Triangular Bézier patch
= Triangular Bézier patch
{title2=$S(u,v,w)=\sum_{i+j+k=n}\frac{n!}{i!j!k!}u^iv^jw^kP_{ijk},\quad u+v+w=1$}
For nonnegative barycentric parameters, these total-degree <Bernstein basis> functions define a surface over a triangle. The triangular <control net> has $(n+1)(n+2)/2$ points. Its index constraint couples the three exponents, so it is not a tensor product of two independent univariate bases. The <multinomial theorem> gives nonnegativity and <partition of unity>.