How do Catmull-Rom and Hermite splines relate?

Question

I'm a little confused as to how they relate. From my class, my professor asked how to fit C1 continuous piecewise Hermite curves to x amount of points with automatically computed tangents. Can someone explain how this works?

Namesake

Answer 1

Hermite spline is a method of representation of cubic curve with two endpoints and two tangent vectors at these endpoints.
Note that there are many approaches to represent the same curve- power basis (at^3+bt^2+ct+d), Bernstein polynomials (for Bezier curves) and so on.

Catmull-Rom spline is a method of construction of a cubic curve (C1 continuous, if some pieces used). Every Catmull-Rom segment is a Hermite spline. If we want to represent a Catmull-Rom spline for the P1-P2 segment of the (P0,P1,P2,P3) point sequence as a Hermite one, we just use P1 and P2 as endpoints, and V1 and V2 as tangent vectors, where

V1 = tau * (P2-P0) 
V2 = tau * (P3-P1) 

(good article here) and tau is parameter of tension (rigidness)

Stealer

Looks to me like the correct answer, and as such should be marked as answer! Although you might have mentioned more detailed (like in bold letters maybe), that a Catmull-Rom spline actually is a Hermite spline. – Nicholasnichole