Gordon surface

We are given a network of curves as mentioned above. It is desired to construct a surface G(u,v) interpolating the given curves. Let us denote given u-curves $G(u,v_{j}), j=1,\ldots,n$ and v-curves $G(u_{i},v), i=1,\ldots,m$. Curves intersect in points $G(u_{i},v_{j}), i=1,\ldots,m, j=1,\ldots,n$. Gordon surface is defined:

G(u,v)=G₁(u,v)+G₂(u,v)-G₁₂(u,v)

where

$$\sum_{i=1}^{m}G(u_{i},v)L_{i}^{m}(u)$$ G₁(u,v) =

$$\sum_{j=1}^{n}G(u,v_{j})L_{j}^{n}(v)$$ G₂(u,v) =

$$\sum_{i=1}^{m}\sum_{j=1}^{n}G(u_{i},v_{j})L_{i}^{m}(u)L_{j}^{n}(v)$$ G₁₂(u,v) =

and L_i^m(u) are blending functions satisfying:

$$L_{i}^{m}(u_{i})=1,\ L_{i}^{m}(u_{k})=0, i\neq k$$ (1)

We will use B₂-splines to construct appropriate blending functions.