Catmull-Rom Spline

A Catmull-Rom spline is a local interpolating cubic spline that passes through a sequence of control points. For uniformly spaced parameters, the tangent assigned to an interior control point is commonly

and consecutive points and tangents determine cubic segments using Hermite's interpolating polynomial.

Each interior segment depends only on four consecutive control points. Different parameterizations, including uniform, chordal, and centripetal parameterizations, change the tangents and therefore the shape. The centripetal choice reduces cusps and self-intersections that can arise with uniform parameters.