three.js/src/math/Euler.js

/**
 * @author mrdoob / http://mrdoob.com/
 * @author WestLangley / http://github.com/WestLangley
 * @author bhouston / http://exocortex.com
 */

THREE.Euler = function ( x, y, z, order ) {

	this.x = x || 0;
	this.y = y || 0;
	this.z = z || 0;
	this.order = order || THREE.Euler.DefaultOrder;

};

THREE.Euler.RotationOrders = [ 'XYZ', 'YZX', 'ZXY', 'XZY', 'YXZ', 'ZYX' ];

THREE.Euler.DefaultOrder = 'XYZ';

THREE.Euler.prototype = {

	constructor: THREE.Euler,

	set: function ( x, y, z, order ) {

		this.x = x;
		this.y = y;
		this.z = z;
		this.order = order || this.order;

		return this;

	},

	copy: function ( e ) {

		this.x = e.x;
		this.y = e.y;
		this.z = e.z;
		this.order = e.order;

		return this;

	},

	setFromRotationMatrix: function ( m, order ) {

		// assumes the upper 3x3 of m is a pure rotation matrix (i.e, unscaled)

		// clamp, to handle numerical problems

		function clamp( x ) {

			return Math.min( Math.max( x, -1 ), 1 );

		}

		var te = m.elements;
		var m11 = te[0], m12 = te[4], m13 = te[8];
		var m21 = te[1], m22 = te[5], m23 = te[9];
		var m31 = te[2], m32 = te[6], m33 = te[10];

		order = order || this.order;

		if ( order === 'XYZ' ) {

			this.y = Math.asin( clamp( m13 ) );

			if ( Math.abs( m13 ) < 0.99999 ) {

				this.x = Math.atan2( - m23, m33 );
				this.z = Math.atan2( - m12, m11 );

			} else {

				this.x = Math.atan2( m32, m22 );
				this.z = 0;

			}

		} else if ( order === 'YXZ' ) {

			this.x = Math.asin( - clamp( m23 ) );

			if ( Math.abs( m23 ) < 0.99999 ) {

				this.y = Math.atan2( m13, m33 );
				this.z = Math.atan2( m21, m22 );

			} else {

				this.y = Math.atan2( - m31, m11 );
				this.z = 0;

			}

		} else if ( order === 'ZXY' ) {

			this.x = Math.asin( clamp( m32 ) );

			if ( Math.abs( m32 ) < 0.99999 ) {

				this.y = Math.atan2( - m31, m33 );
				this.z = Math.atan2( - m12, m22 );

			} else {

				this.y = 0;
				this.z = Math.atan2( m21, m11 );

			}

		} else if ( order === 'ZYX' ) {

			this.y = Math.asin( - clamp( m31 ) );

			if ( Math.abs( m31 ) < 0.99999 ) {

				this.x = Math.atan2( m32, m33 );
				this.z = Math.atan2( m21, m11 );

			} else {

				this.x = 0;
				this.z = Math.atan2( - m12, m22 );

			}

		} else if ( order === 'YZX' ) {

			this.z = Math.asin( clamp( m21 ) );

			if ( Math.abs( m21 ) < 0.99999 ) {

				this.x = Math.atan2( - m23, m22 );
				this.y = Math.atan2( - m31, m11 );

			} else {

				this.x = 0;
				this.y = Math.atan2( m13, m33 );

			}

		} else if ( order === 'XZY' ) {

			this.z = Math.asin( - clamp( m12 ) );

			if ( Math.abs( m12 ) < 0.99999 ) {

				this.x = Math.atan2( m32, m22 );
				this.y = Math.atan2( m13, m11 );

			} else {

				this.x = Math.atan2( - m23, m33 );
				this.y = 0;

			}

		}
		else {

			console.warn( 'WARNING: Euler.setFromRotationMatrix() given unsupported order: ' + order )
		
		}

		this.order = order;

		return this;

	},

	setFromQuaternion: function ( q, order ) {

		// q is assumed to be normalized

		// clamp, to handle numerical problems

		function clamp( x ) {

			return Math.min( Math.max( x, -1 ), 1 );

		}

		// http://www.mathworks.com/matlabcentral/fileexchange/20696-function-to-convert-between-dcm-euler-angles-quaternions-and-euler-vectors/content/SpinCalc.m

		var sqx = q.x * q.x;
		var sqy = q.y * q.y;
		var sqz = q.z * q.z;
		var sqw = q.w * q.w;

		order = order || this.order;

		if ( order === 'XYZ' ) {

			this.x = Math.atan2( 2 * ( q.x * q.w - q.y * q.z ), ( sqw - sqx - sqy + sqz ) );
			this.y = Math.asin(  clamp( 2 * ( q.x * q.z + q.y * q.w ) ) );
			this.z = Math.atan2( 2 * ( q.z * q.w - q.x * q.y ), ( sqw + sqx - sqy - sqz ) );

		} else if ( order ===  'YXZ' ) {

			this.x = Math.asin(  clamp( 2 * ( q.x * q.w - q.y * q.z ) ) );
			this.y = Math.atan2( 2 * ( q.x * q.z + q.y * q.w ), ( sqw - sqx - sqy + sqz ) );
			this.z = Math.atan2( 2 * ( q.x * q.y + q.z * q.w ), ( sqw - sqx + sqy - sqz ) );

		} else if ( order === 'ZXY' ) {

			this.x = Math.asin(  clamp( 2 * ( q.x * q.w + q.y * q.z ) ) );
			this.y = Math.atan2( 2 * ( q.y * q.w - q.z * q.x ), ( sqw - sqx - sqy + sqz ) );
			this.z = Math.atan2( 2 * ( q.z * q.w - q.x * q.y ), ( sqw - sqx + sqy - sqz ) );

		} else if ( order === 'ZYX' ) {

			this.x = Math.atan2( 2 * ( q.x * q.w + q.z * q.y ), ( sqw - sqx - sqy + sqz ) );
			this.y = Math.asin(  clamp( 2 * ( q.y * q.w - q.x * q.z ) ) );
			this.z = Math.atan2( 2 * ( q.x * q.y + q.z * q.w ), ( sqw + sqx - sqy - sqz ) );

		} else if ( order === 'YZX' ) {

			this.x = Math.atan2( 2 * ( q.x * q.w - q.z * q.y ), ( sqw - sqx + sqy - sqz ) );
			this.y = Math.atan2( 2 * ( q.y * q.w - q.x * q.z ), ( sqw + sqx - sqy - sqz ) );
			this.z = Math.asin(  clamp( 2 * ( q.x * q.y + q.z * q.w ) ) );

		} else if ( order === 'XZY' ) {

			this.x = Math.atan2( 2 * ( q.x * q.w + q.y * q.z ), ( sqw - sqx + sqy - sqz ) );
			this.y = Math.atan2( 2 * ( q.x * q.z + q.y * q.w ), ( sqw + sqx - sqy - sqz ) );
			this.z = Math.asin(  clamp( 2 * ( q.z * q.w - q.x * q.y ) ) );

		}
		else {

			console.warn( 'WARNING: Euler.setFromQuaternion() given unsupported order: ' + order )
		
		}

		this.order = order;

		return this;

	},

	reorder: function() {

		// WARNING: this discards revolution information -bhouston

		var q = new THREE.Quaternion();

		return function( newOrder ) {

			q.setFromEuler( this );
			this.setFromQuaternion( q, newOrder );

		};


	}(),

	fromArray: function ( array ) {

		this.x = array[ 0 ];
		this.y = array[ 1 ];
		this.z = array[ 2 ];
		this.order = array[ 3 ];

		return this;

	},

	toArray: function () {

		return [ this.x, this.y, this.z, this.order ];

	},

	equals: function ( rotation ) {

		return ( ( rotation.x === this.x ) && ( rotation.y === this.y ) && ( rotation.z === this.z ) && ( rotation.order === this.order ) );

	},

	clone: function () {

		return new THREE.Euler( this.x, this.y, this.z, this.order );

	}

};