I wanted to recreate the base geometry in this photograph and make it parametric in order to be able to eventually loft it and make it into a tower following this wave profile. I have issues:
1- i cannot make it into a parametric shape without messing up the shape (i have to keep changing other sliders/parameters if i change one)
2- i cannot seem to figure out how to bend the arc in grasshopper to get the wave profile 
A2_TowerBaseGeometrygh.gh (9.8 KB)
In oder to parameterize the shape, you would need to generate a series of numbers that will vary as they go along.
Something like a graph mapper which allow me to vary the numbers as they go…
For the curves, on the innerside of the wave, the curve is not an exact arc, hence I would recommend the interpolate function over the arc function.
A2_TowerBaseGeometrygh_paramed.gh (23.9 KB)
Thank you so much @christopher.ho, this really helps a lot! I might need to tweak it a bit for my project but this is great !! :))