A Primer on Bézier Curves (2013)

I love bezier curves. I'm working on rebuilding a project I started in college, a vector graphics editor. The function for determining intersections between two cubic bezier curves, which I found on a professor's website, is absolutely insane: https://github.com/artursapek/mondrian/blob/master/src/coffe... It's a wall of this: c11.x*c12.y*c13.x*c13.y*c23.x*c23.y - c11.y*c12.x*c13.x*c13.y*c23.x*c23.y + 6*c21.x*c22.x*c13y3*c23.x + 3*c11.x*c12.x*c13.x*c13.y*c23y2 + 6*c10.x*c13.x*c13y2*c23.x*c23.y -…

Wow, every time I see this site I am blown away by how well it is done. I am going to put a couple of book titles out there in case somebody doesn't know about them and could benefit: 1.) "The NURBS book" -- Anybody got this one on their bookshelf? (authors Les Piegl and Wayne Tiller) I can't recommend it enough, if you are into rolling your own traditional B-spline lib with expert help! 2.) Then, for a gentle…

Oh I do love a Bézier Curve post, the math and geometry behind them is just so beautiful. Bartosz Ciechanowski's one from last year is my favourite, a little less math heavy and goes on to explain other curves and surfaces: https://ciechanow.ski/curves-and-surfaces/

Neat site. Unless I missed it, I didn't see a discussion of blossoms, which I've found to be a very nice tool when dealing with Bezier curves. There's a great paper called, "Blossoming : a connect-the-dots approach to splines" by Ramshaw (http://www.hpl.hp.com/techreports/Compaq-DEC/SRC-RR-19.pdf) that discusses these ideas. I've also gained a lot of value out of Goldman's book, "Pyramid Algorithms," (https://books.google.com/books?id=xFuhIl1rb2sC). Finally, it's not a great book, but Prautzsch, Boehm, and…