Creating arch + pleating

Hello, I am trying to figure out the following issues. I am still new to using Grasshopper, and appreciate your patience.

below is the form I am trying to create, with flexibility to control how much xyz movement on the second square footprint:
20.02.12_stitchglue_v0.2 sc0

  1. I created two curves using Bezier span, and then joined the two curves. While it looks fine when the two square footprints are parallel, the curve does not look continuous when the footprints are not parallel - the curve sticking to the tangent of the endpoint at the vertex (sc 1). I couldn’t figure out a better way to create an arch that would allow me to control the height, and would like to know either to 1) fix the issue or 2) a better way to create the geometry.

  2. After creating the base geometry, I would like to create pleated surfaces - like the one below (sc2). The aim of the pleating is to make the doubly-curved surfaces into developable surfaces where the two edges are touching the two footprints. I am unsure where to begin, and would like suggestions for components that may be useful.
    20.02.12_stitchglue_v0.2 sc2

20.02.12_stichglue base (16.8 KB)

You can follow this steps in Rhino based on your reference images.
Ellipse , Project, Sweep 1 Rail …
The script have the geometries only (2.7 KB)

1 Like (13.4 KB) (21.1 KB)

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Welcome @maiokimoto,

Check this out:

20.02.12_stichglue base (15.9 KB)

2 Likes (25.1 KB)

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Thank you, all. I was able to learn from the different versions that were shared.
@Joseph_Oster I ended up using your version to play around with different numbers of pleats for top+bottom v. side surfaces. Thank you!