> what remains is the problem of continuity with adjacent patches, due
> to the fact that each edge now has 7 points, which must seamlessly
> connect with a patch with 4 control points, and also, the center
> control point on each edge must lie on the same line as its
> surrounding two edge points. I wonder if this is mathematical
> conflict, or if it can be solved. 
> 


Hold on, I see my mistake regarding the edges, disregard that comment.
 I shall investigate this further,

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