Wow, this is pretty cool! I've seen some art installations that work through a similar concept: this is one of the more memorable ones: https://www.youtube.com/watch?v=l-GR9IVjU54
I love these projects.
I did a related project where I created a single, solid object that has 4 different silhouettes/shadows from 4 different angles in the same plane. Using more view angles than dimensions makes the problem much more complex. I suspect it is not possible to do this purely programmatically so I did it by hand had to smudge the letters to get everything to work out.
Thanks for sharing. Yes, what we found is that multiple input images often are not consistent with each other (i.e., no physical volume that can satisfy the constraints from all the views). We thus start with a set of consistent voxels and connect them so that the projections are as similar to the inputs as possible.
ZKM in Karlsruhe, Germany has an exhibition called Open Codes, where they have used a single solid object to generate all letters in the alphabet using projections.
There supposed to be a spiral encoded in the first chapter of genesis. And the spiral itself encodes the alphabet the encoding of the spiral is written in. Very quine like ability. I am not familiar with any other alphabet achieving this.
http://meru.org/letteressays/letterindex.html
I suck at math, but just out of curiosity: mathematically speaking, can such "wire" structure be made in N dimensions? Let's say a wire struction in 4 dimensions that will project to different 3D objects.
This is interesting. Imagine that we have a series of multi-view wire structure (i.e., adding a time dimension), then we probably can project three different animations.
In my experience, yes, all N-dimensional expressions are generalizable to other N. It just has no practical application, since you can't physically construct a 4D object.
In Gödel, Escher, Bach: An Eternal Golden Braid (1979, Douglas Hofstadter) https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach ... the author carved a simple object of wood that orthographically projected the letters E,G,B to serve as cover art. Book recommended.
I built a similar (but less cool) project that builds these kinds of shapes out of a bunch of dots: https://jse.li/s-h-a-n-p-e-s/frontend/