四元数在3D计算机图形学中用于表示旋转，因为它们比欧拉角和旋转矩阵更稳定且不容易产生万向节锁问题
# 1、setFromRotationMatrix
改方法的作用是将一个旋转矩阵转换为四元数。
/**
* 从旋转矩阵设置四元数
*
* @param m 旋转矩阵
* @returns 当前四元数对象
*/
setFromRotationMatrix( 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)
const 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;
//
if ( trace > 0 ) {
const 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 ) {
const 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 ) {
const 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 {
const 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;
}
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# 2、setFromEuler
从欧拉角设置四元数
/**
* 从欧拉角设置四元数
*
* @param euler 欧拉角对象，包含x、y、z和order属性
* @param update 是否触发onChangeCallback回调，默认为true
* @returns 返回当前四元数对象
*/
setFromEuler( euler, update = true ) {
const x = euler._x, y = euler._y, z = euler._z, order = euler._order;
// http://www.mathworks.com/matlabcentral/fileexchange/
// 20696-function-to-convert-between-dcm-euler-angles-quaternions-and-euler-vectors/
// content/SpinCalc.m
const cos = Math.cos;
const sin = Math.sin;
const c1 = cos( x / 2 );
const c2 = cos( y / 2 );
const c3 = cos( z / 2 );
const s1 = sin( x / 2 );
const s2 = sin( y / 2 );
const s3 = sin( z / 2 );
switch ( order ) {
case '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;
break;
case '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;
break;
case '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;
break;
case '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;
break;
case '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;
break;
case '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;
break;
default:
console.warn( 'THREE.Quaternion: .setFromEuler() encountered an unknown order: ' + order );
}
if ( update === true ) this._onChangeCallback();
return this;
}
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# 3、setFromAxisAngle
从轴和角度设置四元数
/**
* 从轴和角度设置四元数
*
* @param {Vector3} axis 旋转轴，假设已经单位化
* @param {number} angle 旋转角度，单位为弧度
* @returns {Object} 当前对象
*/
setFromAxisAngle( axis, angle ) {
// http://www.euclideanspace.com/maths/geometry/rotations/conversions/angleToQuaternion/index.htm
// assumes axis is normalized
const 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;
}
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