Linear precision of a geometric basis (source code)

= Linear precision of a geometric basis
{title2=$\sum_j\phi_j(u)=1,\quad\sum_j\xi_j\phi_j(u)=u$}

= Linear precision
{synonym}

A basis with the displayed identities reproduces <affine functions> from their values at the precision sites $\xi_j$. For two such bases, the tensor-product precision sites are $(\xi_j,\eta_k)$: summation independently recovers $u$ and $v$. Affine images of this site grid therefore produce exact planar parameterizations, independent of the chosen control-grid representation.