Given that the article's author used Blender to create their model, I'm surprised they didn't use it's built-in paper model exporter. https://docs.blender.org/manual/en/4.1//addons/import_export...
They mentioned it, seem to prefer pepakura.
3D modeling with paper
41–50 of 52 posts
Re: 3D modeling with paper
#42Earlier quoted context omitted.
> Folds are powerful. One can trisect or n-sect any angle for finite n. Does that mean folding allows you to construct (without trial-and-error) an accurate heptagon, even though you can't with a straight-edge and compass? Intuitively, that seems wrong, I would expect many of the same limitations to apply.
Seems like you can https://origamiusa.org/thefold/article/diagrams-one-cut-hept... The one cut is to remove the perimeter of the square that lies outside the heptagon. Without the cut, you could make a crease, and fold the excess behind the heptagon.
My reading is that it's a convenient near-7 approximation someone developed, like using 22/7 for pi.
Certainly good enough for practical handheld construction purposes, but not geometric-proof-y stuff.
Re: 3D modeling with paper
#43This is ridiculous. I’ll tell you why. Here I quote: “All parts in the assembled model must be made of paper. Each part must be a single, solid color. The parts must not use any printed textures or designs. The model must be represented as a simple polyhedron.” Must. Must. Must. This is a game. Or an art school exercise. Modeling is concerned only with attaining the necessary accuracy. Not conforming to a methodology…
Did you read the sentence above this quote?
> "These are self-imposed limitations that fit my preferred-style for model design"
If you have a different preferred style, then write your own article and how-to, stop complaining and touting nonsense yourself.
Re: 3D modeling with paper
#44You could have replaced a bunch of faces with larger cylindrical/conical faces (aka 3D developable surfaces) to get a more realistic look. Paper can bend! I wonder if there are algorithms for approximating arbitrary geometries with a combination of planar, cylindrical and conical faces? Sheet metal fabrication should be facing the same constraints.
Hey, I'm the original author! I should have elaborated more on this constraint. First, many papercraft models do use cylindrical/conical faces - it's just something I prefer not to do stylistically. Part of the art here is the approximation, rather than aiming for perfect realism. There's also the fact that not all paper bends the same. Papers and cardboards come in various weights and textures, so they each can curve differently. Keeping only flat faces removes these variables from the assembly.
Re: 3D modeling with paper
#45I always wonder what the Elements would have looked like had Euclid had included paper folding as a primitive. Folds are powerful. One can trisect or n-sect any angle for finite n. One still needs the compass though for circle. Straight edge Compass Nuesis Paper folding Makes for a very powerful tool set.
> Folds are powerful. One can trisect or n-sect any angle for finite n. Does that mean folding allows you to construct (without trial-and-error) an accurate heptagon, even though you can't with a straight-edge and compass? Intuitively, that seems wrong, I would expect many of the same limitations to apply.
This paper discusses constructing heptagons, with some history and the maths.
http://origametry.net/papers/heptagon.pdf
It shows both a single sheet and a modular version.
Re: 3D modeling with paper
#46Btw, there's a pretty well known origami version of the SR-71 by Toshikazu Kawasaki. One square, no cuts, the usual. I folded it as a kid from diagrams in "Origami for the Connoisseur". It's not as detailed as the papercraft version, but I think it symbolizes the real airplane very well.
Direct link: https://www.giladorigami.com/BO_Conn.html
Re: 3D modeling with paper
#47I always wonder what the Elements would have looked like had Euclid had included paper folding as a primitive. Folds are powerful. One can trisect or n-sect any angle for finite n. One still needs the compass though for circle. Straight edge Compass Nuesis Paper folding Makes for a very powerful tool set.
> Folds are powerful. One can trisect or n-sect any angle for finite n. Does that mean folding allows you to construct (without trial-and-error) an accurate heptagon, even though you can't with a straight-edge and compass? Intuitively, that seems wrong, I would expect many of the same limitations to apply.
Yes.
But remember one is dealing with idealized / axiomatized folding. The situation is similar with compass and straight edge geometry -- those physical lines and circles marked on paper are approximate but mathematically, in the world of axioms we assume the tools are capable of perfect constructions.
Re: 3D modeling with paper
#48Earlier quoted context omitted.
Seems like you can https://origamiusa.org/thefold/article/diagrams-one-cut-hept... The one cut is to remove the perimeter of the square that lies outside the heptagon. Without the cut, you could make a crease, and fold the excess behind the heptagon.
My reading is that it's a convenient near-7 approximation someone developed, like using 22/7 for pi. Certainly good enough for practical handheld construction purposes, but not geometric-proof-y stuff.
Checkout
Scimemi, Draw of a regular
heptagon by folding.
Proceedings of the 1st
International Meeting of
Origami Science and
Technology. 1989
Are you familiar with Lill's method of finding real roots of polynomials of any degree ? Simultaneous folds are a realization of the same idea
https://en.m.wikipedia.org/wiki/Lill%27s_method#Finding_root...
Re: 3D modeling with paper
#49I like software: open source and only for linux
Re: 3D modeling with paper
#50You could have replaced a bunch of faces with larger cylindrical/conical faces (aka 3D developable surfaces) to get a more realistic look. Paper can bend! I wonder if there are algorithms for approximating arbitrary geometries with a combination of planar, cylindrical and conical faces? Sheet metal fabrication should be facing the same constraints.
That type of shape constraint would be called having a ruled surface with a Gaussian curvature of 0 everywhere, otherwise known as a 'Developable Surface'. Fitting a -single- such surface to a set of points is nearly trivial; finding a way to best fit -multiple- such surfaces together to approximate a non-trivial shape (cloud of points) where they share edges in a way that could be joined like this paper model.... fe…
Human problem? It's probably already solved by one of the many recent machine learning papers, often there is source on GitHub and Transformer models on HuggingFace or some random Google Drive or Biadu drive. So one such human problem is finding how to ask aXiv Assistant what the best SOTA papers for it are and searching for if they finally released code or not (hoping researchers have a real repo not a GitHub site without code).
I recall that Nvidia have some clean solutions. I wish it was a more pure principled solver though with some clean code. Probably OpenEvolve could iterate on a solution to it like the circle packing problem example but 3D.
Sometimes it's funny to think that there are human problems left, which itself really is a human problem.