A seemingly common way to describe a beveled corner is with the radius of the circle that would fit in the corner. This is e.g. how the CSS "border-radius" property works in web design. The screenshot below explains my dilemma, and the diagram under it is what I'm trying to implement. Is there any way to do this automatically in Blender? I'd rather not merge and delete vertices 49 times to make the edges I want.
I don't know what kind of precision you want to achieve (and I hope I have understood the question correctly), but, if you don't want to use curves, I'll do your bevel this way :
Your set-up :
Extruding some faces to get a visual reference :
Loop cut and slide at the right height :
For all the visual marks minus one (because you already have one) :
After the scale on x and y axis of the inner edge :
Grab on z axis each edges individually to match the right height :
It's quite fast (and could be even more precise with the use of snap ?). Is it what you want to achieve ?
Another method you could perhaps use next time :
Create a cross-section of your object then use the Spin tool to fill it out.
Starting from your original setup:
1: Set 3D cursor to center of object.
2: Select vertices that make up the cross-section. (The ones that are selected at the start of the gif anim.).
3: Inverse selection ( Ctrl I ) and delete those newly selected vertices.
4: Select the remaining vertices.
5: Go into top view then from the tools panel choose the Spin tool.
6: In the Operator panel set the number of Steps and Angle of 360°.
7: After the Spin tool has done its job select All and from the tools panel choose Remove Doubles.
8: If necessary Recalculate Normals.
There is no direct way to do it. I just would subdivide or use extruding methods.
Suppose you subdivide the verticals to create a few more ring around that place, then next in edit mode use proportional editing to lift the center up, the proportinal displacement can come close to a circle shape. And finish with a subdiv on your model
Its also possible to use a technical drawing on the background and make you model fit it, then by selecting those extra rings lift them up/down till its visually ok.