Catmull–Rom Splines

What is nowadays known as Catmull–Rom spline (named after Edwin Catmull and Raphael Rom) is a specific member of a whole family of splines introduced in [CR74]. That paper only describes uniform splines, but their definition can be straightforwardly extended to the non-uniform case.

Contrary to popular belief, Overhauser splines (as presented in [Ove68]) are not the same!

A Python implementation of Catmull–Rom splines is available in the splines.CatmullRom class.

• Properties
  • Tangent Vectors
  • Cusps and Self-Intersections
  • Chordal Parameterization
  • Centripetal Parameterization
  • Parameterized Parameterization
• Derivation (Uniform)
  • Blending Functions
  • Cardinal Functions
  • Example Plot
  • Basis Polynomials
  • Basis Matrix
  • Tangent Vectors
• Derivation (Non-Uniform)
  • Tangent Vectors
  • Basis Matrix
• Barry--Goldman Algorithm
  • Triangular Schemes
  • Neville’s Algorithm
  • De Boor’s Algorithm
  • Combining Both Algorithms
  • Step by Step
  • Tangent Vectors
  • Animation