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Sorry for the non descriptive title. I don't know what to call this. Basically I'd like to know if there is an easy and quick way to create bevels like this:

enter image description here

Essentially what are the good ways to create bevels along edges that smoothly go from one radius to another either linearly or expotentially like in the pic. I know I posted a simple cube but imagine that the surface is not flat and has many loop cuts in the middle so manually adjusting bevels is not really an option as it doesn't produce smooth results very easily or quickly.

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It's not parametric, but bevels (tool or modifier) do have a 'Percent' width type, which will bevel the given proportion of the way along adjacent edges. So if you can arrange for adjacent edges to have appropriate lengths...

enter image description here

You might also want to look at all the possibilities offered by the Bridge Edge Loops tool, for connecting open edges.

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