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Re:Mathematical Intuition Behind Bezier Curves by jacobolus on Sunday May 08, 2016 @02:42PM (#11655164)
For anyone with enough formal mathematics background to follow the argument, Lyle Ramshaw’s monograph, On multiplying points: the paired algebras of forms and sites, supplies the clearest formalism for understanding and working with Bézier curves and various CAGD surface primitives. http://www.hpl.hp.com/techreports/Compaq-DEC/SRC-RR-169.html (Note: ~150 page math book, takes some work to follow.)

Also check out the pomax bezier curve primer, which is filled with interactive diagrams and nice explanations of algorithms for doing anything you might like with Bézier curves, http://pomax.github.io/bezierinfo/ (previous discussions, https://news.ycombinator.com/item?id=11402656 https://news.ycombinator.com/item?id=8804691)

Re:Mathematical Intuition Behind Bezier Curves by theoh on Sunday May 08, 2016 @04:26PM (#11655609)
Yes, this (Lyle Ramshaw's paper). My impression is that his work succeeds in finding the simplest human-comprehensible way of defining these objects. It's very much not the pragmatic "local hacker" approach to graphics, which can be forbidding.

I also enjoyed this interview with Tony DeRose: https://www.youtube.com/watch?v=mX0NB9IyYpU

It can be so discouraging for people to encounter this stuff (geometric modelling primitives) as a mysterious incantation, essentially as raw algebraic code. I think there's probably more scope to humanize it, as Ramshaw and DeRose's demonstrations suggest.