How to calculate quaternion from world position of 3 points on a plane

[hofk]

If you have three points, you can easily determine three basis vectors using the cross product.
From the base you calculate the quaternion.

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

These posts and examples are about movement on a curve. Struggling with paths - #14 by hofk Car Racing - For lovers of fast cars! MotionAlongCurve MovementOnCurve CarRacing However, the solution via matrices requires computational effort. I have been looking for a solution with quaternions that requires fewer formula steps. The solution is a new method in the quaternion class. I added it to three.module.129.Quaternion.js in the example BasisToQuaternion. This makes the calculat…

See also from the Collection of examples from discourse.threejs.org
https://hofk.de/main/discourse.threejs/2021/CarRacing/FlightRouteQuaternion.html

Maybe you can get further with this?