How Shipbuilders and Citroën Secretly Invented the Math Behind Every Car and Font
A History of Curves and Surfaces in Computer Aided Geometric Design [pdf]
Gerald Farin traces the history of curves and surfaces in computer-aided geometric design up to the mid-1980s. The story runs from Roman shipbuilding templates and the 18th-century wooden spline to Paul de Casteljau's secret control-polygon breakthrough at Citroën in 1959 and Pierre Bézier's independent work at Renault, which led to the UNISURF system and later CATIA. It also covers Liming's numerical conic constructions for aircraft and Coons' surface patches.
Instead of defining a curve (or surface) through points on it, a control polygon utilizes points near it. Instead of changing the curve (surface) directly, one changes the control polygon, and the curve (surface) follows in a very intuitive way.
- virgil_disgr4ce
I'll take any opportunity to spread the word about Freya Holmér's incredible overview of splines, "The Continuity of Splines": https://www.youtube.com/watch?v=jvPPXbo87ds
It's one of the single most informative and useful math videos I've ever seen, and taught me so much stuff I had no idea existed. I've been using beziers since I was a teen learning a pirated version of adobe illustrator 6 or 7 and I had simply assumed beziers were all you needed. NOPE!!!!
Not only that, it allowed me to realize what was wrong with a game prototype I was working on at the time, which had exactly to do with the continuity problems discussed in the video. Cannot recommend it enough.
- ur-whale
This document strikes me as quite dated.