Here is how the math works for **untrimmed** edges of surfaces. Trimmed edges such as in the example in the first post are different. Using Patch as Pascal suggested is a good method with trimmed edges.

The position of the edge is affected only by the control points along the edge.

The tangency of the surface at the edge is affected by the control points along the edge and the adjacent row of control points.

The curvatue of the surface at the edge is affected by the control points along the edge and the two adjacent rows of control points, (Degree 2 and higher in the direction normal to the edge only.)