For anyone with enough formal mathematics background to follow the argument, Lyle Ramshaw’s monograph, <i>On multiplying points: the paired algebras of forms and sites</i>, supplies the clearest formalism for understanding and working with Bézier curves and various CAGD surface primitives. <a href="http:&#x2F;&#x2F;www.hpl.hp.com&#x2F;techreports&#x2F;Compaq-DEC&#x2F;SRC-RR-169.html" rel="nofollow">http:&#x2F;&#x2F;www.hpl.hp.com&#x2F;techreports&#x2F;Compaq-DEC&#x2F;SRC-RR-169.html</a> (Note: ~150 page math book, takes some work to follow.)<p>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, <a href="http:&#x2F;&#x2F;pomax.github.io&#x2F;bezierinfo&#x2F;" rel="nofollow">http:&#x2F;&#x2F;pomax.github.io&#x2F;bezierinfo&#x2F;</a> (previous discussions, <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=11402656" rel="nofollow">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=11402656</a> <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=8804691" rel="nofollow">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=8804691</a>)