opengl - Interpolate camera movement along an arc of circle -

in scene, have camera defined through position , target in 3d space.

given center c , 2 points pold , pnew, both @ distance of r center, how can interpolate cameras position in arbitrary amount of steps on arc?

my goal perform smooth animation of view around object located @ center point.

it's called spherical linear interpolation, , need can find here.