Curve to a corner

I frequently run into this problem but have not yet found a good solution. That is how to create a surface that takes a surface from a curve to corner (e.g., a right angle). In other words the radius of the curve needs to go from R > 0 to R = 0.

I have attached a file the shows two such corners.

I was wondering of someone had an approach for this that tends to work well??

Problem Corners.3dm (3.2 MB)

Hello - this sort of arrangement may do:

four point surface matched for curvature, preserving Position at the other end.