Bézier surfaces in multivariate \(B\)-form (Q1334064)

The authors present a definition of a surface of multivariate \(B\)-form and a method for constructing such surfaces. For this purpose the following theorem is proved: The \(\mu\)-multiple tensor product Bézier surface of degree \(n\) with given characteristic vertices is the surface of \(n\)th degree \(B\)-form on a \((2^ \mu-1)\)-dimensional simplex. After that relationships between surfaces of multivariate \(B\)-form and Bézier surfaces are discussed.