I’m attempting to project a rectangle onto a curved, open polysurface, such that after the rectangle is projected, the length of all four sides is preserved on the curved surface. The difficulty appears to stem from the fact that the projection spans 4 separate, joined surfaces.

I’ve attempted to convert the polysurface to a Mesh->Squish the mesh->Draw rectangle onto mesh->SquishBack, which produced discontinuities in the projected shape. I also tried to use FlowAlongSrf, which doesn’t seem conducive to polysurfaces.

Projecting the red polygon onto the blue polysurface distorts the rectangle an unacceptable amount (as expected, using Project):

Are there any reliable techniques to project a 4-sided polygon, whose opposing edges are equal in length, onto a convex surface while preserving edge length? Thank you for any useful guidance.

FOAM Demo.3dm (17.7 MB)