three.js/examples/js/animation/MMDPhysics.js

/**
 * @author takahiro / https://github.com/takahirox
 *
 * Dependencies
 *  - Ammo.js https://github.com/kripken/ammo.js
 *
 * MMDPhysics calculates physics with Ammo(Bullet based JavaScript Physics engine)
 * for MMD model loaded by THREE.MMDLoader.
 *
 * TODO
 *  - Physics in Worker
 */

THREE.MMDPhysics = ( function () {

	/**
	 * @param {THREE.SkinnedMesh} mesh
	 * @param {Array<Object>} rigidBodyParams
	 * @param {Array<Object>} (optional) constraintParams
	 * @param {Object} params - (optional)
	 * @param {Number} params.unitStep - Default is 1 / 65.
	 * @param {Integer} params.maxStepNum - Default is 3.
	 * @param {THREE.Vector3} params.gravity - Default is ( 0, - 9.8 * 10, 0 )
	 */
	function MMDPhysics( mesh, rigidBodyParams, constraintParams, params ) {

		if ( typeof Ammo === 'undefined' ) {

			throw new Error( 'THREE.MMDPhysics: Import ammo.js https://github.com/kripken/ammo.js' );

		}

		constraintParams = constraintParams || [];
		params = params || {};

		this.manager = new ResourceManager();

		this.mesh = mesh;

		/*
		 * I don't know why but 1/60 unitStep easily breaks models
		 * so I set it 1/65 so far.
		 * Don't set too small unitStep because
		 * the smaller unitStep can make the performance worse.
		 */
		this.unitStep = ( params.unitStep !== undefined ) ? params.unitStep : 1 / 65;
		this.maxStepNum = ( params.maxStepNum !== undefined ) ? params.maxStepNum : 3;
		this.gravity = new THREE.Vector3( 0, - 9.8 * 10, 0 );

		if ( params.gravity !== undefined ) this.gravity.copy( params.gravity );

		this.world = params.world !== undefined ? params.world : null; // experimental

		this.bodies = [];
		this.constraints = [];

		this._init( mesh, rigidBodyParams, constraintParams );

	}

	MMDPhysics.prototype = {

		constructor: MMDPhysics,

		/**
		 * Advances Physics calculation and updates bones.
		 *
		 * @param {Number} delta - time in second
		 * @return {THREE.MMDPhysics}
		 */
		update: function ( delta ) {

			var manager = this.manager;
			var mesh = this.mesh;

			// rigid bodies and constrains are for
			// mesh's world scale (1, 1, 1).
			// Convert to (1, 1, 1) if it isn't.

			var isNonDefaultScale = false;

			var position = manager.allocThreeVector3();
			var quaternion = manager.allocThreeQuaternion();
			var scale = manager.allocThreeVector3();

			mesh.matrixWorld.decompose( position, quaternion, scale );

			if ( scale.x !== 1 || scale.y !== 1 || scale.z !== 1 ) {

				isNonDefaultScale = true;

			}

			var parent;

			if ( isNonDefaultScale ) {

				parent = mesh.parent;

				if ( parent !== null ) mesh.parent = null;

				scale.copy( this.mesh.scale );

				mesh.scale.set( 1, 1, 1 );
				mesh.updateMatrixWorld( true );

			}

			// calculate physics and update bones

			this._updateRigidBodies();
			this._stepSimulation( delta );
			this._updateBones();

			// restore mesh if converted above

			if ( isNonDefaultScale ) {

				if ( parent !== null ) mesh.parent = parent;

				mesh.scale.copy( scale );

			}

			manager.freeThreeVector3( scale );
			manager.freeThreeQuaternion( quaternion );
			manager.freeThreeVector3( position );

			return this;

		},

		/**
		 * Resets rigid bodies transorm to current bone's.
		 *
		 * @return {THREE.MMDPhysics}
		 */
		reset: function () {

			for ( var i = 0, il = this.bodies.length; i < il; i++ ) {

				this.bodies[ i ].reset();

			}

			return this;

		},

		/**
		 * Warm ups Rigid bodies. Calculates cycles steps.
		 *
		 * @param {Integer} cycles
		 * @return {THREE.MMDPhysics}
		 */
		warmup: function ( cycles ) {

			for ( var i = 0; i < cycles; i++ ) {

				this.update( 1 / 60 );

			}

			return this;

		},

		/**
		 * Sets gravity.
		 *
		 * @param {THREE.Vector3} gravity
		 * @return {MMDPhysicsHelper}
		 */
		setGravity: function ( gravity ) {

			this.world.setGravity( new Ammo.btVector3( gravity.x, gravity.y, gravity.z ) );
			this.gravity.copy( gravity );

			return this;

		},

		/**
		 * Creates MMDPhysicsHelper
		 *
		 * @return {MMDPhysicsHelper}
		 */
		createHelper: function () {

			return new MMDPhysicsHelper( this.mesh, this );

		},

		// private methods

		_init: function ( mesh, rigidBodyParams, constraintParams ) {

			var manager = this.manager;

			// rigid body/constraint parameters are for
			// mesh's default world transform as position(0, 0, 0),
			// quaternion(0, 0, 0, 1) and scale(0, 0, 0)

			var parent = mesh.parent;

			if ( parent !== null ) parent = null;

			var currentPosition = manager.allocThreeVector3();
			var currentQuaternion = manager.allocThreeQuaternion();
			var currentScale = manager.allocThreeVector3();

			currentPosition.copy( mesh.position );
			currentQuaternion.copy( mesh.quaternion );
			currentScale.copy( mesh.scale );

			mesh.position.set( 0, 0, 0 );
			mesh.quaternion.set( 0, 0, 0, 1 );
			mesh.scale.set( 1, 1, 1 );

			mesh.updateMatrixWorld( true );

			if ( this.world === null ) {

				this.world = this._createWorld();
				this.setGravity( this.gravity );

			}

			this._initRigidBodies( rigidBodyParams );
			this._initConstraints( constraintParams );

			if ( parent !== null ) mesh.parent = parent;

			mesh.position.copy( currentPosition );
			mesh.quaternion.copy( currentQuaternion );
			mesh.scale.copy( currentScale );

			mesh.updateMatrixWorld( true );

			this.reset();

			manager.freeThreeVector3( currentPosition );
			manager.freeThreeQuaternion( currentQuaternion );
			manager.freeThreeVector3( currentScale );

		},

		_createWorld: function () {

			var config = new Ammo.btDefaultCollisionConfiguration();
			var dispatcher = new Ammo.btCollisionDispatcher( config );
			var cache = new Ammo.btDbvtBroadphase();
			var solver = new Ammo.btSequentialImpulseConstraintSolver();
			var world = new Ammo.btDiscreteDynamicsWorld( dispatcher, cache, solver, config );
			return world;

		},

		_initRigidBodies: function ( rigidBodies ) {

			for ( var i = 0, il = rigidBodies.length; i < il; i++ ) {

				this.bodies.push( new RigidBody(
					this.mesh, this.world, rigidBodies[ i ], this.manager ) );

			}

		},

		_initConstraints: function ( constraints ) {

			for ( var i = 0, il = constraints.length; i < il; i++ ) {

				var params = constraints[ i ];
				var bodyA = this.bodies[ params.rigidBodyIndex1 ];
				var bodyB = this.bodies[ params.rigidBodyIndex2 ];
				this.constraints.push( new Constraint(
					this.mesh, this.world, bodyA, bodyB, params, this.manager ) );

			}


		},

		_stepSimulation: function ( delta ) {

			var unitStep = this.unitStep;
			var stepTime = delta;
			var maxStepNum = ( ( delta / unitStep ) | 0 ) + 1;

			if ( stepTime < unitStep ) {

				stepTime = unitStep;
				maxStepNum = 1;

			}

			if ( maxStepNum > this.maxStepNum ) {

				maxStepNum = this.maxStepNum;

			}

			this.world.stepSimulation( stepTime, maxStepNum, unitStep );

		},

		_updateRigidBodies: function () {

			for ( var i = 0, il = this.bodies.length; i < il; i++ ) {

				this.bodies[ i ].updateFromBone();

			}

		},

		_updateBones: function () {

			for ( var i = 0, il = this.bodies.length; i < il; i++ ) {

				this.bodies[ i ].updateBone();

			}

		}

	};

	/**
	 * This manager's responsibilies are
	 *
	 * 1. manage Ammo.js and Three.js object resources and
	 *    improve the performance and the memory consumption by
	 *    reusing objects.
	 *
	 * 2. provide simple Ammo object operations.
	 */
	function ResourceManager() {

		// for Three.js
		this.threeVector3s = [];
		this.threeMatrix4s = [];
		this.threeQuaternions = [];
		this.threeEulers = [];

		// for Ammo.js
		this.transforms = [];
		this.quaternions = [];
		this.vector3s = [];

	}

	ResourceManager.prototype = {

		constructor: ResourceManager,

		allocThreeVector3: function () {

			return ( this.threeVector3s.length > 0 )
				? this.threeVector3s.pop()
				: new THREE.Vector3();

		},

		freeThreeVector3: function ( v ) {

			this.threeVector3s.push( v );

		},

		allocThreeMatrix4: function () {

			return ( this.threeMatrix4s.length > 0 )
				? this.threeMatrix4s.pop()
				: new THREE.Matrix4();

		},

		freeThreeMatrix4: function ( m ) {

			this.threeMatrix4s.push( m );

		},

		allocThreeQuaternion: function () {

			return ( this.threeQuaternions.length > 0 )
				? this.threeQuaternions.pop()
				: new THREE.Quaternion();

		},

		freeThreeQuaternion: function ( q ) {

			this.threeQuaternions.push( q );

		},

		allocThreeEuler: function () {

			return ( this.threeEulers.length > 0 )
				? this.threeEulers.pop()
				: new THREE.Euler();

		},

		freeThreeEuler: function ( e ) {

			this.threeEulers.push( e );

		},

		allocTransform: function () {

			return ( this.transforms.length > 0 )
				? this.transforms.pop()
				: new Ammo.btTransform();

		},

		freeTransform: function ( t ) {

			this.transforms.push( t );

		},

		allocQuaternion: function () {

			return ( this.quaternions.length > 0 )
				? this.quaternions.pop()
				: new Ammo.btQuaternion();

		},

		freeQuaternion: function ( q ) {

			this.quaternions.push( q );

		},

		allocVector3: function () {

			return ( this.vector3s.length > 0 )
				? this.vector3s.pop()
				: new Ammo.btVector3();

		},

		freeVector3: function ( v ) {

			this.vector3s.push( v );

		},

		setIdentity: function ( t ) {

			t.setIdentity();

		},

		getBasis: function ( t ) {

			var q = this.allocQuaternion();
			t.getBasis().getRotation( q );
			return q;

		},

		getBasisAsMatrix3: function ( t ) {

			var q = this.getBasis( t );
			var m = this.quaternionToMatrix3( q );
			this.freeQuaternion( q );
			return m;

		},

		getOrigin: function( t ) {

			return t.getOrigin();

		},

		setOrigin: function( t, v ) {

			t.getOrigin().setValue( v.x(), v.y(), v.z() );

		},

		copyOrigin: function( t1, t2 ) {

			var o = t2.getOrigin();
			this.setOrigin( t1, o );

		},

		setBasis: function( t, q ) {

			t.setRotation( q );

		},

		setBasisFromMatrix3: function( t, m ) {

			var q = this.matrix3ToQuaternion( m );
			this.setBasis( t, q );
			this.freeQuaternion( q );

		},

		setOriginFromArray3: function ( t, a ) {

			t.getOrigin().setValue( a[ 0 ], a[ 1 ], a[ 2 ] );

		},

		setOriginFromThreeVector3: function ( t, v ) {

			t.getOrigin().setValue( v.x, v.y, v.z );

		},

		setBasisFromArray3: function ( t, a ) {

			var thQ = this.allocThreeQuaternion();
			var thE = this.allocThreeEuler();
			thE.set( a[ 0 ], a[ 1 ], a[ 2 ] );
			this.setBasisFromThreeQuaternion( t, thQ.setFromEuler( thE ) );

			this.freeThreeEuler( thE );
			this.freeThreeQuaternion( thQ );

		},

		setBasisFromThreeQuaternion: function ( t, a ) {

			var q = this.allocQuaternion();

			q.setX( a.x );
			q.setY( a.y );
			q.setZ( a.z );
			q.setW( a.w );
			this.setBasis( t, q );

			this.freeQuaternion( q );

		},

		multiplyTransforms: function ( t1, t2 ) {

			var t = this.allocTransform();
			this.setIdentity( t );

			var m1 = this.getBasisAsMatrix3( t1 );
			var m2 = this.getBasisAsMatrix3( t2 );

			var o1 = this.getOrigin( t1 );
			var o2 = this.getOrigin( t2 );

			var v1 = this.multiplyMatrix3ByVector3( m1, o2 );
			var v2 = this.addVector3( v1, o1 );
			this.setOrigin( t, v2 );

			var m3 = this.multiplyMatrices3( m1, m2 );
			this.setBasisFromMatrix3( t, m3 );

			this.freeVector3( v1 );
			this.freeVector3( v2 );

			return t;

		},

		inverseTransform: function ( t ) {

			var t2 = this.allocTransform();

			var m1 = this.getBasisAsMatrix3( t );
			var o = this.getOrigin( t );

			var m2 = this.transposeMatrix3( m1 );
			var v1 = this.negativeVector3( o );
			var v2 = this.multiplyMatrix3ByVector3( m2, v1 );

			this.setOrigin( t2, v2 );
			this.setBasisFromMatrix3( t2, m2 );

			this.freeVector3( v1 );
			this.freeVector3( v2 );

			return t2;

		},

		multiplyMatrices3: function ( m1, m2 ) {

			var m3 = [];

			var v10 = this.rowOfMatrix3( m1, 0 );
			var v11 = this.rowOfMatrix3( m1, 1 );
			var v12 = this.rowOfMatrix3( m1, 2 );

			var v20 = this.columnOfMatrix3( m2, 0 );
			var v21 = this.columnOfMatrix3( m2, 1 );
			var v22 = this.columnOfMatrix3( m2, 2 );

			m3[ 0 ] = this.dotVectors3( v10, v20 );
			m3[ 1 ] = this.dotVectors3( v10, v21 );
			m3[ 2 ] = this.dotVectors3( v10, v22 );
			m3[ 3 ] = this.dotVectors3( v11, v20 );
			m3[ 4 ] = this.dotVectors3( v11, v21 );
			m3[ 5 ] = this.dotVectors3( v11, v22 );
			m3[ 6 ] = this.dotVectors3( v12, v20 );
			m3[ 7 ] = this.dotVectors3( v12, v21 );
			m3[ 8 ] = this.dotVectors3( v12, v22 );

			this.freeVector3( v10 );
			this.freeVector3( v11 );
			this.freeVector3( v12 );
			this.freeVector3( v20 );
			this.freeVector3( v21 );
			this.freeVector3( v22 );

			return m3;

		},

		addVector3: function( v1, v2 ) {

			var v = this.allocVector3();
			v.setValue( v1.x() + v2.x(), v1.y() + v2.y(), v1.z() + v2.z() );
			return v;

		},

		dotVectors3: function( v1, v2 ) {

			return v1.x() * v2.x() + v1.y() * v2.y() + v1.z() * v2.z();

		},

		rowOfMatrix3: function( m, i ) {

			var v = this.allocVector3();
			v.setValue( m[ i * 3 + 0 ], m[ i * 3 + 1 ], m[ i * 3 + 2 ] );
			return v;

		},

		columnOfMatrix3: function( m, i ) {

			var v = this.allocVector3();
			v.setValue( m[ i + 0 ], m[ i + 3 ], m[ i + 6 ] );
			return v;

		},

		negativeVector3: function( v ) {

			var v2 = this.allocVector3();
			v2.setValue( -v.x(), -v.y(), -v.z() );
			return v2;

		},

		multiplyMatrix3ByVector3: function ( m, v ) {

			var v4 = this.allocVector3();

			var v0 = this.rowOfMatrix3( m, 0 );
			var v1 = this.rowOfMatrix3( m, 1 );
			var v2 = this.rowOfMatrix3( m, 2 );
			var x = this.dotVectors3( v0, v );
			var y = this.dotVectors3( v1, v );
			var z = this.dotVectors3( v2, v );

			v4.setValue( x, y, z );

			this.freeVector3( v0 );
			this.freeVector3( v1 );
			this.freeVector3( v2 );

			return v4;

		},

		transposeMatrix3: function( m ) {

			var m2 = [];
			m2[ 0 ] = m[ 0 ];
			m2[ 1 ] = m[ 3 ];
			m2[ 2 ] = m[ 6 ];
			m2[ 3 ] = m[ 1 ];
			m2[ 4 ] = m[ 4 ];
			m2[ 5 ] = m[ 7 ];
			m2[ 6 ] = m[ 2 ];
			m2[ 7 ] = m[ 5 ];
			m2[ 8 ] = m[ 8 ];
			return m2;

		},

		quaternionToMatrix3: function ( q ) {

			var m = [];

			var x = q.x();
			var y = q.y();
			var z = q.z();
			var w = q.w();

			var xx = x * x;
			var yy = y * y;
			var zz = z * z;

			var xy = x * y;
			var yz = y * z;
			var zx = z * x;

			var xw = x * w;
			var yw = y * w;
			var zw = z * w;

			m[ 0 ] = 1 - 2 * ( yy + zz );
			m[ 1 ] = 2 * ( xy - zw );
			m[ 2 ] = 2 * ( zx + yw );
			m[ 3 ] = 2 * ( xy + zw );
			m[ 4 ] = 1 - 2 * ( zz + xx );
			m[ 5 ] = 2 * ( yz - xw );
			m[ 6 ] = 2 * ( zx - yw );
			m[ 7 ] = 2 * ( yz + xw );
			m[ 8 ] = 1 - 2 * ( xx + yy );

			return m;

		},

		matrix3ToQuaternion: function( m ) {

			var t = m[ 0 ] + m[ 4 ] + m[ 8 ];
			var s, x, y, z, w;

			if( t > 0 ) {

				s = Math.sqrt( t + 1.0 ) * 2;
				w = 0.25 * s;
				x = ( m[ 7 ] - m[ 5 ] ) / s;
				y = ( m[ 2 ] - m[ 6 ] ) / s;
				z = ( m[ 3 ] - m[ 1 ] ) / s;

			} else if( ( m[ 0 ] > m[ 4 ] ) && ( m[ 0 ] > m[ 8 ] ) ) {

				s = Math.sqrt( 1.0 + m[ 0 ] - m[ 4 ] - m[ 8 ] ) * 2;
				w = ( m[ 7 ] - m[ 5 ] ) / s;
				x = 0.25 * s;
				y = ( m[ 1 ] + m[ 3 ] ) / s;
				z = ( m[ 2 ] + m[ 6 ] ) / s;

			} else if( m[ 4 ] > m[ 8 ] ) {

				s = Math.sqrt( 1.0 + m[ 4 ] - m[ 0 ] - m[ 8 ] ) * 2;
				w = ( m[ 2 ] - m[ 6 ] ) / s;
				x = ( m[ 1 ] + m[ 3 ] ) / s;
				y = 0.25 * s;
				z = ( m[ 5 ] + m[ 7 ] ) / s;

			} else {

				s = Math.sqrt( 1.0 + m[ 8 ] - m[ 0 ] - m[ 4 ] ) * 2;
				w = ( m[ 3 ] - m[ 1 ] ) / s;
				x = ( m[ 2 ] + m[ 6 ] ) / s;
				y = ( m[ 5 ] + m[ 7 ] ) / s;
				z = 0.25 * s;

			}

			var q = this.allocQuaternion();
			q.setX( x );
			q.setY( y );
			q.setZ( z );
			q.setW( w );
			return q;

		}

	};

	/**
	 * @param {THREE.SkinnedMesh} mesh
	 * @param {Ammo.btDiscreteDynamicsWorld} world
	 * @param {Object} params
	 * @param {ResourceManager} manager
	 */
	function RigidBody( mesh, world, params, manager ) {

		this.mesh  = mesh;
		this.world = world;
		this.params = params;
		this.manager = manager;

		this.body = null;
		this.bone = null;
		this.boneOffsetForm = null;
		this.boneOffsetFormInverse = null;

		this._init();

	}

	RigidBody.prototype = {

		constructor: MMDPhysics.RigidBody,

		/**
		 * Resets rigid body transform to the current bone's.
		 *
		 * @return {RigidBody}
		 */
		reset: function () {

			this._setTransformFromBone();
			return this;

		},

		/**
		 * Updates rigid body's transform from the current bone.
		 *
		 * @return {RidigBody}
		 */
		updateFromBone: function () {

			if ( this.params.boneIndex !== - 1 &&
				this.params.type === 0 ) {

				this._setTransformFromBone();

			}

			return this;

		},

		/**
		 * Updates bone from the current ridid body's transform.
		 *
		 * @return {RidigBody}
		 */
		updateBone: function () {

			if ( this.params.type === 0 ||
				this.params.boneIndex === - 1 ) {

				return this;

			}

			this._updateBoneRotation();

			if ( this.params.type === 1 ) {

				this._updateBonePosition();

			}

			this.bone.updateMatrixWorld( true );

			if ( this.params.type === 2 ) {

				this._setPositionFromBone();

			}

			return this;

		},

		// private methods

		_init: function () {

			function generateShape( p ) {

				switch( p.shapeType ) {

					case 0:
						return new Ammo.btSphereShape( p.width );

					case 1:
						return new Ammo.btBoxShape( new Ammo.btVector3( p.width, p.height, p.depth ) );

					case 2:
						return new Ammo.btCapsuleShape( p.width, p.height );

					default:
						throw 'unknown shape type ' + p.shapeType;

				}

			}

			var manager = this.manager;
			var params = this.params;
			var bones = this.mesh.skeleton.bones;
			var bone = ( params.boneIndex === - 1 )
				? new THREE.Bone()
				: bones[ params.boneIndex ];

			var shape = generateShape( params );
			var weight = ( params.type === 0 ) ? 0 : params.weight;
			var localInertia = manager.allocVector3();
			localInertia.setValue( 0, 0, 0 );

			if( weight !== 0 ) {

				shape.calculateLocalInertia( weight, localInertia );

			}

			var boneOffsetForm = manager.allocTransform();
			manager.setIdentity( boneOffsetForm );
			manager.setOriginFromArray3( boneOffsetForm, params.position );
			manager.setBasisFromArray3( boneOffsetForm, params.rotation );

			var vector = manager.allocThreeVector3();
			var boneForm = manager.allocTransform();
			manager.setIdentity( boneForm );
			manager.setOriginFromThreeVector3( boneForm, bone.getWorldPosition( vector ) );

			var form = manager.multiplyTransforms( boneForm, boneOffsetForm );
			var state = new Ammo.btDefaultMotionState( form );

			var info = new Ammo.btRigidBodyConstructionInfo( weight, state, shape, localInertia );
			info.set_m_friction( params.friction );
			info.set_m_restitution( params.restitution );

			var body = new Ammo.btRigidBody( info );

			if ( params.type === 0 ) {

				body.setCollisionFlags( body.getCollisionFlags() | 2 );

				/*
				 * It'd be better to comment out this line though in general I should call this method
				 * because I'm not sure why but physics will be more like MMD's
				 * if I comment out.
				 */
				body.setActivationState( 4 );

			}

			body.setDamping( params.positionDamping, params.rotationDamping );
			body.setSleepingThresholds( 0, 0 );

			this.world.addRigidBody( body, 1 << params.groupIndex, params.groupTarget );

			this.body = body;
			this.bone = bone;
			this.boneOffsetForm = boneOffsetForm;
			this.boneOffsetFormInverse = manager.inverseTransform( boneOffsetForm );

			manager.freeVector3( localInertia );
			manager.freeTransform( form );
			manager.freeTransform( boneForm );
			manager.freeThreeVector3( vector );

		},

		_getBoneTransform: function () {

			var manager = this.manager;
			var p = manager.allocThreeVector3();
			var q = manager.allocThreeQuaternion();
			var s = manager.allocThreeVector3();

			this.bone.matrixWorld.decompose( p, q, s );

			var tr = manager.allocTransform();
			manager.setOriginFromThreeVector3( tr, p );
			manager.setBasisFromThreeQuaternion( tr, q );

			var form = manager.multiplyTransforms( tr, this.boneOffsetForm );

			manager.freeTransform( tr );
			manager.freeThreeVector3( s );
			manager.freeThreeQuaternion( q );
			manager.freeThreeVector3( p );

			return form;

		},

		_getWorldTransformForBone: function () {

			var manager = this.manager;
			var tr = this.body.getCenterOfMassTransform();
			return manager.multiplyTransforms( tr, this.boneOffsetFormInverse );

		},

		_setTransformFromBone: function () {

			var manager = this.manager;
			var form = this._getBoneTransform();

			// TODO: check the most appropriate way to set
			//this.body.setWorldTransform( form );
			this.body.setCenterOfMassTransform( form );
			this.body.getMotionState().setWorldTransform( form );

			manager.freeTransform( form );

		},

		_setPositionFromBone: function () {

			var manager = this.manager;
			var form = this._getBoneTransform();

			var tr = manager.allocTransform();
			this.body.getMotionState().getWorldTransform( tr );
			manager.copyOrigin( tr, form );

			// TODO: check the most appropriate way to set
			//this.body.setWorldTransform( tr );
			this.body.setCenterOfMassTransform( tr );
			this.body.getMotionState().setWorldTransform( tr );

			manager.freeTransform( tr );
			manager.freeTransform( form );

		},

		_updateBoneRotation: function () {

			var manager = this.manager;

			var tr = this._getWorldTransformForBone();
			var q = manager.getBasis( tr );

			var thQ = manager.allocThreeQuaternion();
			var thQ2 = manager.allocThreeQuaternion();
			var thQ3 = manager.allocThreeQuaternion();

			thQ.set( q.x(), q.y(), q.z(), q.w() );
			thQ2.setFromRotationMatrix( this.bone.matrixWorld );
			thQ2.conjugate();
			thQ2.multiply( thQ );

			//this.bone.quaternion.multiply( thQ2 );

			thQ3.setFromRotationMatrix( this.bone.matrix );
			this.bone.quaternion.copy( thQ2.multiply( thQ3 ) );

			manager.freeThreeQuaternion( thQ );
			manager.freeThreeQuaternion( thQ2 );
			manager.freeThreeQuaternion( thQ3 );

			manager.freeQuaternion( q );
			manager.freeTransform( tr );

		},

		_updateBonePosition: function () {

			var manager = this.manager;

			var tr = this._getWorldTransformForBone();

			var thV = manager.allocThreeVector3();

			var o = manager.getOrigin( tr );
			thV.set( o.x(), o.y(), o.z() );

			if ( this.bone.parent ) {

				this.bone.parent.worldToLocal( thV );

			}

			this.bone.position.copy( thV );

			manager.freeThreeVector3( thV );

			manager.freeTransform( tr );

		}

	};

	/**
	 * @param {THREE.SkinnedMesh} mesh
	 * @param {Ammo.btDiscreteDynamicsWorld} world
	 * @param {RigidBody} bodyA
	 * @param {RigidBody} bodyB
	 * @param {Object} params
	 * @param {ResourceManager} manager
	 */
	function Constraint( mesh, world, bodyA, bodyB, params, manager ) {

		this.mesh  = mesh;
		this.world = world;
		this.bodyA = bodyA;
		this.bodyB = bodyB;
		this.params = params;
		this.manager = manager;

		this.constraint = null;

		this._init();

	}

	Constraint.prototype = {

		constructor: Constraint,

		// private method

		_init: function () {

			var manager = this.manager;
			var params = this.params;
			var bodyA = this.bodyA;
			var bodyB = this.bodyB;

			var form = manager.allocTransform();
			manager.setIdentity( form );
			manager.setOriginFromArray3( form, params.position );
			manager.setBasisFromArray3( form, params.rotation );

			var formA = manager.allocTransform();
			var formB = manager.allocTransform();

			bodyA.body.getMotionState().getWorldTransform( formA );
			bodyB.body.getMotionState().getWorldTransform( formB );

			var formInverseA = manager.inverseTransform( formA );
			var formInverseB = manager.inverseTransform( formB );

			var formA2 = manager.multiplyTransforms( formInverseA, form );
			var formB2 = manager.multiplyTransforms( formInverseB, form );

			var constraint = new Ammo.btGeneric6DofSpringConstraint( bodyA.body, bodyB.body, formA2, formB2, true );

			var lll = manager.allocVector3();
			var lul = manager.allocVector3();
			var all = manager.allocVector3();
			var aul = manager.allocVector3();

			lll.setValue( params.translationLimitation1[ 0 ],
			              params.translationLimitation1[ 1 ],
			              params.translationLimitation1[ 2 ] );
			lul.setValue( params.translationLimitation2[ 0 ],
			              params.translationLimitation2[ 1 ],
			              params.translationLimitation2[ 2 ] );
			all.setValue( params.rotationLimitation1[ 0 ],
			              params.rotationLimitation1[ 1 ],
			              params.rotationLimitation1[ 2 ] );
			aul.setValue( params.rotationLimitation2[ 0 ],
			              params.rotationLimitation2[ 1 ],
			              params.rotationLimitation2[ 2 ] );

			constraint.setLinearLowerLimit( lll );
			constraint.setLinearUpperLimit( lul );
			constraint.setAngularLowerLimit( all );
			constraint.setAngularUpperLimit( aul );

			for ( var i = 0; i < 3; i++ ) {

				if( params.springPosition[ i ] !== 0 ) {

					constraint.enableSpring( i, true );
					constraint.setStiffness( i, params.springPosition[ i ] );

				}

			}

			for ( var i = 0; i < 3; i++ ) {

				if( params.springRotation[ i ] !== 0 ) {

					constraint.enableSpring( i + 3, true );
					constraint.setStiffness( i + 3, params.springRotation[ i ] );

				}

			}

			/*
			 * Currently(10/31/2016) official ammo.js doesn't support
			 * btGeneric6DofSpringConstraint.setParam method.
			 * You need custom ammo.js (add the method into idl) if you wanna use.
			 * By setting this parameter, physics will be more like MMD's
			 */
			if ( constraint.setParam !== undefined ) {

				for ( var i = 0; i < 6; i ++ ) {

					// this parameter is from http://www20.atpages.jp/katwat/three.js_r58/examples/mytest37/mmd.three.js
					constraint.setParam( 2, 0.475, i );

				}

			}

			this.world.addConstraint( constraint, true );
			this.constraint = constraint;

			manager.freeTransform( form );
			manager.freeTransform( formA );
			manager.freeTransform( formB );
			manager.freeTransform( formInverseA );
			manager.freeTransform( formInverseB );
			manager.freeTransform( formA2 );
			manager.freeTransform( formB2 );
			manager.freeVector3( lll );
			manager.freeVector3( lul );
			manager.freeVector3( all );
			manager.freeVector3( aul );

		}

	};

	/**
	 * Visualize Rigid bodies
	 *
	 * @param {THREE.SkinnedMesh} mesh
	 * @param {THREE.Physics} physics
	 */
	function MMDPhysicsHelper( mesh, physics ) {

		THREE.Object3D.call( this );

		this.root = mesh;
		this.physics = physics;

		this.matrix.copy( mesh.matrixWorld );
		this.matrixAutoUpdate = false;

		this.materials = [];

		this.materials.push(
			new THREE.MeshBasicMaterial( {
				color: new THREE.Color( 0xff8888 ),
				wireframe: true,
				depthTest: false,
				depthWrite: false,
				opacity: 0.25,
				transparent: true
			} )
		);

		this.materials.push(
			new THREE.MeshBasicMaterial( {
				color: new THREE.Color( 0x88ff88 ),
				wireframe: true,
				depthTest: false,
				depthWrite: false,
				opacity: 0.25,
				transparent: true
			} )
		);

		this.materials.push(
			new THREE.MeshBasicMaterial( {
				color: new THREE.Color( 0x8888ff ),
				wireframe: true,
				depthTest: false,
				depthWrite: false,
				opacity: 0.25,
				transparent: true
			} )
		);

		this._init();

	}

	MMDPhysicsHelper.prototype = Object.assign( Object.create( THREE.Object3D.prototype ), {

		constructor: MMDPhysicsHelper,

		/**
		 * Updates Rigid Bodies visualization.
		 */
		updateMatrixWorld: function () {

			var position = new THREE.Vector3();
			var quaternion = new THREE.Quaternion();
			var scale = new THREE.Vector3();
			var matrixWorldInv = new THREE.Matrix4();

			return function updateMatrixWorld( force ) {

				var mesh = this.root;

				if ( this.visible ) {

					var bodies = this.physics.bodies;

					matrixWorldInv
						.copy( mesh.matrixWorld )
						.decompose( position, quaternion, scale )
						.compose( position, quaternion, scale.set( 1, 1, 1 ) )
						.getInverse( matrixWorldInv );

					for ( var i = 0, il = bodies.length; i < il; i ++ ) {

						var body = bodies[ i ].body;
						var child = this.children[ i ];

						var tr = body.getCenterOfMassTransform();
						var origin = tr.getOrigin();
						var rotation = tr.getRotation();

						child.position
							.set( origin.x(), origin.y(), origin.z() )
							.applyMatrix4( matrixWorldInv );

						child.quaternion
							.setFromRotationMatrix( matrixWorldInv )
							.multiply(
								quaternion.set(
									rotation.x(), rotation.y(), rotation.z(), rotation.w() )
							);

					}

				}

				this.matrix
					.copy( mesh.matrixWorld )
					.decompose( position, quaternion, scale )
					.compose( position, quaternion, scale.set( 1, 1, 1 ) );

				THREE.Object3D.prototype.updateMatrixWorld.call( this, force );

			};

		}(),

		// private method

		_init: function () {

			var bodies = this.physics.bodies;

			function createGeometry( param ) {

				switch ( param.shapeType ) {

					case 0:
						return new THREE.SphereBufferGeometry( param.width, 16, 8 );

					case 1:
						return new THREE.BoxBufferGeometry( param.width * 2, param.height * 2, param.depth * 2, 8, 8, 8 );

					case 2:
						return new createCapsuleGeometry( param.width, param.height, 16, 8 );

					default:
						return null;

				}

			}

			// copy from http://www20.atpages.jp/katwat/three.js_r58/examples/mytest37/mytest37.js?ver=20160815
			function createCapsuleGeometry( radius, cylinderHeight, segmentsRadius, segmentsHeight ) {

				var geometry = new THREE.CylinderBufferGeometry( radius, radius, cylinderHeight, segmentsRadius, segmentsHeight, true );
				var upperSphere = new THREE.Mesh( new THREE.SphereBufferGeometry( radius, segmentsRadius, segmentsHeight, 0, Math.PI * 2, 0, Math.PI / 2 ) );
				var lowerSphere = new THREE.Mesh( new THREE.SphereBufferGeometry( radius, segmentsRadius, segmentsHeight, 0, Math.PI * 2, Math.PI / 2, Math.PI / 2 ) );

				upperSphere.position.set( 0, cylinderHeight / 2, 0 );
				lowerSphere.position.set( 0, - cylinderHeight / 2, 0 );

				upperSphere.updateMatrix();
				lowerSphere.updateMatrix();

				geometry.merge( upperSphere.geometry, upperSphere.matrix );
				geometry.merge( lowerSphere.geometry, lowerSphere.matrix );

				return geometry;

			}

			for ( var i = 0, il = bodies.length; i < il; i ++ ) {

				var param = bodies[ i ].params;
				this.add( new THREE.Mesh( createGeometry( param ), this.materials[ param.type ] ) );

			}

		}

	} );

	return MMDPhysics;

} )();