Using three.js Routines to Compute Aircraft Rotation

Questions
2

I have never looked closely at motor vehicle or aircraft rotation. But when I created the visualization Quaternion - Axis, Angle Visualization a few years ago, I read a little about it.

This year I wanted to move a model on an arbitrary 3D curve and took another look at quaternions.

The result was a function to derive the quaternion directly from a base e1, e2, e3 in the simplest form.

Possibly one can use this?

Quaternion - method .setFromBasis( e1, e2, e3 )

Example BasisToQuaternion uses three.module.129.Quaternion.js
Car Racing - For lovers of fast cars!

THREE.Quaternion.prototype.setFromBasis = function( e1, e2, e3 ) {
	
	const	m11 = e1.x, m12 = e1.y, m13 = e1.z,
			m21 = e2.x, m22 = e2.y, m23 = e2.z,
			m31 = e3.x, m32 = e3.y, m33 = e3.z,
			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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