Subdivision schemes: how to create diagrams from subdivision masks?

Question

I came across this interesting example on the cambridge website

The Catmull-Clark bivariate subdivision scheme is a bivariate generalization of the univariate 1/8 [1, 4, 6, 4, 1] subdivision scheme. It creates new vertices as blends of old vertices in the following ways:

subdivision scheme diagram

Provide similar diagrams for the bivariate generalization of the univariate four-point interpolating subdivision scheme 1/16 [-1, 0, 9, 16, 9, 0,-1].

I have now spent some time researching and reading some papers on the subject and basically I found out that such such mask weights are calculated based on how far away they are. (The further away, the weaker the weighting).

Unfortunately I haven't been able to figure out how to go from a subdivision mask of this bivariate generalization of the four-point interpolation scheme 1/16 [-1, 0, 9, 16, 9, 0,-1] to a similar diagram like in the example above.

Any tipps or hints are much appreciated