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@@ -219,6 +219,158 @@ THREE.extend( THREE.Vector4.prototype, {
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},
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+ setAxisAngleFromQuaternion: function ( q ) {
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+
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+ // http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToAngle/index.htm
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+
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+ // q is assumed to be normalized
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+
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+ this.w = 2 * Math.acos( q.w );
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+
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+ var s = Math.sqrt( 1 - q.w * q.w );
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+
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+ if ( s < 0.0001 ) {
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+
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+ this.x = 1;
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+ this.y = 0;
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+ this.z = 0;
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+
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+ } else {
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+
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+ this.x = q.x / s;
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+ this.y = q.y / s;
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+ this.z = q.z / s;
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+
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+ }
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+
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+ return this;
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+
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+ },
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+
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+ setAxisAngleFromRotationMatrix: function ( m ) {
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+
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+ // http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToAngle/index.htm
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+
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+ // assumes the upper 3x3 of m is a pure rotation matrix (i.e, unscaled)
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+
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+ var angle, x, y, z, // variables for result
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+ epsilon = 0.01, // margin to allow for rounding errors
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+ epsilon2 = 0.1, // margin to distinguish between 0 and 180 degrees
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+
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+ te = m.elements,
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+
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+ m11 = te[0], m12 = te[4], m13 = te[8],
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+ m21 = te[1], m22 = te[5], m23 = te[9],
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+ m31 = te[2], m32 = te[6], m33 = te[10];
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+
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+ if ( ( Math.abs( m12 - m21 ) < epsilon )
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+ && ( Math.abs( m13 - m31 ) < epsilon )
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+ && ( Math.abs( m23 - m32 ) < epsilon ) ) {
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+
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+ // singularity found
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+ // first check for identity matrix which must have +1 for all terms
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+ // in leading diagonal and zero in other terms
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+
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+ if ( ( Math.abs( m12 + m21 ) < epsilon2 )
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+ && ( Math.abs( m13 + m31 ) < epsilon2 )
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+ && ( Math.abs( m23 + m32 ) < epsilon2 )
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+ && ( Math.abs( m11 + m22 + m33 - 3 ) < epsilon2 ) ) {
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+
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+ // this singularity is identity matrix so angle = 0
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+
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+ this.set( 1, 0, 0, 0 );
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+
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+ return this; // zero angle, arbitrary axis
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+
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+ }
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+
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+ // otherwise this singularity is angle = 180
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+
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+ angle = Math.PI;
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+
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+ var xx = ( m11 + 1 ) / 2;
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+ var yy = ( m22 + 1 ) / 2;
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+ var zz = ( m33 + 1 ) / 2;
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+ var xy = ( m12 + m21 ) / 4;
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+ var xz = ( m13 + m31 ) / 4;
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+ var yz = ( m23 + m32 ) / 4;
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+
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+ if ( ( xx > yy ) && ( xx > zz ) ) { // m11 is the largest diagonal term
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+
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+ if ( xx < epsilon ) {
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+
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+ x = 0;
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+ y = 0.707106781;
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+ z = 0.707106781;
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+
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+ } else {
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+
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+ x = Math.sqrt( xx );
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+ y = xy / x;
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+ z = xz / x;
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+
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+ }
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+
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+ } else if ( yy > zz ) { // m22 is the largest diagonal term
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+
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+ if ( yy < epsilon ) {
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+
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+ x = 0.707106781;
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+ y = 0;
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+ z = 0.707106781;
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+
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+ } else {
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+
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+ y = Math.sqrt( yy );
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+ x = xy / y;
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+ z = yz / y;
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+
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+ }
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+
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+ } else { // m33 is the largest diagonal term so base result on this
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+
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+ if ( zz < epsilon ) {
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+
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+ x = 0.707106781;
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+ y = 0.707106781;
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+ z = 0;
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+
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+ } else {
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+
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+ z = Math.sqrt( zz );
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+ x = xz / z;
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+ y = yz / z;
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+
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+ }
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+
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+ }
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+
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+ this.set( x, y, z, angle );
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+
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+ return this; // return 180 deg rotation
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+
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+ }
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+
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+ // as we have reached here there are no singularities so we can handle normally
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+
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+ var s = Math.sqrt( ( m32 - m23 ) * ( m32 - m23 )
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+ + ( m13 - m31 ) * ( m13 - m31 )
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+ + ( m21 - m12 ) * ( m21 - m12 ) ); // used to normalize
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+
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+ if ( Math.abs( s ) < 0.001 ) s = 1;
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+
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+ // prevent divide by zero, should not happen if matrix is orthogonal and should be
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+ // caught by singularity test above, but I've left it in just in case
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+
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+ this.x = ( m32 - m23 ) / s;
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+ this.y = ( m13 - m31 ) / s;
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+ this.z = ( m21 - m12 ) / s;
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+ this.w = Math.acos( ( m11 + m22 + m33 - 1 ) / 2 );
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+
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+ return this;
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+
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+ },
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+
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min: function ( v ) {
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if ( this.x > v.x ) {
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@@ -403,158 +555,6 @@ THREE.extend( THREE.Vector4.prototype, {
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return new THREE.Vector4( this.x, this.y, this.z, this.w );
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- },
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-
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- setAxisAngleFromQuaternion: function ( q ) {
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-
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- // http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToAngle/index.htm
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-
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- // q is assumed to be normalized
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-
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- this.w = 2 * Math.acos( q.w );
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-
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- var s = Math.sqrt( 1 - q.w * q.w );
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-
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- if ( s < 0.0001 ) {
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-
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- this.x = 1;
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- this.y = 0;
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- this.z = 0;
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-
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- } else {
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-
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- this.x = q.x / s;
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- this.y = q.y / s;
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- this.z = q.z / s;
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-
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- }
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-
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- return this;
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-
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- },
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-
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- setAxisAngleFromRotationMatrix: function ( m ) {
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-
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- // http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToAngle/index.htm
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-
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- // assumes the upper 3x3 of m is a pure rotation matrix (i.e, unscaled)
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|
|
-
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|
|
- var angle, x, y, z, // variables for result
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|
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- epsilon = 0.01, // margin to allow for rounding errors
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- epsilon2 = 0.1, // margin to distinguish between 0 and 180 degrees
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-
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- te = m.elements,
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-
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- m11 = te[0], m12 = te[4], m13 = te[8],
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- m21 = te[1], m22 = te[5], m23 = te[9],
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- m31 = te[2], m32 = te[6], m33 = te[10];
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-
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- if ( ( Math.abs( m12 - m21 ) < epsilon )
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- && ( Math.abs( m13 - m31 ) < epsilon )
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- && ( Math.abs( m23 - m32 ) < epsilon ) ) {
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-
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- // singularity found
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- // first check for identity matrix which must have +1 for all terms
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- // in leading diagonal and zero in other terms
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-
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- if ( ( Math.abs( m12 + m21 ) < epsilon2 )
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- && ( Math.abs( m13 + m31 ) < epsilon2 )
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- && ( Math.abs( m23 + m32 ) < epsilon2 )
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- && ( Math.abs( m11 + m22 + m33 - 3 ) < epsilon2 ) ) {
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-
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- // this singularity is identity matrix so angle = 0
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-
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- this.set( 1, 0, 0, 0 );
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-
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- return this; // zero angle, arbitrary axis
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-
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- }
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-
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- // otherwise this singularity is angle = 180
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-
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- angle = Math.PI;
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-
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- var xx = ( m11 + 1 ) / 2;
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- var yy = ( m22 + 1 ) / 2;
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- var zz = ( m33 + 1 ) / 2;
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- var xy = ( m12 + m21 ) / 4;
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- var xz = ( m13 + m31 ) / 4;
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- var yz = ( m23 + m32 ) / 4;
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-
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- if ( ( xx > yy ) && ( xx > zz ) ) { // m11 is the largest diagonal term
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-
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- if ( xx < epsilon ) {
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-
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- x = 0;
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- y = 0.707106781;
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- z = 0.707106781;
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-
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- } else {
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-
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- x = Math.sqrt( xx );
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- y = xy / x;
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- z = xz / x;
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-
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- }
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-
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- } else if ( yy > zz ) { // m22 is the largest diagonal term
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-
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- if ( yy < epsilon ) {
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-
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- x = 0.707106781;
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- y = 0;
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- z = 0.707106781;
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-
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- } else {
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-
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- y = Math.sqrt( yy );
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- x = xy / y;
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- z = yz / y;
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-
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- }
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-
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- } else { // m33 is the largest diagonal term so base result on this
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-
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- if ( zz < epsilon ) {
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-
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- x = 0.707106781;
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- y = 0.707106781;
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- z = 0;
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-
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- } else {
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-
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- z = Math.sqrt( zz );
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- x = xz / z;
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- y = yz / z;
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-
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- }
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-
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- }
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-
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- this.set( x, y, z, angle );
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-
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- return this; // return 180 deg rotation
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-
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- }
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-
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- // as we have reached here there are no singularities so we can handle normally
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-
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- var s = Math.sqrt( ( m32 - m23 ) * ( m32 - m23 )
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- + ( m13 - m31 ) * ( m13 - m31 )
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- + ( m21 - m12 ) * ( m21 - m12 ) ); // used to normalize
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-
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- if ( Math.abs( s ) < 0.001 ) s = 1;
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-
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- // prevent divide by zero, should not happen if matrix is orthogonal and should be
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- // caught by singularity test above, but I've left it in just in case
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-
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- this.x = ( m32 - m23 ) / s;
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- this.y = ( m13 - m31 ) / s;
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- this.z = ( m21 - m12 ) / s;
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- this.w = Math.acos( ( m11 + m22 + m33 - 1 ) / 2 );
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-
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- return this;
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-
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}
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} );
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