onPointerCancel = () => {

		this._touchStart.splice( 0, this._touchStart.length );
		this._touchCurrent.splice( 0, this._touchCurrent.length );
		this._input = INPUT.NONE;

	};

	onPointerDown = ( event ) => {

		if ( event.button == 0 && event.isPrimary ) {

			this._downValid = true;
			this._downEvents.push( event );
			this._downStart = performance.now();

		} else {

			this._downValid = false;

		}

		if ( event.pointerType == 'touch' && this._input != INPUT.CURSOR ) {

			this._touchStart.push( event );
			this._touchCurrent.push( event );

			switch ( this._input ) {

				case INPUT.NONE:

					//singleStart
					this._input = INPUT.ONE_FINGER;
					this.onSinglePanStart( event, 'ROTATE' );

					window.addEventListener( 'pointermove', this.onPointerMove );
					window.addEventListener( 'pointerup', this.onPointerUp );

					break;

				case INPUT.ONE_FINGER:
				case INPUT.ONE_FINGER_SWITCHED:

					//doubleStart
					this._input = INPUT.TWO_FINGER;

					this.onRotateStart();
					this.onPinchStart();
					this.onDoublePanStart();

					break;

				case INPUT.TWO_FINGER:

					//multipleStart
					this._input = INPUT.MULT_FINGER;
					this.onTriplePanStart( event );
					break;

			}

		} else if ( event.pointerType != 'touch' && this._input == INPUT.NONE ) {

			let modifier = null;

			if ( event.ctrlKey || event.metaKey ) {

				modifier = 'CTRL';

			} else if ( event.shiftKey ) {

				modifier = 'SHIFT';

			}

			this._mouseOp = this.getOpFromAction( event.button, modifier );
			if ( this._mouseOp != null ) {

				window.addEventListener( 'pointermove', this.onPointerMove );
				window.addEventListener( 'pointerup', this.onPointerUp );

				//singleStart
				this._input = INPUT.CURSOR;
				this._button = event.button;
				this.onSinglePanStart( event, this._mouseOp );

			}

		}

	};

	onPointerMove = ( event ) => {

		if ( event.pointerType == 'touch' && this._input != INPUT.CURSOR ) {

			switch ( this._input ) {

				case INPUT.ONE_FINGER:

					//singleMove
					this.updateTouchEvent( event );

					this.onSinglePanMove( event, STATE.ROTATE );
					break;

				case INPUT.ONE_FINGER_SWITCHED:

					const movement = this.calculatePointersDistance( this._touchCurrent[ 0 ], event ) * this._devPxRatio;

					if ( movement >= this._switchSensibility ) {

						//singleMove
						this._input = INPUT.ONE_FINGER;
						this.updateTouchEvent( event );

						this.onSinglePanStart( event, 'ROTATE' );
						break;

					}

					break;

				case INPUT.TWO_FINGER:

					//rotate/pan/pinchMove
					this.updateTouchEvent( event );

					this.onRotateMove();
					this.onPinchMove();
					this.onDoublePanMove();

					break;

				case INPUT.MULT_FINGER:

					//multMove
					this.updateTouchEvent( event );

					this.onTriplePanMove( event );
					break;

			}

		} else if ( event.pointerType != 'touch' && this._input == INPUT.CURSOR ) {

			let modifier = null;

			if ( event.ctrlKey || event.metaKey ) {

				modifier = 'CTRL';

			} else if ( event.shiftKey ) {

				modifier = 'SHIFT';

			}

			const mouseOpState = this.getOpStateFromAction( this._button, modifier );

			if ( mouseOpState != null ) {

				this.onSinglePanMove( event, mouseOpState );

			}

		}

		//checkDistance
		if ( this._downValid ) {

			const movement = this.calculatePointersDistance( this._downEvents[ this._downEvents.length - 1 ], event ) * this._devPxRatio;
			if ( movement > this._movementThreshold ) {

				this._downValid = false;

			}

		}

	};

	onPointerUp = ( event ) => {

		if ( event.pointerType == 'touch' && this._input != INPUT.CURSOR ) {

			const nTouch = this._touchCurrent.length;

			for ( let i = 0; i < nTouch; i ++ ) {

				if ( this._touchCurrent[ i ].pointerId == event.pointerId ) {

					this._touchCurrent.splice( i, 1 );
					this._touchStart.splice( i, 1 );
					break;

				}

			}

			switch ( this._input ) {

				case INPUT.ONE_FINGER:
				case INPUT.ONE_FINGER_SWITCHED:

					//singleEnd
					window.removeEventListener( 'pointermove', this.onPointerMove );
					window.removeEventListener( 'pointerup', this.onPointerUp );

					this._input = INPUT.NONE;
					this.onSinglePanEnd();

					break;

				case INPUT.TWO_FINGER:

					//doubleEnd
					this.onDoublePanEnd( event );
					this.onPinchEnd( event );
					this.onRotateEnd( event );

					//switching to singleStart
					this._input = INPUT.ONE_FINGER_SWITCHED;

					break;

				case INPUT.MULT_FINGER:

					if ( this._touchCurrent.length == 0 ) {

						window.removeEventListener( 'pointermove', this.onPointerMove );
						window.removeEventListener( 'pointerup', this.onPointerUp );

						//multCancel
						this._input = INPUT.NONE;
						this.onTriplePanEnd();

					}

					break;

			}

		} else if ( event.pointerType != 'touch' && this._input == INPUT.CURSOR ) {

			window.removeEventListener( 'pointermove', this.onPointerMove );
			window.removeEventListener( 'pointerup', this.onPointerUp );

			this._input = INPUT.NONE;
			this.onSinglePanEnd();
			this._button = - 1;

		}

		if ( event.isPrimary ) {

			if ( this._downValid ) {

				const downTime = event.timeStamp - this._downEvents[ this._downEvents.length - 1 ].timeStamp;

				if ( downTime <= this._maxDownTime ) {

					if ( this._nclicks == 0 ) {

						//first valid click detected
						this._nclicks = 1;
						this._clickStart = performance.now();

					} else {

						const clickInterval = event.timeStamp - this._clickStart;
						const movement = this.calculatePointersDistance( this._downEvents[ 1 ], this._downEvents[ 0 ] ) * this._devPxRatio;

						if ( clickInterval <= this._maxInterval && movement <= this._posThreshold ) {

							//second valid click detected
							//fire double tap and reset values
							this._nclicks = 0;
							this._downEvents.splice( 0, this._downEvents.length );
							this.onDoubleTap( event );

						} else {

							//new 'first click'
							this._nclicks = 1;
							this._downEvents.shift();
							this._clickStart = performance.now();

						}

					}

				} else {

					this._downValid = false;
					this._nclicks = 0;
					this._downEvents.splice( 0, this._downEvents.length );

				}

			} else {

				this._nclicks = 0;
				this._downEvents.splice( 0, this._downEvents.length );

			}

		}

	};

	onWheel = ( event ) => {

		if ( this.enabled && this.enableZoom ) {

			let modifier = null;

			if ( event.ctrlKey || event.metaKey ) {

				modifier = 'CTRL';

			} else if ( event.shiftKey ) {

				modifier = 'SHIFT';

			}

			const mouseOp = this.getOpFromAction( 'WHEEL', modifier );

			if ( mouseOp != null ) {

				event.preventDefault();
				this.dispatchEvent( _startEvent );

				const notchDeltaY = 125; //distance of one notch of mouse wheel
				let sgn = event.deltaY / notchDeltaY;

				let size = 1;

				if ( sgn > 0 ) {

					size = 1 / this.scaleFactor;

				} else if ( sgn < 0 ) {

					size = this.scaleFactor;

				}

				switch ( mouseOp ) {

					case 'ZOOM':

						this.updateTbState( STATE.SCALE, true );

						if ( sgn > 0 ) {

							size = 1 / ( Math.pow( this.scaleFactor, sgn ) );

						} else if ( sgn < 0 ) {

							size = Math.pow( this.scaleFactor, - sgn );

						}

						if ( this.cursorZoom && this.enablePan ) {

							let scalePoint;

							if ( this.camera.isOrthographicCamera ) {

								scalePoint = this.unprojectOnTbPlane( this.camera, event.clientX, event.clientY, this.domElement ).applyQuaternion( this.camera.quaternion ).multiplyScalar( 1 / this.camera.zoom ).add( this._gizmos.position );

							} else if ( this.camera.isPerspectiveCamera ) {

								scalePoint = this.unprojectOnTbPlane( this.camera, event.clientX, event.clientY, this.domElement ).applyQuaternion( this.camera.quaternion ).add( this._gizmos.position );

							}

							this.applyTransformMatrix( this.scale( size, scalePoint ) );

						} else {

							this.applyTransformMatrix( this.scale( size, this._gizmos.position ) );

						}

						if ( this._grid != null ) {

							this.disposeGrid();
							this.drawGrid();

						}

						this.updateTbState( STATE.IDLE, false );

						this.dispatchEvent( _changeEvent );
						this.dispatchEvent( _endEvent );

						break;

					case 'FOV':

						if ( this.camera.isPerspectiveCamera ) {

							this.updateTbState( STATE.FOV, true );


							//Vertigo effect

							//	  fov / 2
							//		|\
							//		| \
							//		|  \
							//	x	|	\
							//		| 	 \
							//		| 	  \
							//		| _ _ _\
							//			y

							//check for iOs shift shortcut
							if ( event.deltaX != 0 ) {

								sgn = event.deltaX / notchDeltaY;

								size = 1;

								if ( sgn > 0 ) {

									size = 1 / ( Math.pow( this.scaleFactor, sgn ) );

								} else if ( sgn < 0 ) {

									size = Math.pow( this.scaleFactor, - sgn );

								}

							}

							this._v3_1.setFromMatrixPosition( this._cameraMatrixState );
							const x = this._v3_1.distanceTo( this._gizmos.position );
							let xNew = x / size;	//distance between camera and gizmos if scale(size, scalepoint) would be performed

							//check min and max distance
							xNew = MathUtils.clamp( xNew, this.minDistance, this.maxDistance );

							const y = x * Math.tan( MathUtils.DEG2RAD * this.camera.fov * 0.5 );

							//calculate new fov
							let newFov = MathUtils.RAD2DEG * ( Math.atan( y / xNew ) * 2 );

							//check min and max fov
							if ( newFov > this.maxFov ) {

								newFov = this.maxFov;

							} else if ( newFov < this.minFov ) {

								newFov = this.minFov;

							}

							const newDistance = y / Math.tan( MathUtils.DEG2RAD * ( newFov / 2 ) );
							size = x / newDistance;

							this.setFov( newFov );
							this.applyTransformMatrix( this.scale( size, this._gizmos.position, false ) );

						}

						if ( this._grid != null ) {

							this.disposeGrid();
							this.drawGrid();

						}

						this.updateTbState( STATE.IDLE, false );

						this.dispatchEvent( _changeEvent );
						this.dispatchEvent( _endEvent );

						break;

				}

			}

		}

	};

	onSinglePanStart = ( event, operation ) => {

		if ( this.enabled ) {

			this.dispatchEvent( _startEvent );

			this.setCenter( event.clientX, event.clientY );

			switch ( operation ) {

				case 'PAN':

					if ( ! this.enablePan ) {

						return;

					}

					if ( this._animationId != - 1 ) {

						cancelAnimationFrame( this._animationId );
						this._animationId = - 1;
						this._timeStart = - 1;

						this.activateGizmos( false );
						this.dispatchEvent( _changeEvent );

					}

					this.updateTbState( STATE.PAN, true );
					this._startCursorPosition.copy( this.unprojectOnTbPlane( this.camera, _center.x, _center.y, this.domElement ) );
					if ( this.enableGrid ) {

						this.drawGrid();
						this.dispatchEvent( _changeEvent );

					}

					break;

				case 'ROTATE':

					if ( ! this.enableRotate ) {

						return;

					}

					if ( this._animationId != - 1 ) {

						cancelAnimationFrame( this._animationId );
						this._animationId = - 1;
						this._timeStart = - 1;

					}

					this.updateTbState( STATE.ROTATE, true );
					this._startCursorPosition.copy( this.unprojectOnTbSurface( this.camera, _center.x, _center.y, this.domElement, this._tbRadius ) );
					this.activateGizmos( true );
					if ( this.enableAnimations ) {

						this._timePrev = this._timeCurrent = performance.now();
						this._angleCurrent = this._anglePrev = 0;
						this._cursorPosPrev.copy( this._startCursorPosition );
						this._cursorPosCurr.copy( this._cursorPosPrev );
						this._wCurr = 0;
						this._wPrev = this._wCurr;

					}

					this.dispatchEvent( _changeEvent );
					break;

				case 'FOV':

					if ( ! this.camera.isPerspectiveCamera || ! this.enableZoom ) {

						return;

					}

					if ( this._animationId != - 1 ) {

						cancelAnimationFrame( this._animationId );
						this._animationId = - 1;
						this._timeStart = - 1;

						this.activateGizmos( false );
						this.dispatchEvent( _changeEvent );

					}

					this.updateTbState( STATE.FOV, true );
					this._startCursorPosition.setY( this.getCursorNDC( _center.x, _center.y, this.domElement ).y * 0.5 );
					this._currentCursorPosition.copy( this._startCursorPosition );
					break;

				case 'ZOOM':

					if ( ! this.enableZoom ) {

						return;

					}

					if ( this._animationId != - 1 ) {

						cancelAnimationFrame( this._animationId );
						this._animationId = - 1;
						this._timeStart = - 1;

						this.activateGizmos( false );
						this.dispatchEvent( _changeEvent );

					}

					this.updateTbState( STATE.SCALE, true );
					this._startCursorPosition.setY( this.getCursorNDC( _center.x, _center.y, this.domElement ).y * 0.5 );
					this._currentCursorPosition.copy( this._startCursorPosition );
					break;

			}

		}

	};

	onSinglePanMove = ( event, opState ) => {

		if ( this.enabled ) {

			const restart = opState != this._state;
			this.setCenter( event.clientX, event.clientY );

			switch ( opState ) {

				case STATE.PAN:

					if ( this.enablePan ) {

						if ( restart ) {

							//switch to pan operation

							this.dispatchEvent( _endEvent );
							this.dispatchEvent( _startEvent );

							this.updateTbState( opState, true );
							this._startCursorPosition.copy( this.unprojectOnTbPlane( this.camera, _center.x, _center.y, this.domElement ) );
							if ( this.enableGrid ) {

								this.drawGrid();

							}

							this.activateGizmos( false );

						} else {

							//continue with pan operation
							this._currentCursorPosition.copy( this.unprojectOnTbPlane( this.camera, _center.x, _center.y, this.domElement ) );
							this.applyTransformMatrix( this.pan( this._startCursorPosition, this._currentCursorPosition ) );

						}

					}

					break;

				case STATE.ROTATE:

					if ( this.enableRotate ) {

						if ( restart ) {

							//switch to rotate operation

							this.dispatchEvent( _endEvent );
							this.dispatchEvent( _startEvent );

							this.updateTbState( opState, true );
							this._startCursorPosition.copy( this.unprojectOnTbSurface( this.camera, _center.x, _center.y, this.domElement, this._tbRadius ) );

							if ( this.enableGrid ) {

								this.disposeGrid();

							}

							this.activateGizmos( true );

						} else {

							//continue with rotate operation
							this._currentCursorPosition.copy( this.unprojectOnTbSurface( this.camera, _center.x, _center.y, this.domElement, this._tbRadius ) );

							const distance = this._startCursorPosition.distanceTo( this._currentCursorPosition );
							const angle = this._startCursorPosition.angleTo( this._currentCursorPosition );
							const amount = Math.max( distance / this._tbRadius, angle ); //effective rotation angle

							this.applyTransformMatrix( this.rotate( this.calculateRotationAxis( this._startCursorPosition, this._currentCursorPosition ), amount ) );

							if ( this.enableAnimations ) {

								this._timePrev = this._timeCurrent;
								this._timeCurrent = performance.now();
								this._anglePrev = this._angleCurrent;
								this._angleCurrent = amount;
								this._cursorPosPrev.copy( this._cursorPosCurr );
								this._cursorPosCurr.copy( this._currentCursorPosition );
								this._wPrev = this._wCurr;
								this._wCurr = this.calculateAngularSpeed( this._anglePrev, this._angleCurrent, this._timePrev, this._timeCurrent );

							}

						}

					}

					break;

				case STATE.SCALE:

					if ( this.enableZoom ) {

						if ( restart ) {

							//switch to zoom operation

							this.dispatchEvent( _endEvent );
							this.dispatchEvent( _startEvent );

							this.updateTbState( opState, true );
							this._startCursorPosition.setY( this.getCursorNDC( _center.x, _center.y, this.domElement ).y * 0.5 );
							this._currentCursorPosition.copy( this._startCursorPosition );

							if ( this.enableGrid ) {

								this.disposeGrid();

							}

							this.activateGizmos( false );

						} else {

							//continue with zoom operation
							const screenNotches = 8;	//how many wheel notches corresponds to a full screen pan
							this._currentCursorPosition.setY( this.getCursorNDC( _center.x, _center.y, this.domElement ).y * 0.5 );

							const movement = this._currentCursorPosition.y - this._startCursorPosition.y;

							let size = 1;

							if ( movement < 0 ) {

								size = 1 / ( Math.pow( this.scaleFactor, - movement * screenNotches ) );

							} else if ( movement > 0 ) {

								size = Math.pow( this.scaleFactor, movement * screenNotches );

							}

							this.applyTransformMatrix( this.scale( size, this._gizmos.position ) );

						}

					}

					break;

				case STATE.FOV:

					if ( this.enableZoom && this.camera.isPerspectiveCamera ) {

						if ( restart ) {

							//switch to fov operation

							this.dispatchEvent( _endEvent );
							this.dispatchEvent( _startEvent );

							this.updateTbState( opState, true );
							this._startCursorPosition.setY( this.getCursorNDC( _center.x, _center.y, this.domElement ).y * 0.5 );
							this._currentCursorPosition.copy( this._startCursorPosition );

							if ( this.enableGrid ) {

								this.disposeGrid();

							}

							this.activateGizmos( false );

						} else {

							//continue with fov operation
							const screenNotches = 8;	//how many wheel notches corresponds to a full screen pan
							this._currentCursorPosition.setY( this.getCursorNDC( _center.x, _center.y, this.domElement ).y * 0.5 );

							const movement = this._currentCursorPosition.y - this._startCursorPosition.y;

							let size = 1;

							if ( movement < 0 ) {

								size = 1 / ( Math.pow( this.scaleFactor, - movement * screenNotches ) );

							} else if ( movement > 0 ) {

								size = Math.pow( this.scaleFactor, movement * screenNotches );

							}

							this._v3_1.setFromMatrixPosition( this._cameraMatrixState );
							const x = this._v3_1.distanceTo( this._gizmos.position );
							let xNew = x / size; //distance between camera and gizmos if scale(size, scalepoint) would be performed

							//check min and max distance
							xNew = MathUtils.clamp( xNew, this.minDistance, this.maxDistance );

							const y = x * Math.tan( MathUtils.DEG2RAD * this._fovState * 0.5 );

							//calculate new fov
							let newFov = MathUtils.RAD2DEG * ( Math.atan( y / xNew ) * 2 );

							//check min and max fov
							newFov = MathUtils.clamp( newFov, this.minFov, this.maxFov );

							const newDistance = y / Math.tan( MathUtils.DEG2RAD * ( newFov / 2 ) );
							size = x / newDistance;
							this._v3_2.setFromMatrixPosition( this._gizmoMatrixState );

							this.setFov( newFov );
							this.applyTransformMatrix( this.scale( size, this._v3_2, false ) );

							//adjusting distance
							_offset.copy( this._gizmos.position ).sub( this.camera.position ).normalize().multiplyScalar( newDistance / x );
							this._m4_1.makeTranslation( _offset.x, _offset.y, _offset.z );

						}

					}

					break;

			}

			this.dispatchEvent( _changeEvent );

		}

	};

	onSinglePanEnd = () => {

		if ( this._state == STATE.ROTATE ) {


			if ( ! this.enableRotate ) {

				return;

			}

			if ( this.enableAnimations ) {

				//perform rotation animation
				const deltaTime = ( performance.now() - this._timeCurrent );
				if ( deltaTime < 120 ) {

					const w = Math.abs( ( this._wPrev + this._wCurr ) / 2 );

					const self = this;
					this._animationId = window.requestAnimationFrame( function ( t ) {

						self.updateTbState( STATE.ANIMATION_ROTATE, true );
						const rotationAxis = self.calculateRotationAxis( self._cursorPosPrev, self._cursorPosCurr );

						self.onRotationAnim( t, rotationAxis, Math.min( w, self.wMax ) );

					} );

				} else {

					//cursor has been standing still for over 120 ms since last movement
					this.updateTbState( STATE.IDLE, false );
					this.activateGizmos( false );
					this.dispatchEvent( _changeEvent );

				}

			} else {

				this.updateTbState( STATE.IDLE, false );
				this.activateGizmos( false );
				this.dispatchEvent( _changeEvent );

			}

		} else if ( this._state == STATE.PAN || this._state == STATE.IDLE ) {

			this.updateTbState( STATE.IDLE, false );

			if ( this.enableGrid ) {

				this.disposeGrid();

			}

			this.activateGizmos( false );
			this.dispatchEvent( _changeEvent );


		}

		this.dispatchEvent( _endEvent );

	};

	onDoubleTap = ( event ) => {

		if ( this.enabled && this.enablePan && this.scene != null ) {

			this.dispatchEvent( _startEvent );

			this.setCenter( event.clientX, event.clientY );
			const hitP = this.unprojectOnObj( this.getCursorNDC( _center.x, _center.y, this.domElement ), this.camera );

			if ( hitP != null && this.enableAnimations ) {

				const self = this;
				if ( this._animationId != - 1 ) {

					window.cancelAnimationFrame( this._animationId );

				}

				this._timeStart = - 1;
				this._animationId = window.requestAnimationFrame( function ( t ) {

					self.updateTbState( STATE.ANIMATION_FOCUS, true );
					self.onFocusAnim( t, hitP, self._cameraMatrixState, self._gizmoMatrixState );

				} );

			} else if ( hitP != null && ! this.enableAnimations ) {

				this.updateTbState( STATE.FOCUS, true );
				this.focus( hitP, this.scaleFactor );
				this.updateTbState( STATE.IDLE, false );
				this.dispatchEvent( _changeEvent );

			}

		}

		this.dispatchEvent( _endEvent );

	};

	onDoublePanStart = () => {

		if ( this.enabled && this.enablePan ) {

			this.dispatchEvent( _startEvent );

			this.updateTbState( STATE.PAN, true );

			this.setCenter( ( this._touchCurrent[ 0 ].clientX + this._touchCurrent[ 1 ].clientX ) / 2, ( this._touchCurrent[ 0 ].clientY + this._touchCurrent[ 1 ].clientY ) / 2 );
			this._startCursorPosition.copy( this.unprojectOnTbPlane( this.camera, _center.x, _center.y, this.domElement, true ) );
			this._currentCursorPosition.copy( this._startCursorPosition );

			this.activateGizmos( false );

		}

	};

	onDoublePanMove = () => {

		if ( this.enabled && this.enablePan ) {

			this.setCenter( ( this._touchCurrent[ 0 ].clientX + this._touchCurrent[ 1 ].clientX ) / 2, ( this._touchCurrent[ 0 ].clientY + this._touchCurrent[ 1 ].clientY ) / 2 );

			if ( this._state != STATE.PAN ) {

				this.updateTbState( STATE.PAN, true );
				this._startCursorPosition.copy( this._currentCursorPosition );

			}

			this._currentCursorPosition.copy( this.unprojectOnTbPlane( this.camera, _center.x, _center.y, this.domElement, true ) );
			this.applyTransformMatrix( this.pan( this._startCursorPosition, this._currentCursorPosition, true ) );
			this.dispatchEvent( _changeEvent );

		}

	};

	onDoublePanEnd = () => {

		this.updateTbState( STATE.IDLE, false );
		this.dispatchEvent( _endEvent );

	};


	onRotateStart = () => {

		if ( this.enabled && this.enableRotate ) {

			this.dispatchEvent( _startEvent );

			this.updateTbState( STATE.ZROTATE, true );

			//this._startFingerRotation = event.rotation;

			this._startFingerRotation = this.getAngle( this._touchCurrent[ 1 ], this._touchCurrent[ 0 ] ) + this.getAngle( this._touchStart[ 1 ], this._touchStart[ 0 ] );
			this._currentFingerRotation = this._startFingerRotation;

			this.camera.getWorldDirection( this._rotationAxis ); //rotation axis

			if ( ! this.enablePan && ! this.enableZoom ) {

				this.activateGizmos( true );

			}

		}

	};

	onRotateMove = () => {

		if ( this.enabled && this.enableRotate ) {

			this.setCenter( ( this._touchCurrent[ 0 ].clientX + this._touchCurrent[ 1 ].clientX ) / 2, ( this._touchCurrent[ 0 ].clientY + this._touchCurrent[ 1 ].clientY ) / 2 );
			let rotationPoint;

			if ( this._state != STATE.ZROTATE ) {

				this.updateTbState( STATE.ZROTATE, true );
				this._startFingerRotation = this._currentFingerRotation;

			}

			//this._currentFingerRotation = event.rotation;
			this._currentFingerRotation = this.getAngle( this._touchCurrent[ 1 ], this._touchCurrent[ 0 ] ) + this.getAngle( this._touchStart[ 1 ], this._touchStart[ 0 ] );

			if ( ! this.enablePan ) {

				rotationPoint = new Vector3().setFromMatrixPosition( this._gizmoMatrixState );

			} else {

				this._v3_2.setFromMatrixPosition( this._gizmoMatrixState );
				rotationPoint = this.unprojectOnTbPlane( this.camera, _center.x, _center.y, this.domElement ).applyQuaternion( this.camera.quaternion ).multiplyScalar( 1 / this.camera.zoom ).add( this._v3_2 );

			}

			const amount = MathUtils.DEG2RAD * ( this._startFingerRotation - this._currentFingerRotation );

			this.applyTransformMatrix( this.zRotate( rotationPoint, amount ) );
			this.dispatchEvent( _changeEvent );

		}

	};

	onRotateEnd = () => {

		this.updateTbState( STATE.IDLE, false );
		this.activateGizmos( false );
		this.dispatchEvent( _endEvent );

	};

	onPinchStart = () => {

		if ( this.enabled && this.enableZoom ) {

			this.dispatchEvent( _startEvent );
			this.updateTbState( STATE.SCALE, true );

			this._startFingerDistance = this.calculatePointersDistance( this._touchCurrent[ 0 ], this._touchCurrent[ 1 ] );
			this._currentFingerDistance = this._startFingerDistance;

			this.activateGizmos( false );

		}

	};

	onPinchMove = () => {

		if ( this.enabled && this.enableZoom ) {

			this.setCenter( ( this._touchCurrent[ 0 ].clientX + this._touchCurrent[ 1 ].clientX ) / 2, ( this._touchCurrent[ 0 ].clientY + this._touchCurrent[ 1 ].clientY ) / 2 );
			const minDistance = 12; //minimum distance between fingers (in css pixels)

			if ( this._state != STATE.SCALE ) {

				this._startFingerDistance = this._currentFingerDistance;
				this.updateTbState( STATE.SCALE, true );

			}

			this._currentFingerDistance = Math.max( this.calculatePointersDistance( this._touchCurrent[ 0 ], this._touchCurrent[ 1 ] ), minDistance * this._devPxRatio );
			const amount = this._currentFingerDistance / this._startFingerDistance;

			let scalePoint;

			if ( ! this.enablePan ) {

				scalePoint = this._gizmos.position;

			} else {

				if ( this.camera.isOrthographicCamera ) {

					scalePoint = this.unprojectOnTbPlane( this.camera, _center.x, _center.y, this.domElement )
						.applyQuaternion( this.camera.quaternion )
						.multiplyScalar( 1 / this.camera.zoom )
						.add( this._gizmos.position );

				} else if ( this.camera.isPerspectiveCamera ) {

					scalePoint = this.unprojectOnTbPlane( this.camera, _center.x, _center.y, this.domElement )
						.applyQuaternion( this.camera.quaternion )
						.add( this._gizmos.position );

				}

			}

			this.applyTransformMatrix( this.scale( amount, scalePoint ) );
			this.dispatchEvent( _changeEvent );

		}

	};

	onPinchEnd = () => {

		this.updateTbState( STATE.IDLE, false );
		this.dispatchEvent( _endEvent );

	};

	onTriplePanStart = () => {

		if ( this.enabled && this.enableZoom ) {

			this.dispatchEvent( _startEvent );

			this.updateTbState( STATE.SCALE, true );

			//const center = event.center;
			let clientX = 0;
			let clientY = 0;
			const nFingers = this._touchCurrent.length;

			for ( let i = 0; i < nFingers; i ++ ) {

				clientX += this._touchCurrent[ i ].clientX;
				clientY += this._touchCurrent[ i ].clientY;

			}

			this.setCenter( clientX / nFingers, clientY / nFingers );

			this._startCursorPosition.setY( this.getCursorNDC( _center.x, _center.y, this.domElement ).y * 0.5 );
			this._currentCursorPosition.copy( this._startCursorPosition );

		}

	};

	onTriplePanMove = () => {

		if ( this.enabled && this.enableZoom ) {

			//	  fov / 2
			//		|\
			//		| \
			//		|  \
			//	x	|	\
			//		| 	 \
			//		| 	  \
			//		| _ _ _\
			//			y

			//const center = event.center;
			let clientX = 0;
			let clientY = 0;
			const nFingers = this._touchCurrent.length;

			for ( let i = 0; i < nFingers; i ++ ) {

				clientX += this._touchCurrent[ i ].clientX;
				clientY += this._touchCurrent[ i ].clientY;

			}

			this.setCenter( clientX / nFingers, clientY / nFingers );

			const screenNotches = 8;	//how many wheel notches corresponds to a full screen pan
			this._currentCursorPosition.setY( this.getCursorNDC( _center.x, _center.y, this.domElement ).y * 0.5 );

			const movement = this._currentCursorPosition.y - this._startCursorPosition.y;

			let size = 1;

			if ( movement < 0 ) {

				size = 1 / ( Math.pow( this.scaleFactor, - movement * screenNotches ) );

			} else if ( movement > 0 ) {

				size = Math.pow( this.scaleFactor, movement * screenNotches );

			}

			this._v3_1.setFromMatrixPosition( this._cameraMatrixState );
			const x = this._v3_1.distanceTo( this._gizmos.position );
			let xNew = x / size; //distance between camera and gizmos if scale(size, scalepoint) would be performed

			//check min and max distance
			xNew = MathUtils.clamp( xNew, this.minDistance, this.maxDistance );

			const y = x * Math.tan( MathUtils.DEG2RAD * this._fovState * 0.5 );

			//calculate new fov
			let newFov = MathUtils.RAD2DEG * ( Math.atan( y / xNew ) * 2 );

			//check min and max fov
			newFov = MathUtils.clamp( newFov, this.minFov, this.maxFov );

			const newDistance = y / Math.tan( MathUtils.DEG2RAD * ( newFov / 2 ) );
			size = x / newDistance;
			this._v3_2.setFromMatrixPosition( this._gizmoMatrixState );

			this.setFov( newFov );
			this.applyTransformMatrix( this.scale( size, this._v3_2, false ) );

			//adjusting distance
			_offset.copy( this._gizmos.position ).sub( this.camera.position ).normalize().multiplyScalar( newDistance / x );
			this._m4_1.makeTranslation( _offset.x, _offset.y, _offset.z );

			this.dispatchEvent( _changeEvent );

		}

	};

	onTriplePanEnd = () => {

		this.updateTbState( STATE.IDLE, false );
		this.dispatchEvent( _endEvent );
		//this.dispatchEvent( _changeEvent );

	};

	/**
	 * Set _center's x/y coordinates
	 * @param {Number} clientX
	 * @param {Number} clientY
	 */
	setCenter = ( clientX, clientY ) => {

		_center.x = clientX;
		_center.y = clientY;

	};

	/**
	 * Set default mouse actions
	 */
	initializeMouseActions = () => {

		this.setMouseAction( 'PAN', 0, 'CTRL' );
		this.setMouseAction( 'PAN', 2 );

		this.setMouseAction( 'ROTATE', 0 );

		this.setMouseAction( 'ZOOM', 'WHEEL' );
		this.setMouseAction( 'ZOOM', 1 );

		this.setMouseAction( 'FOV', 'WHEEL', 'SHIFT' );
		this.setMouseAction( 'FOV', 1, 'SHIFT' );


	};

	/**
	 * Compare two mouse actions
	 * @param {Object} action1
	 * @param {Object} action2
	 * @returns {Boolean} True if action1 and action 2 are the same mouse action, false otherwise
	 */
	compareMouseAction = ( action1, action2 ) => {

		if ( action1.operation == action2.operation ) {

			if ( action1.mouse == action2.mouse && action1.key == action2.key ) {

				return true;

			} else {

				return false;

			}

		} else {

			return false;

		}

	};

	/**
	 * Set a new mouse action by specifying the operation to be performed and a mouse/key combination. In case of conflict, replaces the existing one
	 * @param {String} operation The operation to be performed ('PAN', 'ROTATE', 'ZOOM', 'FOV)
	 * @param {*} mouse A mouse button (0, 1, 2) or 'WHEEL' for wheel notches
	 * @param {*} key The keyboard modifier ('CTRL', 'SHIFT') or null if key is not needed
	 * @returns {Boolean} True if the mouse action has been successfully added, false otherwise
	 */
	setMouseAction = ( operation, mouse, key = null ) => {

		const operationInput = [ 'PAN', 'ROTATE', 'ZOOM', 'FOV' ];
		const mouseInput = [ 0, 1, 2, 'WHEEL' ];
		const keyInput = [ 'CTRL', 'SHIFT', null ];
		let state;

		if ( ! operationInput.includes( operation ) || ! mouseInput.includes( mouse ) || ! keyInput.includes( key ) ) {

			//invalid parameters
			return false;

		}

		if ( mouse == 'WHEEL' ) {

			if ( operation != 'ZOOM' && operation != 'FOV' ) {

				//cannot associate 2D operation to 1D input
				return false;

			}

		}

		switch ( operation ) {

			case 'PAN':

				state = STATE.PAN;
				break;

			case 'ROTATE':

				state = STATE.ROTATE;
				break;

			case 'ZOOM':

				state = STATE.SCALE;
				break;

			case 'FOV':

				state = STATE.FOV;
				break;

		}

		const action = {

			operation: operation,
			mouse: mouse,
			key: key,
			state: state

		};

		for ( let i = 0; i < this.mouseActions.length; i ++ ) {

			if ( this.mouseActions[ i ].mouse == action.mouse && this.mouseActions[ i ].key == action.key ) {

				this.mouseActions.splice( i, 1, action );
				return true;

			}

		}

		this.mouseActions.push( action );
		return true;

	};

	/**
	 * Remove a mouse action by specifying its mouse/key combination
	 * @param {*} mouse A mouse button (0, 1, 2) or 'WHEEL' for wheel notches
	 * @param {*} key The keyboard modifier ('CTRL', 'SHIFT') or null if key is not needed
	 * @returns {Boolean} True if the operation has been succesfully removed, false otherwise
	 */
	unsetMouseAction = ( mouse, key = null ) => {

		for ( let i = 0; i < this.mouseActions.length; i ++ ) {

			if ( this.mouseActions[ i ].mouse == mouse && this.mouseActions[ i ].key == key ) {

				this.mouseActions.splice( i, 1 );
				return true;

			}

		}

		return false;

	};

	/**
	 * Return the operation associated to a mouse/keyboard combination
	 * @param {*} mouse A mouse button (0, 1, 2) or 'WHEEL' for wheel notches
	 * @param {*} key The keyboard modifier ('CTRL', 'SHIFT') or null if key is not needed
	 * @returns The operation if it has been found, null otherwise
	 */
	getOpFromAction = ( mouse, key ) => {

		let action;

		for ( let i = 0; i < this.mouseActions.length; i ++ ) {

			action = this.mouseActions[ i ];
			if ( action.mouse == mouse && action.key == key ) {

				return action.operation;

			}

		}

		if ( key != null ) {

			for ( let i = 0; i < this.mouseActions.length; i ++ ) {

				action = this.mouseActions[ i ];
				if ( action.mouse == mouse && action.key == null ) {

					return action.operation;

				}

			}

		}

		return null;

	};

	/**
	 * Get the operation associated to mouse and key combination and returns the corresponding FSA state
	 * @param {Number} mouse Mouse button
	 * @param {String} key Keyboard modifier
	 * @returns The FSA state obtained from the operation associated to mouse/keyboard combination
	 */
	getOpStateFromAction = ( mouse, key ) => {

		let action;

		for ( let i = 0; i < this.mouseActions.length; i ++ ) {

			action = this.mouseActions[ i ];
			if ( action.mouse == mouse && action.key == key ) {

				return action.state;

			}

		}

		if ( key != null ) {

			for ( let i = 0; i < this.mouseActions.length; i ++ ) {

				action = this.mouseActions[ i ];
				if ( action.mouse == mouse && action.key == null ) {

					return action.state;

				}

			}

		}

		return null;

	};

	/**
	 * Calculate the angle between two pointers
	 * @param {PointerEvent} p1
	 * @param {PointerEvent} p2
	 * @returns {Number} The angle between two pointers in degrees
	 */
	getAngle = ( p1, p2 ) => {

		return Math.atan2( p2.clientY - p1.clientY, p2.clientX - p1.clientX ) * 180 / Math.PI;

	};

	/**
	 * Update a PointerEvent inside current pointerevents array
	 * @param {PointerEvent} event
	 */
	updateTouchEvent = ( event ) => {

		for ( let i = 0; i < this._touchCurrent.length; i ++ ) {

			if ( this._touchCurrent[ i ].pointerId == event.pointerId ) {

				this._touchCurrent.splice( i, 1, event );
				break;

			}

		}

	};

	/**
	 * Apply a transformation matrix, to the camera and gizmos
	 * @param {Object} transformation Object containing matrices to apply to camera and gizmos
	 */
	applyTransformMatrix( transformation ) {

		if ( transformation.camera != null ) {

			this._m4_1.copy( this._cameraMatrixState ).premultiply( transformation.camera );
			this._m4_1.decompose( this.camera.position, this.camera.quaternion, this.camera.scale );
			this.camera.updateMatrix();

			//update camera up vector
			if ( this._state == STATE.ROTATE || this._state == STATE.ZROTATE || this._state == STATE.ANIMATION_ROTATE ) {

				this.camera.up.copy( this._upState ).applyQuaternion( this.camera.quaternion );

			}

		}

		if ( transformation.gizmos != null ) {

			this._m4_1.copy( this._gizmoMatrixState ).premultiply( transformation.gizmos );
			this._m4_1.decompose( this._gizmos.position, this._gizmos.quaternion, this._gizmos.scale );
			this._gizmos.updateMatrix();

		}

		if ( this._state == STATE.SCALE || this._state == STATE.FOCUS || this._state == STATE.ANIMATION_FOCUS ) {

			this._tbRadius = this.calculateTbRadius( this.camera );

			if ( this.adjustNearFar ) {

				const cameraDistance = this.camera.position.distanceTo( this._gizmos.position );

				const bb = new Box3();
				bb.setFromObject( this._gizmos );
				const sphere = new Sphere();
				bb.getBoundingSphere( sphere );

				const adjustedNearPosition = Math.max( this._nearPos0, sphere.radius + sphere.center.length() );
				const regularNearPosition = cameraDistance - this._initialNear;

				const minNearPos = Math.min( adjustedNearPosition, regularNearPosition );
				this.camera.near = cameraDistance - minNearPos;


				const adjustedFarPosition = Math.min( this._farPos0, - sphere.radius + sphere.center.length() );
				const regularFarPosition = cameraDistance - this._initialFar;

				const minFarPos = Math.min( adjustedFarPosition, regularFarPosition );
				this.camera.far = cameraDistance - minFarPos;

				this.camera.updateProjectionMatrix();

			} else {

				let update = false;

				if ( this.camera.near != this._initialNear ) {

					this.camera.near = this._initialNear;
					update = true;

				}

				if ( this.camera.far != this._initialFar ) {

					this.camera.far = this._initialFar;
					update = true;

				}

				if ( update ) {

					this.camera.updateProjectionMatrix();

				}

			}

		}

	}

	/**
	 * Calculate the angular speed
	 * @param {Number} p0 Position at t0
	 * @param {Number} p1 Position at t1
	 * @param {Number} t0 Initial time in milliseconds
	 * @param {Number} t1 Ending time in milliseconds
	 */
	calculateAngularSpeed = ( p0, p1, t0, t1 ) => {

		const s = p1 - p0;
		const t = ( t1 - t0 ) / 1000;
		if ( t == 0 ) {

			return 0;

		}

		return s / t;

	};

	/**
	 * Calculate the distance between two pointers
	 * @param {PointerEvent} p0 The first pointer
	 * @param {PointerEvent} p1 The second pointer
	 * @returns {number} The distance between the two pointers
	 */
	calculatePointersDistance = ( p0, p1 ) => {

		return Math.sqrt( Math.pow( p1.clientX - p0.clientX, 2 ) + Math.pow( p1.clientY - p0.clientY, 2 ) );

	};

	/**
	 * Calculate the rotation axis as the vector perpendicular between two vectors
	 * @param {Vector3} vec1 The first vector
	 * @param {Vector3} vec2 The second vector
	 * @returns {Vector3} The normalized rotation axis
	 */
	calculateRotationAxis = ( vec1, vec2 ) => {

		this._rotationMatrix.extractRotation( this._cameraMatrixState );
		this._quat.setFromRotationMatrix( this._rotationMatrix );

		this._rotationAxis.crossVectors( vec1, vec2 ).applyQuaternion( this._quat );
		return this._rotationAxis.normalize().clone();

	};

	/**
	 * Calculate the trackball radius so that gizmo's diamater will be 2/3 of the minimum side of the camera frustum
	 * @param {Camera} camera
	 * @returns {Number} The trackball radius
	 */
	calculateTbRadius = ( camera ) => {

		const distance = camera.position.distanceTo( this._gizmos.position );

		if ( camera.type == 'PerspectiveCamera' ) {

			const halfFovV = MathUtils.DEG2RAD * camera.fov * 0.5; //vertical fov/2 in radians
			const halfFovH = Math.atan( ( camera.aspect ) * Math.tan( halfFovV ) ); //horizontal fov/2 in radians
			return Math.tan( Math.min( halfFovV, halfFovH ) ) * distance * this.radiusFactor;

		} else if ( camera.type == 'OrthographicCamera' ) {

			return Math.min( camera.top, camera.right ) * this.radiusFactor;

		}

	};

	/**
	 * Focus operation consist of positioning the point of interest in front of the camera and a slightly zoom in
	 * @param {Vector3} point The point of interest
	 * @param {Number} size Scale factor
	 * @param {Number} amount Amount of operation to be completed (used for focus animations, default is complete full operation)
	 */
	focus = ( point, size, amount = 1 ) => {

		//move center of camera (along with gizmos) towards point of interest
		_offset.copy( point ).sub( this._gizmos.position ).multiplyScalar( amount );
		this._translationMatrix.makeTranslation( _offset.x, _offset.y, _offset.z );

		_gizmoMatrixStateTemp.copy( this._gizmoMatrixState );
		this._gizmoMatrixState.premultiply( this._translationMatrix );
		this._gizmoMatrixState.decompose( this._gizmos.position, this._gizmos.quaternion, this._gizmos.scale );

		_cameraMatrixStateTemp.copy( this._cameraMatrixState );
		this._cameraMatrixState.premultiply( this._translationMatrix );
		this._cameraMatrixState.decompose( this.camera.position, this.camera.quaternion, this.camera.scale );

		//apply zoom
		if ( this.enableZoom ) {

			this.applyTransformMatrix( this.scale( size, this._gizmos.position ) );

		}

		this._gizmoMatrixState.copy( _gizmoMatrixStateTemp );
		this._cameraMatrixState.copy( _cameraMatrixStateTemp );

	};

	/**
	 * Draw a grid and add it to the scene
	 */
	drawGrid = () => {

		if ( this.scene != null ) {

			const color = 0x888888;
			const multiplier = 3;
			let size, divisions, maxLength, tick;

			if ( this.camera.isOrthographicCamera ) {

				const width = this.camera.right - this.camera.left;
				const height = this.camera.bottom - this.camera.top;

				maxLength = Math.max( width, height );
				tick = maxLength / 20;

				size = maxLength / this.camera.zoom * multiplier;
				divisions = size / tick * this.camera.zoom;

			} else if ( this.camera.isPerspectiveCamera ) {

				const distance = this.camera.position.distanceTo( this._gizmos.position );
				const halfFovV = MathUtils.DEG2RAD * this.camera.fov * 0.5;
				const halfFovH = Math.atan( ( this.camera.aspect ) * Math.tan( halfFovV ) );

				maxLength = Math.tan( Math.max( halfFovV, halfFovH ) ) * distance * 2;
				tick = maxLength / 20;

				size = maxLength * multiplier;
				divisions = size / tick;

			}

			if ( this._grid == null ) {

				this._grid = new GridHelper( size, divisions, color, color );
				this._grid.position.copy( this._gizmos.position );
				this._gridPosition.copy( this._grid.position );
				this._grid.quaternion.copy( this.camera.quaternion );
				this._grid.rotateX( Math.PI * 0.5 );

				this.scene.add( this._grid );

			}

		}

	};

	/**
	 * Remove all listeners, stop animations and clean scene
	 */
	dispose = () => {

		if ( this._animationId != - 1 ) {

			window.cancelAnimationFrame( this._animationId );

		}

		this.domElement.removeEventListener( 'pointerdown', this.onPointerDown );
		this.domElement.removeEventListener( 'pointercancel', this.onPointerCancel );
		this.domElement.removeEventListener( 'wheel', this.onWheel );
		this.domElement.removeEventListener( 'contextmenu', this.onContextMenu );

		window.removeEventListener( 'pointermove', this.onPointerMove );
		window.removeEventListener( 'pointerup', this.onPointerUp );

		window.removeEventListener( 'resize', this.onWindowResize );

		if ( this.scene !== null ) this.scene.remove( this._gizmos );
		this.disposeGrid();

	};

	/**
	 * remove the grid from the scene
	 */
	disposeGrid = () => {

		if ( this._grid != null && this.scene != null ) {

			this.scene.remove( this._grid );
			this._grid = null;

		}

	};

	/**
	 * Compute the easing out cubic function for ease out effect in animation
	 * @param {Number} t The absolute progress of the animation in the bound of 0 (beginning of the) and 1 (ending of animation)
	 * @returns {Number} Result of easing out cubic at time t
	 */
	easeOutCubic = ( t ) => {

		return 1 - Math.pow( 1 - t, 3 );

	};

	/**
	 * Make rotation gizmos more or less visible
	 * @param {Boolean} isActive If true, make gizmos more visible
	 */
	activateGizmos = ( isActive ) => {

		const gizmoX = this._gizmos.children[ 0 ];
		const gizmoY = this._gizmos.children[ 1 ];
		const gizmoZ = this._gizmos.children[ 2 ];

		if ( isActive ) {

			gizmoX.material.setValues( { opacity: 1 } );
			gizmoY.material.setValues( { opacity: 1 } );
			gizmoZ.material.setValues( { opacity: 1 } );

		} else {

			gizmoX.material.setValues( { opacity: 0.6 } );
			gizmoY.material.setValues( { opacity: 0.6 } );
			gizmoZ.material.setValues( { opacity: 0.6 } );

		}

	};

	/**
	 * Calculate the cursor position in NDC
	 * @param {number} x Cursor horizontal coordinate within the canvas
	 * @param {number} y Cursor vertical coordinate within the canvas
	 * @param {HTMLElement} canvas The canvas where the renderer draws its output
	 * @returns {Vector2} Cursor normalized position inside the canvas
	 */
	getCursorNDC = ( cursorX, cursorY, canvas ) => {

		const canvasRect = canvas.getBoundingClientRect();
		this._v2_1.setX( ( ( cursorX - canvasRect.left ) / canvasRect.width ) * 2 - 1 );
		this._v2_1.setY( ( ( canvasRect.bottom - cursorY ) / canvasRect.height ) * 2 - 1 );
		return this._v2_1.clone();

	};

	/**
	 * Calculate the cursor position inside the canvas x/y coordinates with the origin being in the center of the canvas
	 * @param {Number} x Cursor horizontal coordinate within the canvas
	 * @param {Number} y Cursor vertical coordinate within the canvas
	 * @param {HTMLElement} canvas The canvas where the renderer draws its output
	 * @returns {Vector2} Cursor position inside the canvas
	 */
	getCursorPosition = ( cursorX, cursorY, canvas ) => {

		this._v2_1.copy( this.getCursorNDC( cursorX, cursorY, canvas ) );
		this._v2_1.x *= ( this.camera.right - this.camera.left ) * 0.5;
		this._v2_1.y *= ( this.camera.top - this.camera.bottom ) * 0.5;
		return this._v2_1.clone();

	};

	/**
	 * Set the camera to be controlled
	 * @param {Camera} camera The virtual camera to be controlled
	 */
	setCamera = ( camera ) => {

		camera.lookAt( this.target );
		camera.updateMatrix();

		//setting state
		if ( camera.type == 'PerspectiveCamera' ) {

			this._fov0 = camera.fov;
			this._fovState = camera.fov;

		}

		this._cameraMatrixState0.copy( camera.matrix );
		this._cameraMatrixState.copy( this._cameraMatrixState0 );
		this._cameraProjectionState.copy( camera.projectionMatrix );
		this._zoom0 = camera.zoom;
		this._zoomState = this._zoom0;

		this._initialNear = camera.near;
		this._nearPos0 = camera.position.distanceTo( this.target ) - camera.near;
		this._nearPos = this._initialNear;

		this._initialFar = camera.far;
		this._farPos0 = camera.position.distanceTo( this.target ) - camera.far;
		this._farPos = this._initialFar;

		this._up0.copy( camera.up );
		this._upState.copy( camera.up );

		this.camera = camera;
		this.camera.updateProjectionMatrix();

		//making gizmos
		this._tbRadius = this.calculateTbRadius( camera );
		this.makeGizmos( this.target, this._tbRadius );

	};

	/**
	 * Set gizmos visibility
	 * @param {Boolean} value Value of gizmos visibility
	 */
	setGizmosVisible( value ) {

		this._gizmos.visible = value;
		this.dispatchEvent( _changeEvent );

	}

	/**
	 * Set gizmos radius factor and redraws gizmos
	 * @param {Float} value Value of radius factor
	 */
	setTbRadius( value ) {

		this.radiusFactor = value;
		this._tbRadius = this.calculateTbRadius( this.camera );

		const curve = new EllipseCurve( 0, 0, this._tbRadius, this._tbRadius );
		const points = curve.getPoints( this._curvePts );
		const curveGeometry = new BufferGeometry().setFromPoints( points );


		for ( const gizmo in this._gizmos.children ) {

			this._gizmos.children[ gizmo ].geometry = curveGeometry;

		}

		this.dispatchEvent( _changeEvent );

	}

	/**
	 * Creates the rotation gizmos matching trackball center and radius
	 * @param {Vector3} tbCenter The trackball center
	 * @param {number} tbRadius The trackball radius
	 */
	makeGizmos = ( tbCenter, tbRadius ) => {

		const curve = new EllipseCurve( 0, 0, tbRadius, tbRadius );
		const points = curve.getPoints( this._curvePts );

		//geometry
		const curveGeometry = new BufferGeometry().setFromPoints( points );

		//material
		const curveMaterialX = new LineBasicMaterial( { color: 0xff8080, fog: false, transparent: true, opacity: 0.6 } );
		const curveMaterialY = new LineBasicMaterial( { color: 0x80ff80, fog: false, transparent: true, opacity: 0.6 } );
		const curveMaterialZ = new LineBasicMaterial( { color: 0x8080ff, fog: false, transparent: true, opacity: 0.6 } );

		//line
		const gizmoX = new Line( curveGeometry, curveMaterialX );
		const gizmoY = new Line( curveGeometry, curveMaterialY );
		const gizmoZ = new Line( curveGeometry, curveMaterialZ );

		const rotation = Math.PI * 0.5;
		gizmoX.rotation.x = rotation;
		gizmoY.rotation.y = rotation;


		//setting state
		this._gizmoMatrixState0.identity().setPosition( tbCenter );
		this._gizmoMatrixState.copy( this._gizmoMatrixState0 );

		if ( this.camera.zoom != 1 ) {

			//adapt gizmos size to camera zoom
			const size = 1 / this.camera.zoom;
			this._scaleMatrix.makeScale( size, size, size );
			this._translationMatrix.makeTranslation( - tbCenter.x, - tbCenter.y, - tbCenter.z );

			this._gizmoMatrixState.premultiply( this._translationMatrix ).premultiply( this._scaleMatrix );
			this._translationMatrix.makeTranslation( tbCenter.x, tbCenter.y, tbCenter.z );
			this._gizmoMatrixState.premultiply( this._translationMatrix );

		}

		this._gizmoMatrixState.decompose( this._gizmos.position, this._gizmos.quaternion, this._gizmos.scale );

		this._gizmos.clear();

		this._gizmos.add( gizmoX );
		this._gizmos.add( gizmoY );
		this._gizmos.add( gizmoZ );

	};

	/**
	 * Perform animation for focus operation
	 * @param {Number} time Instant in which this function is called as performance.now()
	 * @param {Vector3} point Point of interest for focus operation
	 * @param {Matrix4} cameraMatrix Camera matrix
	 * @param {Matrix4} gizmoMatrix Gizmos matrix
	 */
	onFocusAnim = ( time, point, cameraMatrix, gizmoMatrix ) => {

		if ( this._timeStart == - 1 ) {

			//animation start
			this._timeStart = time;

		}

		if ( this._state == STATE.ANIMATION_FOCUS ) {

			const deltaTime = time - this._timeStart;
			const animTime = deltaTime / this.focusAnimationTime;

			this._gizmoMatrixState.copy( gizmoMatrix );

			if ( animTime >= 1 ) {

				//animation end

				this._gizmoMatrixState.decompose( this._gizmos.position, this._gizmos.quaternion, this._gizmos.scale );

				this.focus( point, this.scaleFactor );

				this._timeStart = - 1;
				this.updateTbState( STATE.IDLE, false );
				this.activateGizmos( false );

				this.dispatchEvent( _changeEvent );

			} else {

				const amount = this.easeOutCubic( animTime );
				const size = ( ( 1 - amount ) + ( this.scaleFactor * amount ) );

				this._gizmoMatrixState.decompose( this._gizmos.position, this._gizmos.quaternion, this._gizmos.scale );
				this.focus( point, size, amount );

				this.dispatchEvent( _changeEvent );
				const self = this;
				this._animationId = window.requestAnimationFrame( function ( t ) {

					self.onFocusAnim( t, point, cameraMatrix, gizmoMatrix.clone() );

				} );

			}

		} else {

			//interrupt animation

			this._animationId = - 1;
			this._timeStart = - 1;

		}

	};

	/**
	 * Perform animation for rotation operation
	 * @param {Number} time Instant in which this function is called as performance.now()
	 * @param {Vector3} rotationAxis Rotation axis
	 * @param {number} w0 Initial angular velocity
	 */
	onRotationAnim = ( time, rotationAxis, w0 ) => {

		if ( this._timeStart == - 1 ) {

			//animation start
			this._anglePrev = 0;
			this._angleCurrent = 0;
			this._timeStart = time;

		}

		if ( this._state == STATE.ANIMATION_ROTATE ) {

			//w = w0 + alpha * t
			const deltaTime = ( time - this._timeStart ) / 1000;
			const w = w0 + ( ( - this.dampingFactor ) * deltaTime );

			if ( w > 0 ) {

				//tetha = 0.5 * alpha * t^2 + w0 * t + tetha0
				this._angleCurrent = 0.5 * ( - this.dampingFactor ) * Math.pow( deltaTime, 2 ) + w0 * deltaTime + 0;
				this.applyTransformMatrix( this.rotate( rotationAxis, this._angleCurrent ) );
				this.dispatchEvent( _changeEvent );
				const self = this;
				this._animationId = window.requestAnimationFrame( function ( t ) {

					self.onRotationAnim( t, rotationAxis, w0 );

				} );

			} else {

				this._animationId = - 1;
				this._timeStart = - 1;

				this.updateTbState( STATE.IDLE, false );
				this.activateGizmos( false );

				this.dispatchEvent( _changeEvent );

			}

		} else {

			//interrupt animation

			this._animationId = - 1;
			this._timeStart = - 1;

			if ( this._state != STATE.ROTATE ) {

				this.activateGizmos( false );
				this.dispatchEvent( _changeEvent );

			}

		}

	};


	/**
	 * Perform pan operation moving camera between two points
	 * @param {Vector3} p0 Initial point
	 * @param {Vector3} p1 Ending point
	 * @param {Boolean} adjust If movement should be adjusted considering camera distance (Perspective only)
	 */
	pan = ( p0, p1, adjust = false ) => {

		const movement = p0.clone().sub( p1 );

		if ( this.camera.isOrthographicCamera ) {

			//adjust movement amount
			movement.multiplyScalar( 1 / this.camera.zoom );

		} else if ( this.camera.isPerspectiveCamera && adjust ) {

			//adjust movement amount
			this._v3_1.setFromMatrixPosition( this._cameraMatrixState0 );	//camera's initial position
			this._v3_2.setFromMatrixPosition( this._gizmoMatrixState0 );	//gizmo's initial position
			const distanceFactor = this._v3_1.distanceTo( this._v3_2 ) / this.camera.position.distanceTo( this._gizmos.position );
			movement.multiplyScalar( 1 / distanceFactor );

		}

		this._v3_1.set( movement.x, movement.y, 0 ).applyQuaternion( this.camera.quaternion );

		this._m4_1.makeTranslation( this._v3_1.x, this._v3_1.y, this._v3_1.z );

		this.setTransformationMatrices( this._m4_1, this._m4_1 );
		return _transformation;

	};

	/**
	 * Reset trackball
	 */
	reset = () => {

		this.camera.zoom = this._zoom0;

		if ( this.camera.isPerspectiveCamera ) {

			this.camera.fov = this._fov0;

		}

		this.camera.near = this._nearPos;
		this.camera.far = this._farPos;
		this._cameraMatrixState.copy( this._cameraMatrixState0 );
		this._cameraMatrixState.decompose( this.camera.position, this.camera.quaternion, this.camera.scale );
		this.camera.up.copy( this._up0 );

		this.camera.updateMatrix();
		this.camera.updateProjectionMatrix();

		this._gizmoMatrixState.copy( this._gizmoMatrixState0 );
		this._gizmoMatrixState0.decompose( this._gizmos.position, this._gizmos.quaternion, this._gizmos.scale );
		this._gizmos.updateMatrix();

		this._tbRadius = this.calculateTbRadius( this.camera );
		this.makeGizmos( this._gizmos.position, this._tbRadius );

		this.camera.lookAt( this._gizmos.position );

		this.updateTbState( STATE.IDLE, false );

		this.dispatchEvent( _changeEvent );

	};

	/**
	 * Rotate the camera around an axis passing by trackball's center
	 * @param {Vector3} axis Rotation axis
	 * @param {number} angle Angle in radians
	 * @returns {Object} Object with 'camera' field containing transformation matrix resulting from the operation to be applied to the camera
	 */
	rotate = ( axis, angle ) => {

		const point = this._gizmos.position; //rotation center
		this._translationMatrix.makeTranslation( - point.x, - point.y, - point.z );
		this._rotationMatrix.makeRotationAxis( axis, - angle );

		//rotate camera
		this._m4_1.makeTranslation( point.x, point.y, point.z );
		this._m4_1.multiply( this._rotationMatrix );
		this._m4_1.multiply( this._translationMatrix );

		this.setTransformationMatrices( this._m4_1 );

		return _transformation;

	};

	copyState = () => {

		let state;
		if ( this.camera.isOrthographicCamera ) {

			state = JSON.stringify( { arcballState: {

				cameraFar: this.camera.far,
				cameraMatrix: this.camera.matrix,
				cameraNear: this.camera.near,
				cameraUp: this.camera.up,
				cameraZoom: this.camera.zoom,
				gizmoMatrix: this._gizmos.matrix

			} } );

		} else if ( this.camera.isPerspectiveCamera ) {

			state = JSON.stringify( { arcballState: {
				cameraFar: this.camera.far,
				cameraFov: this.camera.fov,
				cameraMatrix: this.camera.matrix,
				cameraNear: this.camera.near,
				cameraUp: this.camera.up,
				cameraZoom: this.camera.zoom,
				gizmoMatrix: this._gizmos.matrix

			} } );

		}

		navigator.clipboard.writeText( state );

	};

	pasteState = () => {

		const self = this;
		navigator.clipboard.readText().then( function resolved( value ) {

			self.setStateFromJSON( value );

		} );

	};

	/**
	 * Save the current state of the control. This can later be recover with .reset
	 */
	saveState = () => {

		this._cameraMatrixState0.copy( this.camera.matrix );
		this._gizmoMatrixState0.copy( this._gizmos.matrix );
		this._nearPos = this.camera.near;
		this._farPos = this.camera.far;
		this._zoom0 = this.camera.zoom;
		this._up0.copy( this.camera.up );

		if ( this.camera.isPerspectiveCamera ) {

			this._fov0 = this.camera.fov;

		}

	};

	/**
	 * Perform uniform scale operation around a given point
	 * @param {Number} size Scale factor
	 * @param {Vector3} point Point around which scale
	 * @param {Boolean} scaleGizmos If gizmos should be scaled (Perspective only)
	 * @returns {Object} Object with 'camera' and 'gizmo' fields containing transformation matrices resulting from the operation to be applied to the camera and gizmos
	 */
	scale = ( size, point, scaleGizmos = true ) => {

		_scalePointTemp.copy( point );
		let sizeInverse = 1 / size;

		if ( this.camera.isOrthographicCamera ) {

			//camera zoom
			this.camera.zoom = this._zoomState;
			this.camera.zoom *= size;

			//check min and max zoom
			if ( this.camera.zoom > this.maxZoom ) {

				this.camera.zoom = this.maxZoom;
				sizeInverse = this._zoomState / this.maxZoom;

			} else if ( this.camera.zoom < this.minZoom ) {

				this.camera.zoom = this.minZoom;
				sizeInverse = this._zoomState / this.minZoom;

			}

			this.camera.updateProjectionMatrix();

			this._v3_1.setFromMatrixPosition( this._gizmoMatrixState );	//gizmos position

			//scale gizmos so they appear in the same spot having the same dimension
			this._scaleMatrix.makeScale( sizeInverse, sizeInverse, sizeInverse );
			this._translationMatrix.makeTranslation( - this._v3_1.x, - this._v3_1.y, - this._v3_1.z );

			this._m4_2.makeTranslation( this._v3_1.x, this._v3_1.y, this._v3_1.z ).multiply( this._scaleMatrix );
			this._m4_2.multiply( this._translationMatrix );


			//move camera and gizmos to obtain pinch effect
			_scalePointTemp.sub( this._v3_1 );

			const amount = _scalePointTemp.clone().multiplyScalar( sizeInverse );
			_scalePointTemp.sub( amount );

			this._m4_1.makeTranslation( _scalePointTemp.x, _scalePointTemp.y, _scalePointTemp.z );
			this._m4_2.premultiply( this._m4_1 );

			this.setTransformationMatrices( this._m4_1, this._m4_2 );
			return _transformation;

		} else if ( this.camera.isPerspectiveCamera ) {

			this._v3_1.setFromMatrixPosition( this._cameraMatrixState );
			this._v3_2.setFromMatrixPosition( this._gizmoMatrixState );

			//move camera
			let distance = this._v3_1.distanceTo( _scalePointTemp );
			let amount = distance - ( distance * sizeInverse );

			//check min and max distance
			const newDistance = distance - amount;
			if ( newDistance < this.minDistance ) {

				sizeInverse = this.minDistance / distance;
				amount = distance - ( distance * sizeInverse );

			} else if ( newDistance > this.maxDistance ) {

				sizeInverse = this.maxDistance / distance;
				amount = distance - ( distance * sizeInverse );

			}

			_offset.copy( _scalePointTemp ).sub( this._v3_1 ).normalize().multiplyScalar( amount );

			this._m4_1.makeTranslation( _offset.x, _offset.y, _offset.z );


			if ( scaleGizmos ) {

				//scale gizmos so they appear in the same spot having the same dimension
				const pos = this._v3_2;

				distance = pos.distanceTo( _scalePointTemp );
				amount = distance - ( distance * sizeInverse );
				_offset.copy( _scalePointTemp ).sub( this._v3_2 ).normalize().multiplyScalar( amount );

				this._translationMatrix.makeTranslation( pos.x, pos.y, pos.z );
				this._scaleMatrix.makeScale( sizeInverse, sizeInverse, sizeInverse );

				this._m4_2.makeTranslation( _offset.x, _offset.y, _offset.z ).multiply( this._translationMatrix );
				this._m4_2.multiply( this._scaleMatrix );

				this._translationMatrix.makeTranslation( - pos.x, - pos.y, - pos.z );

				this._m4_2.multiply( this._translationMatrix );
				this.setTransformationMatrices( this._m4_1, this._m4_2 );


			} else {

				this.setTransformationMatrices( this._m4_1 );

			}

			return _transformation;

		}

	};

	/**
	 * Set camera fov
	 * @param {Number} value fov to be setted
	 */
	setFov = ( value ) => {

		if ( this.camera.isPerspectiveCamera ) {

			this.camera.fov = MathUtils.clamp( value, this.minFov, this.maxFov );
			this.camera.updateProjectionMatrix();

		}

	};

	/**
	 * Set values in transformation object
	 * @param {Matrix4} camera Transformation to be applied to the camera
	 * @param {Matrix4} gizmos Transformation to be applied to gizmos
	 */
	 setTransformationMatrices( camera = null, gizmos = null ) {

		if ( camera != null ) {

			if ( _transformation.camera != null ) {

				_transformation.camera.copy( camera );

			} else {

				_transformation.camera = camera.clone();

			}

		} else {

			_transformation.camera = null;

		}

		if ( gizmos != null ) {

			if ( _transformation.gizmos != null ) {

				_transformation.gizmos.copy( gizmos );

			} else {

				_transformation.gizmos = gizmos.clone();

			}

		} else {

			_transformation.gizmos = null;

		}

	}

	/**
	 * Rotate camera around its direction axis passing by a given point by a given angle
	 * @param {Vector3} point The point where the rotation axis is passing trough
	 * @param {Number} angle Angle in radians
	 * @returns The computed transormation matix
	 */
	zRotate = ( point, angle ) => {

		this._rotationMatrix.makeRotationAxis( this._rotationAxis, angle );
		this._translationMatrix.makeTranslation( - point.x, - point.y, - point.z );

		this._m4_1.makeTranslation( point.x, point.y, point.z );
		this._m4_1.multiply( this._rotationMatrix );
		this._m4_1.multiply( this._translationMatrix );

		this._v3_1.setFromMatrixPosition( this._gizmoMatrixState ).sub( point );	//vector from rotation center to gizmos position
		this._v3_2.copy( this._v3_1 ).applyAxisAngle( this._rotationAxis, angle );	//apply rotation
		this._v3_2.sub( this._v3_1 );

		this._m4_2.makeTranslation( this._v3_2.x, this._v3_2.y, this._v3_2.z );

		this.setTransformationMatrices( this._m4_1, this._m4_2 );
		return _transformation;

	};


	getRaycaster() {

		return _raycaster;

	}


	/**
	 * Unproject the cursor on the 3D object surface
	 * @param {Vector2} cursor Cursor coordinates in NDC
	 * @param {Camera} camera Virtual camera
	 * @returns {Vector3} The point of intersection with the model, if exist, null otherwise
	 */
	unprojectOnObj = ( cursor, camera ) => {

		const raycaster = this.getRaycaster();
		raycaster.near = camera.near;
		raycaster.far = camera.far;
		raycaster.setFromCamera( cursor, camera );

		const intersect = raycaster.intersectObjects( this.scene.children, true );

		for ( let i = 0; i < intersect.length; i ++ ) {

			if ( intersect[ i ].object.uuid != this._gizmos.uuid && intersect[ i ].face != null ) {

				return intersect[ i ].point.clone();

			}

		}

		return null;

	};

	/**
	 * Unproject the cursor on the trackball surface
	 * @param {Camera} camera The virtual camera
	 * @param {Number} cursorX Cursor horizontal coordinate on screen
	 * @param {Number} cursorY Cursor vertical coordinate on screen
	 * @param {HTMLElement} canvas The canvas where the renderer draws its output
	 * @param {number} tbRadius The trackball radius
	 * @returns {Vector3} The unprojected point on the trackball surface
	 */
	unprojectOnTbSurface = ( camera, cursorX, cursorY, canvas, tbRadius ) => {

		if ( camera.type == 'OrthographicCamera' ) {

			this._v2_1.copy( this.getCursorPosition( cursorX, cursorY, canvas ) );
			this._v3_1.set( this._v2_1.x, this._v2_1.y, 0 );

			const x2 = Math.pow( this._v2_1.x, 2 );
			const y2 = Math.pow( this._v2_1.y, 2 );
			const r2 = Math.pow( this._tbRadius, 2 );

			if ( x2 + y2 <= r2 * 0.5 ) {

				//intersection with sphere
				this._v3_1.setZ( Math.sqrt( r2 - ( x2 + y2 ) ) );

			} else {

				//intersection with hyperboloid
				this._v3_1.setZ( ( r2 * 0.5 ) / ( Math.sqrt( x2 + y2 ) ) );

			}

			return this._v3_1;

		} else if ( camera.type == 'PerspectiveCamera' ) {

			//unproject cursor on the near plane
			this._v2_1.copy( this.getCursorNDC( cursorX, cursorY, canvas ) );

			this._v3_1.set( this._v2_1.x, this._v2_1.y, - 1 );
			this._v3_1.applyMatrix4( camera.projectionMatrixInverse );

			const rayDir = this._v3_1.clone().normalize(); //unprojected ray direction
			const cameraGizmoDistance = camera.position.distanceTo( this._gizmos.position );
			const radius2 = Math.pow( tbRadius, 2 );

			//	  camera
			//		|\
			//		| \
			//		|  \
			//	h	|	\
			//		| 	 \
			//		| 	  \
			//	_ _ | _ _ _\ _ _  near plane
			//			l

			const h = this._v3_1.z;
			const l = Math.sqrt( Math.pow( this._v3_1.x, 2 ) + Math.pow( this._v3_1.y, 2 ) );

			if ( l == 0 ) {

				//ray aligned with camera
				rayDir.set( this._v3_1.x, this._v3_1.y, tbRadius );
				return rayDir;

			}

			const m = h / l;
			const q = cameraGizmoDistance;

			/*
			 * calculate intersection point between unprojected ray and trackball surface
			 *|y = m * x + q
			 *|x^2 + y^2 = r^2
			 *
			 * (m^2 + 1) * x^2 + (2 * m * q) * x + q^2 - r^2 = 0
			 */
			let a = Math.pow( m, 2 ) + 1;
			let b = 2 * m * q;
			let c = Math.pow( q, 2 ) - radius2;
			let delta = Math.pow( b, 2 ) - ( 4 * a * c );

			if ( delta >= 0 ) {

				//intersection with sphere
				this._v2_1.setX( ( - b - Math.sqrt( delta ) ) / ( 2 * a ) );
				this._v2_1.setY( m * this._v2_1.x + q );

				const angle = MathUtils.RAD2DEG * this._v2_1.angle();

				if ( angle >= 45 ) {

					//if angle between intersection point and X' axis is >= 45°, return that point
					//otherwise, calculate intersection point with hyperboloid

					const rayLength = Math.sqrt( Math.pow( this._v2_1.x, 2 ) + Math.pow( ( cameraGizmoDistance - this._v2_1.y ), 2 ) );
					rayDir.multiplyScalar( rayLength );
					rayDir.z += cameraGizmoDistance;
					return rayDir;

				}

			}

			//intersection with hyperboloid
			/*
			 *|y = m * x + q
			 *|y = (1 / x) * (r^2 / 2)
			 *
			 * m * x^2 + q * x - r^2 / 2 = 0
			 */

			a = m;
			b = q;
			c = - radius2 * 0.5;
			delta = Math.pow( b, 2 ) - ( 4 * a * c );
			this._v2_1.setX( ( - b - Math.sqrt( delta ) ) / ( 2 * a ) );
			this._v2_1.setY( m * this._v2_1.x + q );

			const rayLength = Math.sqrt( Math.pow( this._v2_1.x, 2 ) + Math.pow( ( cameraGizmoDistance - this._v2_1.y ), 2 ) );

			rayDir.multiplyScalar( rayLength );
			rayDir.z += cameraGizmoDistance;
			return rayDir;

		}

	};


	/**
	 * Unproject the cursor on the plane passing through the center of the trackball orthogonal to the camera
	 * @param {Camera} camera The virtual camera
	 * @param {Number} cursorX Cursor horizontal coordinate on screen
	 * @param {Number} cursorY Cursor vertical coordinate on screen
	 * @param {HTMLElement} canvas The canvas where the renderer draws its output
	 * @param {Boolean} initialDistance If initial distance between camera and gizmos should be used for calculations instead of current (Perspective only)
	 * @returns {Vector3} The unprojected point on the trackball plane
	 */
	unprojectOnTbPlane = ( camera, cursorX, cursorY, canvas, initialDistance = false ) => {

		if ( camera.type == 'OrthographicCamera' ) {

			this._v2_1.copy( this.getCursorPosition( cursorX, cursorY, canvas ) );
			this._v3_1.set( this._v2_1.x, this._v2_1.y, 0 );

			return this._v3_1.clone();

		} else if ( camera.type == 'PerspectiveCamera' ) {

			this._v2_1.copy( this.getCursorNDC( cursorX, cursorY, canvas ) );

			//unproject cursor on the near plane
			this._v3_1.set( this._v2_1.x, this._v2_1.y, - 1 );
			this._v3_1.applyMatrix4( camera.projectionMatrixInverse );

			const rayDir = this._v3_1.clone().normalize(); //unprojected ray direction

			//	  camera
			//		|\
			//		| \
			//		|  \
			//	h	|	\
			//		| 	 \
			//		| 	  \
			//	_ _ | _ _ _\ _ _  near plane
			//			l

			const h = this._v3_1.z;
			const l = Math.sqrt( Math.pow( this._v3_1.x, 2 ) + Math.pow( this._v3_1.y, 2 ) );
			let cameraGizmoDistance;

			if ( initialDistance ) {

				cameraGizmoDistance = this._v3_1.setFromMatrixPosition( this._cameraMatrixState0 ).distanceTo( this._v3_2.setFromMatrixPosition( this._gizmoMatrixState0 ) );

			} else {

				cameraGizmoDistance = camera.position.distanceTo( this._gizmos.position );

			}

			/*
			 * calculate intersection point between unprojected ray and the plane
			 *|y = mx + q
			 *|y = 0
			 *
			 * x = -q/m
			*/
			if ( l == 0 ) {

				//ray aligned with camera
				rayDir.set( 0, 0, 0 );
				return rayDir;

			}

			const m = h / l;
			const q = cameraGizmoDistance;
			const x = - q / m;

			const rayLength = Math.sqrt( Math.pow( q, 2 ) + Math.pow( x, 2 ) );
			rayDir.multiplyScalar( rayLength );
			rayDir.z = 0;
			return rayDir;

		}

	};

	/**
	 * Update camera and gizmos state
	 */
	updateMatrixState = () => {

		//update camera and gizmos state
		this._cameraMatrixState.copy( this.camera.matrix );
		this._gizmoMatrixState.copy( this._gizmos.matrix );

		if ( this.camera.isOrthographicCamera ) {

			this._cameraProjectionState.copy( this.camera.projectionMatrix );
			this.camera.updateProjectionMatrix();
			this._zoomState = this.camera.zoom;

		} else if ( this.camera.isPerspectiveCamera ) {

			this._fovState = this.camera.fov;

		}

	};

	/**
	 * Update the trackball FSA
	 * @param {STATE} newState New state of the FSA
	 * @param {Boolean} updateMatrices If matriices state should be updated
	 */
	updateTbState = ( newState, updateMatrices ) => {

		this._state = newState;
		if ( updateMatrices ) {

			this.updateMatrixState();

		}

	};

	update = () => {

		const EPS = 0.000001;

		if ( this.target.equals( this._currentTarget ) === false ) {

			this._gizmos.position.copy( this.target );	//for correct radius calculation
			this._tbRadius = this.calculateTbRadius( this.camera );
			this.makeGizmos( this.target, this._tbRadius );
			this._currentTarget.copy( this.target );

		}

		//check min/max parameters
		if ( this.camera.isOrthographicCamera ) {

			//check zoom
			if ( this.camera.zoom > this.maxZoom || this.camera.zoom < this.minZoom ) {

				const newZoom = MathUtils.clamp( this.camera.zoom, this.minZoom, this.maxZoom );
				this.applyTransformMatrix( this.scale( newZoom / this.camera.zoom, this._gizmos.position, true ) );

			}

		} else if ( this.camera.isPerspectiveCamera ) {

			//check distance
			const distance = this.camera.position.distanceTo( this._gizmos.position );

			if ( distance > this.maxDistance + EPS || distance < this.minDistance - EPS ) {

				const newDistance = MathUtils.clamp( distance, this.minDistance, this.maxDistance );
				this.applyTransformMatrix( this.scale( newDistance / distance, this._gizmos.position ) );
				this.updateMatrixState();

			 }

			//check fov
			if ( this.camera.fov < this.minFov || this.camera.fov > this.maxFov ) {

				this.camera.fov = MathUtils.clamp( this.camera.fov, this.minFov, this.maxFov );
				this.camera.updateProjectionMatrix();

			}

			const oldRadius = this._tbRadius;
			this._tbRadius = this.calculateTbRadius( this.camera );

			if ( oldRadius < this._tbRadius - EPS || oldRadius > this._tbRadius + EPS ) {

				const scale = ( this._gizmos.scale.x + this._gizmos.scale.y + this._gizmos.scale.z ) / 3;
				const newRadius = this._tbRadius / scale;
				const curve = new EllipseCurve( 0, 0, newRadius, newRadius );
				const points = curve.getPoints( this._curvePts );
				const curveGeometry = new BufferGeometry().setFromPoints( points );

				for ( const gizmo in this._gizmos.children ) {

					this._gizmos.children[ gizmo ].geometry = curveGeometry;

				}

			}

		}

		this.camera.lookAt( this._gizmos.position );

	};

	setStateFromJSON = ( json ) => {

		const state = JSON.parse( json );

		if ( state.arcballState != undefined ) {

			this._cameraMatrixState.fromArray( state.arcballState.cameraMatrix.elements );
			this._cameraMatrixState.decompose( this.camera.position, this.camera.quaternion, this.camera.scale );

			this.camera.up.copy( state.arcballState.cameraUp );
			this.camera.near = state.arcballState.cameraNear;
			this.camera.far = state.arcballState.cameraFar;

			this.camera.zoom = state.arcballState.cameraZoom;

			if ( this.camera.isPerspectiveCamera ) {

				this.camera.fov = state.arcballState.cameraFov;

			}

			this._gizmoMatrixState.fromArray( state.arcballState.gizmoMatrix.elements );
			this._gizmoMatrixState.decompose( this._gizmos.position, this._gizmos.quaternion, this._gizmos.scale );

			this.camera.updateMatrix();
			this.camera.updateProjectionMatrix();

			this._gizmos.updateMatrix();

			this._tbRadius = this.calculateTbRadius( this.camera );
			const gizmoTmp = new Matrix4().copy( this._gizmoMatrixState0 );
			this.makeGizmos( this._gizmos.position, this._tbRadius );
			this._gizmoMatrixState0.copy( gizmoTmp );

			this.camera.lookAt( this._gizmos.position );
			this.updateTbState( STATE.IDLE, false );

			this.dispatchEvent( _changeEvent );

		}

	};

}

export { ArcballControls };