Convert Beziér control points to Catmull-Rom control points

Question

I am doing some smooth camera transitions in 3D and use a small library that handles the transition of my camera.

Unfortunately, it only performs Catmull-Rom transitions. I am also using some information out of a publication and they use Beziér curves for their transition.

So my question is: Given a set of Bézier control points. How can I transform them into Catmull-Rom points?

If it is possible, I would be able to use this library. Else, I will have to implement Bézier curves from scratch.

UPDATE
I should mention that the control points itself are fine. The curve does not have to be exactly the same. Only the same behaviour is desired.

Answer 1

Catmull-Rom uses the adjacent points of the pair of points being analysed to build tangents, whereas Bezier curves use the tangent data given to them per point. So in principle can't you just sample a point, on the Bezier curve, on either side of each existing point to 'fake' the implicitly generated tangent data the Catmull-Rom curve uses?