Cubic Splines - De Casteljau Bezier Curves Using Linear Algebra

Explore the elegant world of de Casteljau Bezier curves in this 33-minute video lecture. Discover how these curves, originally developed for automobile design in the 1960s, are created by combining linked convex and affine motions along line segments. Learn about the surprisingly simple algebraic formulas for these curves using Bernstein polynomials, with a focus on cubic cases. Gain insights into higher degree curves and surfaces, and understand why these techniques are now widely used in various design fields. Delve into the mathematical foundations of modern computer-aided design and graphics through this informative presentation on cubic splines and their applications.

Introduction
Presentation
Convex combination
Algebra
Cubic splines
Quartic curves
Types of cubic curves