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"Bald Eagle" <cre### [at] netscape net> wrote:
> The original thread is here:
>
>
https://news.povray.org/povray.advanced-users/thread/%3Cweb.5a6fdd3c85506b565cafe28e0%40news.povray.org%3E/
>
> 7 years later, with a bit more experience with dot products, matrices, and all
> manner of other things:
>
> Placing a heavy weight on the top corner of a box, and having the vertical edge
> partially collapse in an accordian fashion would likely require subdividing the
> edge into numerous segments, and then rotating the vertices into place,
> maintaining a constant linear "arc length" of the linear spline.
>
> From there, one would have to determine suitable vertices in the two box faces
>
> Theorem. That would introduce new perturbations in the sheet face, and the
> vertices connected to the crumpled edge would have to be displaced.
>
> Those perturbations and displacements would need to be processed by some sort of
> algorithm that worked out the cascade of displacements throughout the rest of
> the box, ensuring that the lengths and areas stayed constant.
>
>
https://people.math.ethz.ch/~acannas/Student_Papers/BSc_Theses/2024_bsc_kunz_mathematics_of_origami.pdf
>
> https://community.wolfram.com/groups/-/m/t/148287
>
> Although I was a graduate student in organic chemistry at the time, when I first
> discovered POV-Ray I was very interested in sheet metal development, and I would
> say that the books and software concerning making 3D shapes out of flat sheets
> of metal ("development") would be an invaluable resource as well.
>
> Doing the reverse: starting with a 3D mesh and unfolding it into a flat sheet
> (if possible) would be an amazing accomplishment - it's how professional
> packages uv-unwrap meshes.
>
> - BE
The java library code would give you the ability to find the vertices in the
crushed region and give you the connects to neighboring vertices via the face
triangles. Writing the code to move them in accordance with the rules above is
another rabbit hole that I may have to dive into eventually.
-- Chris R
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