If $\left\{P_{k,l}^{0}\right\}_{k,l=0}^{n}$ is a set of $\left(n+1\right)^2$ three-dimensional points, and
$ P_{k,l}^{r+1}\left(t,s\right)=\left(P_{k+1,l+1}^{r}+P_{k+1,l}^{r}+P_{k,l+1}^{r}+P_{k,l}^{r}\right)ts,\tag{$*$} $
then, is $P_{0,0}^{n}(t,s)$ the parametric equation of a surface?
I tried plotting this with a set of test points and obtained a spatial, straight line, when I was instead aiming to obtain a surface (since I am making use of the two parameters $t$ and $s$).
What is the problem with $(*)$? I am just interested in knowing whether this is a surface or not. Thanks in advance!