How to represent a Bezier curve through a circle?

Question

Mathematics

The Bezier curve is given by 3 points: P0, P1, P2. How to find the equation of a circle that will be as close as possible to a Bezier curve?
Is it possible to do this? Or are additional conditions required?

Answer 1

And what is the purpose?
If it is only necessary to preserve the direction of the curve in P ₀ and P ₂ , then it is quite simple. We build a perpendicular to P ₀ P ₁ at the point P ₀ , a perpendicular to P ₁ P ₂ at the point P ₂ , we find the intersection of the perpendiculars, we get the center of the circle.
If the most accurate approximation, but without maintaining the direction at the extreme points, then there will already be three-story formulas.