Formula for calculating the movement of a point along a circle in three-dimensional space?

Question

Geometry

I want to visualize the movement of a point in a circle on the screen.
I will draw like this - I draw a dot, then I erase it.
We need formulas for three-dimensional space.
Programming on QB64.

Answer 1

Probably the simplest representation in this case is with three vectors.
Let the center of the circle be at the origin of coordinates, f1 be some vector that the point with its coordinates lies on the circle, n be the vector of the unit normal to the plane of the circle. Then the circle is given:
r(t) = f1 Cos(t) + [nx f1] Sin(t), 0 < t < 2pi ([nx f1] -- vector product)
You can move the center of the circle to any point by adding the vector r0 : r'(t) = r0 + r(t).