The Beauty of Bézier Curves

Explore the fascinating world of Bézier curves in this 24-minute video tutorial. Dive into the mathematics and applications of these versatile curves used in animation, text rendering, and various curved shapes. Learn about linear interpolation, quadratic and cubic Béziers, De Casteljau's algorithm, and the Bernstein polynomial form. Discover how to calculate derivatives, tangents, normals, curvature, and bounding boxes. Delve into arc length computation and parameterization for uniform animation. Gain insights into the beauty and practicality of Bézier curves through clear explanations and visually engaging demonstrations created using the Unity game engine and custom tools.

Intro
Use Cases of Bézier Curves
Lerp
Quadratic Béziers
Cubic Béziers
De Casteljau's Algorithm
Bernstein Polynomial Form
1st Derivative Velocity
Tangents & Normals
2nd Derivative Acceleration
3rd Derivative Jerk/Jolt
Curvature
Bounding Box
Arc Length
Arc Length Parameterization & Uniform Animation
Outro
Credits
Thor helping me record this at 2am