What is the best procedure to create a surface for filling a corner with continuity with the two surfaces that split/ branch?
I think I have a mental block about how to approach this. It seems like it should be simple. cornerPiece.3dm (1.4 MB)
I assumed you want continuous curvature, though the large surfaces are not all curvature continuous.
One Method:
Use the fillet you already have.
ExtractIsoCurve along the outer surfaces at the corners of the fillet.
BlendCrv to create curves connecting the extracted isocurves.
NetworkSrf with curvature continuous at the large surface edges to create surfaces to fill the missing triangles.
ExtendSrf to extend both ends of the fillet so that it completely intersects the fill surfaces.
Trim the fill surfaces and the fillet with each other.
Example: cornerPiece_DC01.3dm (2.0 MB)
Hi
I would avoid making any sliver patches. I would use surface split at isocurve with shrink on. To divide the surfaces at the fillet. Then match one of the surfaces to the other. Then use the fillet surface to trim away the overlap. You will also need to do some more surface matches to make everything smooth and water tight. If you are planing on filleting the loop edges. I would delete and rebuild both the red and blue surfaces as one single surface. Otherwise the fillet will bomb on the on the trimmed out edge of the red surf. 
@davidcockey @Stratosfear Thank-you for the help. It’s very interesting to see how others solve a given problem.
You hit the nail on the head. It’s best avoided, but that’s the issue I keep running into. It inevitably requires finding work-arounds and I keep designing stuff with details like these:
The answer of course is I probably shouldn’t. I’m still trying to wrap my mind around what method or work around to use in a given situation. Ideally I’d like to solve issues cleanly and elegantly with curvature continuity and single span surfaces (and in a reasonable amount of time).
Stratosfear’s procedure appears to be preferable to the one I posted.