After working with several tests connecting the foam board pieces together directly with hot glue, I realized that the projection surface would need to be more flexible. The best solution seemed to be to attach the foam board to a spandex surface, pulled tight over the projection surface for flexibility and to take care of the issue of the “joints” expanding as the surface is pushed/pulled.
I briefly considered using the spandex surface on it’s own as the projection surface, but it’s very transparent I was unable to capture the faceted look that I desired, everything looked like ghost hands in a horror movie. The surface needed to be rigid and geometric (but flowing) not smooth, so the next step was to attach foam board to the surface.
Using the triangles I was able to measure how far the surface would need to be “pushed” to make a dramatic effect as it moves.