Tensor-product surface basis (source code)

= Tensor-product surface basis
{title2=$b_{jk}(u,v)=\phi_j(u)\psi_k(v)$}

Products of two univariate bases form a surface basis. Nonnegativity, <partition of unity> and coordinate-wise <linear precision> pass to the products by multiplication of the respective univariate identities. If the factors are $C^r$ and $C^s$, each mixed <derivative> through orders $r,s$ is the product of the corresponding <derivatives>, giving continuous mixed <derivatives> and joint $C^{\min(r,s)}$ regularity.