Align the plane in the direction of the normal, is it possible, or do I need to use rotation matrices?

Question

3D

Is it possible to solve in a simpler way. *

In general, the question is, you need to set the display angle of the plane based on the normal of the point of incidence of the tracing ray on the object or geometric irregularity.

Video with the wrong location of the plane in dyne ...

In general, you need the plane to look in the direction of the normal (white arrow), and the formula for calculating the angle of the plane is ang (v1-v2) , while v2 is a dynamically changing point on the video in order to orient . I think that it is necessary to somehow enter the normal into the formula, but I have no idea.

Answer 1

In general, in 3D, all operations: displacement, rotation, scaling, are implemented using displacement, rotation, scaling matrices. If the rotation occurs immediately along all axes, and not just along one, then you also need to remember about quaternions.

Answer 2

And, actually, it is possible the mathematical formulation of the problem?