Bézier Splines

Named after Pierre Bézier, Bézier curves are defined by means of Bernstein polynomials [Far12], which are named after Sergei Bernstein. A popular method to evaluate Bézier curves at given parameter values is De Casteljau’s algorithm. A very good online resource with many interactive examples is the website https://pomax.github.io/bezierinfo/.

Bézier splines are composed of Bézier curve segments.

A Python implementation is available in the class splines.Bernstein.

• Properties
• De Casteljau’s Algorithm
  • Preparations
  • Degree 1 (Linear)
  • Degree 2 (Quadratic)
  • Degree 3 (Cubic)
  • Degree 4 (Quartic)
  • Arbitrary Degree
• Non-Uniform (Cubic) Bézier Splines
  • Tangent Vectors
  • Control Points From Tangent Vectors