> knowledge on 2nd derivative continuity Which means that the radius of curvature of the "seams" of the spline is the same for both curves in the common point

> knowledge on 2nd derivative continuity Which means that the radius of curvature of the "seams" of the spline is the same for both curves in the common point - the spline is "smoother", there is no jump in the curvature. Like C1 means, that each point (except for start and end) of the spline has a tangent (the samé tangent from the left and the right side), no spikes. And C3 is about the torsion of (3D, as in "not contained in a plane") curves.