Interpolate camera movement along an arc of circle

Question

In my scene, i have a camera defined through a position and a target in 3d space.

Given the center C and two points Pold and PNew, both at a distance of R from the center, how can i interpolate the cameras position in arbitrary amount of steps on an arc?

My goal to is to perform a smooth animation of the view around an object located at the center point.

Answer 1

It's called spherical linear interpolation, and all you need you can find here.