How to loft a surface maintaining cross-sectional area?

I have a surface (blue) which I would like "offset" inwards (yellow) while maintaining the same cross-sectional area (red).

I am new to grasshopper, and would like to know if it is suitable for generating the cross sections, and creating the final yellow surface.

If anyone has suggestions for how to accomplish this in grasshopper, rhino, python, or other CAD software, that would be great!

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Permalink Reply by Ethan Gross on August 21, 2015 at 2:45am

Hi Edan,

I don't think a strict offset would generally work, so the approach I took was to scale the profile curves so the difference between the original area of each and your target was constant. If the original curve has area A1 and it is scaled by a factor b, then the resulting curve has area A1*b^2. The difference between these areas is your target A2, so we need to solve for the factor b. This is sqrt(1-(A2/A1)) and will be different for each curve. Then we can loft the external and internal curves, cap, and subtract to get the final solid. It's then verified by slicing with normal planes and calculating the areas of the cross sections.

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