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How to offset/loft a surface while maintaining cross-sectional area?


New member
I am stuck on a modeling problem. I have a surface (blue) which I would like "offset" inwards (yellow) while maintaining a constant cross-sectional area (red) throughout the part, as shown in the pic below. Only three sections are shown, but I would like to use at least 4 or 5. The problem is how to model this parametrically, using optimisation, with a script, etc. but not manually. Loft is probably the correct method, since the cross-sections can be defined.

I am not limited by Solidworks. CATIA, Alias, Rhino, Blender, etc. are all fine to use. Any help is much appreciated.