Bernstein-Bézier Form and its Role in Studying Multivariate Splines

This note offers a friendly introduction to Bernstein-Bézier techniques for bivariate splines guided by geometric ideas rather than rigorous proofs. We give insight into several key concepts involving the Bernstein-Bézier form including domain points, control points, minimal determining sets, and Bernstein-Bézier smoothness conditions. We conclude the note with an informal description of the famous Clough-Tocher macro-element.