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NON-TANGENT FILLET

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if you can subdivide the face where you want the radius to create a sharp corner you can do it with a face blend selecting the edge of the subdivide face as a coincident edge

Ron
Design Analyst
 
After reviewing again I’ve found you can use ‘edge blend’ and uncheck the option ‘roll over smooth edges’ and the blend will stop at the edge of the subdivided face.

Ron
Design Analyst
 
I've done something similar by applying a chamfer then blending one of the resulting chamfer edges.
 
The more difficult case is the opposite of what John shows. It used to be supported as what was called a cliff edged edge blend, but I haven't seen that for several versions now. That functionality is still supported under face blending however and continues to work quite well.

Cheers

Hudson
 
The image that rep001 provides shows the blend being applied to an outside corner rather than an inside corner.

The 'cliff edge' edge blend lives on - according to the help files (and personal experience) a cliff edge blend will be automatically applied when necessary. Perhaps the option to explicitly add a cliff edge blend has been removed (or well hidden) in recent versions.
 
That's true but on a number of occasions i have found that you are able to force a desired result using face blend which an edge bland baulked at. Whether it could do those cases in the past is a matter for conjecture but possibly it was always necessary to use the face blend version from time to time.

Cheers

Hudson
 
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