> - Two cylinders of different radii R_1 and R_2, intersecting each other
> (perpendicular and with intersecting axes, for starters), with a
> "melting" inset radius of R_i.
>
> - Three planes intersecting each others (perpendicular, for starters),
> with different radii for the "melting" insets between the pairs, R_i_1,
> R_i_2 and R_i_3. Of course the corner where the three planes meet is
> also expected to be smooth.
>
> This might give you a /basic/ idea of the fundamental challenges involved.

The above are both a piece of cake for CAD software (see images 
attached) - but I hate to imagine the maths/algorithms behind this. 
Hopefully the images backup the idea that this would be *hard* to do in 
the general case.

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