123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419420421422423424425426427428429430431432433434435436437438439440441442443444445446447448449450451452453454455456457458459460461462463464465466467468469470471472473474475476477478479480481482483484485486487488489490491492493494495496497498499500501502503504505506507508509510511512 |
- /**
- * @author mikael emtinger / http://gomo.se/
- * @author alteredq / http://alteredqualia.com/
- * @author WestLangley / http://github.com/WestLangley
- * @author bhouston / http://exocortex.com
- */
- THREE.Quaternion = function ( x, y, z, w ) {
- this._x = x || 0;
- this._y = y || 0;
- this._z = z || 0;
- this._w = ( w !== undefined ) ? w : 1;
- };
- THREE.Quaternion.prototype = {
- constructor: THREE.Quaternion,
- _x: 0,_y: 0, _z: 0, _w: 0,
- get x () {
- return this._x;
- },
- set x ( value ) {
- this._x = value;
- this.onChangeCallback();
- },
- get y () {
- return this._y;
- },
- set y ( value ) {
- this._y = value;
- this.onChangeCallback();
- },
- get z () {
- return this._z;
- },
- set z ( value ) {
- this._z = value;
- this.onChangeCallback();
- },
- get w () {
- return this._w;
- },
- set w ( value ) {
- this._w = value;
- this.onChangeCallback();
- },
- set: function ( x, y, z, w ) {
- this._x = x;
- this._y = y;
- this._z = z;
- this._w = w;
- this.onChangeCallback();
- return this;
- },
- copy: function ( quaternion ) {
- this._x = quaternion.x;
- this._y = quaternion.y;
- this._z = quaternion.z;
- this._w = quaternion.w;
- this.onChangeCallback();
- return this;
- },
- setFromEuler: function ( euler, update ) {
- if ( euler instanceof THREE.Euler === false ) {
- throw new Error( 'THREE.Quaternion: .setFromEuler() now expects a Euler rotation rather than a Vector3 and order.' );
- }
- // http://www.mathworks.com/matlabcentral/fileexchange/
- // 20696-function-to-convert-between-dcm-euler-angles-quaternions-and-euler-vectors/
- // content/SpinCalc.m
- var c1 = Math.cos( euler._x / 2 );
- var c2 = Math.cos( euler._y / 2 );
- var c3 = Math.cos( euler._z / 2 );
- var s1 = Math.sin( euler._x / 2 );
- var s2 = Math.sin( euler._y / 2 );
- var s3 = Math.sin( euler._z / 2 );
- if ( euler.order === 'XYZ' ) {
- this._x = s1 * c2 * c3 + c1 * s2 * s3;
- this._y = c1 * s2 * c3 - s1 * c2 * s3;
- this._z = c1 * c2 * s3 + s1 * s2 * c3;
- this._w = c1 * c2 * c3 - s1 * s2 * s3;
- } else if ( euler.order === 'YXZ' ) {
- this._x = s1 * c2 * c3 + c1 * s2 * s3;
- this._y = c1 * s2 * c3 - s1 * c2 * s3;
- this._z = c1 * c2 * s3 - s1 * s2 * c3;
- this._w = c1 * c2 * c3 + s1 * s2 * s3;
- } else if ( euler.order === 'ZXY' ) {
- this._x = s1 * c2 * c3 - c1 * s2 * s3;
- this._y = c1 * s2 * c3 + s1 * c2 * s3;
- this._z = c1 * c2 * s3 + s1 * s2 * c3;
- this._w = c1 * c2 * c3 - s1 * s2 * s3;
- } else if ( euler.order === 'ZYX' ) {
- this._x = s1 * c2 * c3 - c1 * s2 * s3;
- this._y = c1 * s2 * c3 + s1 * c2 * s3;
- this._z = c1 * c2 * s3 - s1 * s2 * c3;
- this._w = c1 * c2 * c3 + s1 * s2 * s3;
- } else if ( euler.order === 'YZX' ) {
- this._x = s1 * c2 * c3 + c1 * s2 * s3;
- this._y = c1 * s2 * c3 + s1 * c2 * s3;
- this._z = c1 * c2 * s3 - s1 * s2 * c3;
- this._w = c1 * c2 * c3 - s1 * s2 * s3;
- } else if ( euler.order === 'XZY' ) {
- this._x = s1 * c2 * c3 - c1 * s2 * s3;
- this._y = c1 * s2 * c3 - s1 * c2 * s3;
- this._z = c1 * c2 * s3 + s1 * s2 * c3;
- this._w = c1 * c2 * c3 + s1 * s2 * s3;
- }
- if ( update !== false ) this.onChangeCallback();
- return this;
- },
- setFromAxisAngle: function ( axis, angle ) {
- // http://www.euclideanspace.com/maths/geometry/rotations/conversions/angleToQuaternion/index.htm
- // assumes axis is normalized
- var halfAngle = angle / 2, s = Math.sin( halfAngle );
- this._x = axis.x * s;
- this._y = axis.y * s;
- this._z = axis.z * s;
- this._w = Math.cos( halfAngle );
- this.onChangeCallback();
- return this;
- },
- setFromRotationMatrix: function ( m ) {
- // http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm
- // assumes the upper 3x3 of m is a pure rotation matrix (i.e, unscaled)
- var te = m.elements,
- m11 = te[ 0 ], m12 = te[ 4 ], m13 = te[ 8 ],
- m21 = te[ 1 ], m22 = te[ 5 ], m23 = te[ 9 ],
- m31 = te[ 2 ], m32 = te[ 6 ], m33 = te[ 10 ],
- trace = m11 + m22 + m33,
- s;
- if ( trace > 0 ) {
- s = 0.5 / Math.sqrt( trace + 1.0 );
- this._w = 0.25 / s;
- this._x = ( m32 - m23 ) * s;
- this._y = ( m13 - m31 ) * s;
- this._z = ( m21 - m12 ) * s;
- } else if ( m11 > m22 && m11 > m33 ) {
- s = 2.0 * Math.sqrt( 1.0 + m11 - m22 - m33 );
- this._w = ( m32 - m23 ) / s;
- this._x = 0.25 * s;
- this._y = ( m12 + m21 ) / s;
- this._z = ( m13 + m31 ) / s;
- } else if ( m22 > m33 ) {
- s = 2.0 * Math.sqrt( 1.0 + m22 - m11 - m33 );
- this._w = ( m13 - m31 ) / s;
- this._x = ( m12 + m21 ) / s;
- this._y = 0.25 * s;
- this._z = ( m23 + m32 ) / s;
- } else {
- s = 2.0 * Math.sqrt( 1.0 + m33 - m11 - m22 );
- this._w = ( m21 - m12 ) / s;
- this._x = ( m13 + m31 ) / s;
- this._y = ( m23 + m32 ) / s;
- this._z = 0.25 * s;
- }
- this.onChangeCallback();
- return this;
- },
- setFromUnitVectors: function () {
- // http://lolengine.net/blog/2014/02/24/quaternion-from-two-vectors-final
- // assumes direction vectors vFrom and vTo are normalized
- var v1, r;
- var EPS = 0.000001;
- return function ( vFrom, vTo ) {
- if ( v1 === undefined ) v1 = new THREE.Vector3();
- r = vFrom.dot( vTo ) + 1;
- if ( r < EPS ) {
- r = 0;
- if ( Math.abs( vFrom.x ) > Math.abs( vFrom.z ) ) {
- v1.set( - vFrom.y, vFrom.x, 0 );
- } else {
- v1.set( 0, - vFrom.z, vFrom.y );
- }
- } else {
- v1.crossVectors( vFrom, vTo );
- }
- this._x = v1.x;
- this._y = v1.y;
- this._z = v1.z;
- this._w = r;
- this.normalize();
- return this;
- }
- }(),
- inverse: function () {
- this.conjugate().normalize();
- return this;
- },
- conjugate: function () {
- this._x *= - 1;
- this._y *= - 1;
- this._z *= - 1;
- this.onChangeCallback();
- return this;
- },
- dot: function ( v ) {
- return this._x * v._x + this._y * v._y + this._z * v._z + this._w * v._w;
- },
- lengthSq: function () {
- return this._x * this._x + this._y * this._y + this._z * this._z + this._w * this._w;
- },
- length: function () {
- return Math.sqrt( this._x * this._x + this._y * this._y + this._z * this._z + this._w * this._w );
- },
- normalize: function () {
- var l = this.length();
- if ( l === 0 ) {
- this._x = 0;
- this._y = 0;
- this._z = 0;
- this._w = 1;
- } else {
- l = 1 / l;
- this._x = this._x * l;
- this._y = this._y * l;
- this._z = this._z * l;
- this._w = this._w * l;
- }
- this.onChangeCallback();
- return this;
- },
- multiply: function ( q, p ) {
- if ( p !== undefined ) {
- console.warn( 'THREE.Quaternion: .multiply() now only accepts one argument. Use .multiplyQuaternions( a, b ) instead.' );
- return this.multiplyQuaternions( q, p );
- }
- return this.multiplyQuaternions( this, q );
- },
- multiplyQuaternions: function ( a, b ) {
- // from http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/code/index.htm
- var qax = a._x, qay = a._y, qaz = a._z, qaw = a._w;
- var qbx = b._x, qby = b._y, qbz = b._z, qbw = b._w;
- this._x = qax * qbw + qaw * qbx + qay * qbz - qaz * qby;
- this._y = qay * qbw + qaw * qby + qaz * qbx - qax * qbz;
- this._z = qaz * qbw + qaw * qbz + qax * qby - qay * qbx;
- this._w = qaw * qbw - qax * qbx - qay * qby - qaz * qbz;
- this.onChangeCallback();
- return this;
- },
- multiplyVector3: function ( vector ) {
- console.warn( 'THREE.Quaternion: .multiplyVector3() has been removed. Use is now vector.applyQuaternion( quaternion ) instead.' );
- return vector.applyQuaternion( this );
- },
- slerp: function ( qb, t ) {
- if ( t === 0 ) return this;
- if ( t === 1 ) return this.copy( qb );
- var x = this._x, y = this._y, z = this._z, w = this._w;
- // http://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/slerp/
- var cosHalfTheta = w * qb._w + x * qb._x + y * qb._y + z * qb._z;
- if ( cosHalfTheta < 0 ) {
- this._w = - qb._w;
- this._x = - qb._x;
- this._y = - qb._y;
- this._z = - qb._z;
- cosHalfTheta = - cosHalfTheta;
- } else {
- this.copy( qb );
- }
- if ( cosHalfTheta >= 1.0 ) {
- this._w = w;
- this._x = x;
- this._y = y;
- this._z = z;
- return this;
- }
- var halfTheta = Math.acos( cosHalfTheta );
- var sinHalfTheta = Math.sqrt( 1.0 - cosHalfTheta * cosHalfTheta );
- if ( Math.abs( sinHalfTheta ) < 0.001 ) {
- this._w = 0.5 * ( w + this._w );
- this._x = 0.5 * ( x + this._x );
- this._y = 0.5 * ( y + this._y );
- this._z = 0.5 * ( z + this._z );
- return this;
- }
- var ratioA = Math.sin( ( 1 - t ) * halfTheta ) / sinHalfTheta,
- ratioB = Math.sin( t * halfTheta ) / sinHalfTheta;
- this._w = ( w * ratioA + this._w * ratioB );
- this._x = ( x * ratioA + this._x * ratioB );
- this._y = ( y * ratioA + this._y * ratioB );
- this._z = ( z * ratioA + this._z * ratioB );
- this.onChangeCallback();
- return this;
- },
- equals: function ( quaternion ) {
- return ( quaternion._x === this._x ) && ( quaternion._y === this._y ) && ( quaternion._z === this._z ) && ( quaternion._w === this._w );
- },
- fromArray: function ( array ) {
- this._x = array[ 0 ];
- this._y = array[ 1 ];
- this._z = array[ 2 ];
- this._w = array[ 3 ];
- this.onChangeCallback();
- return this;
- },
- toArray: function () {
- return [ this._x, this._y, this._z, this._w ];
- },
- onChange: function ( callback ) {
- this.onChangeCallback = callback;
- return this;
- },
- onChangeCallback: function () {},
- clone: function () {
- return new THREE.Quaternion( this._x, this._y, this._z, this._w );
- }
- };
- THREE.Quaternion.slerp = function ( qa, qb, qm, t ) {
- return qm.copy( qa ).slerp( qb, t );
- }
|