3D modeling with paper

The Hacker News discussion centers around a post detailing 3D modeling the SR-71 Blackbird with paper. Key themes that emerged include the effectiveness of the title, the craft of paper modeling itself, the mathematical and historical implications of paper folding, and practical aspects of creating and assembling paper models.

Title and Reach

A significant portion of the discussion revolved around the potential impact of the article's title. Some users suggested alternative titles to attract a wider audience, while others defended the current title's broad appeal.

Suggestion for broader appeal: "xnx: Very cool. Would probably get even more attention with the title "3D Modeling the SR-71 Blackbird with Paper"."
Counterarguments for mass appeal: "dieggsy: I actually think the title as it is now has more mass appeal; it's very general and might pique your curiosity if you're interested in either 3-D modelling or paper crafting. On the other hand if it had the "SR-71 Blackbird" in the title, some readers might shy away due to either not knowing what that is, or thinking "well, I'm not really interested in planes"."
Geographical consideration: "aleph_minus_one: Whether this article would get more or less attention with this changed title depends a lot on the ratio "viewers from the USA"/"viewers from other countries"."

The Art and Craft of Paper Modeling

The quality of the final product and the techniques involved in paper modeling were a major point of discussion, with many users expressing admiration for the precision and detail achievable.

Appreciation for the final result: "pupppet: The final build looks great, I thought I was looking at a 3D render."
Personal experiences with papercraft: "the_af: I do some cardboard / papercraft, but mine is completely unplanned and without this high level of precision. So mine is not suitable for accurate scale model building, but rather for building random houses / castles / vehicles."
Comparison to 3D rendering: "Stevvo: "3D Rendering with Paper" might have been a more accurate title. The modelling process is very similar to regular 3D modelling."
Nostalgia and early experiences: "coldfoundry: Oh wow, this brought me back! I used to be obsessed with papercraft back in the day as a kid, specifically “pepakura”. I used to print out halo 3 helmets and build them and wear them. It was like a puzzle on steroids in the cool department! ... Was a cheap way for me to have fun, and definitely holds a special place in my heart forever. Great share and thank you for posting! Brought me through memory lane."
Software and tools: "WillAdams: While there are a lot of models available for purchase/download, the classic tool for this sort of thing is https://pepakura.tamasoft.co.jp/pepakura_designer/ as noted by coldfoundry --- that said, an unlikely tool which has this is PythonSCAD: https://pythonscad.org/ which allows one to use OpenSCAD or Python to create a 3D model and export it in a number of formats, including "Foldable PS" which automates this process."
Challenges in UV mapping for paper models: "RodgerTheGreat: UV maps, especially for low-poly models, do not generally have a 1:1 geometric relationship with polygons in the original model. Areas with more significant detail will get more space on the UV map, mirrored or repeating areas will be overlapped, and of course UV maps will never include the tabs you'd need to physically glue parts together."
Historical availability in certain regions: "RivieraKid: I remember paper models being very widespread when I was a kid in the Czech Republic, they were always included in a popular magazine for kids, no idea whether it has changed. Per ChatGPT this is unique for this region - Czech Republic, Poland, Slovakia." and "obscurette: These were popular in Soviet Union as well. At least in seventies in Baltic states where I grew up."
Canon's papercraft offerings: "turtlebits: Semi-related, but Canon has a great papercraft site, with varying difficulties. My kid especially loves the moving models. https://creativepark.canon/en/categories/CAT-ST01-0071/top.h..."
Homeworld game models: "rimunroe: If anyone's a fan of papercraft models and the game Homeworld, you might enjoy this collection of models from the games. I remember my sister put together several of these back in the early/mid 2000s. https://www.homeworldaccess.net/infusions/downloads/download..." and "NortySpock: Hey, thanks for posting this! The Kushan Carrier looks exactly like the one I put together as a kid after playing Homeworld, right down to the readme file saying "if you've never done anything like this before, I'd suggest starting with something else"... a warning I ignored as a kid!"
Evolution of paper model complexity: "majgr: Is it/was it quite popular in Poland. 35 years ago, as a kid, I was assembling paper models. Planes were the easiest, usually it took about 2 days to do one. Couple of years ago I wanted to get back to it, so I bought a plane. Well, it turned out that fashion for paper models had changed and now 'reductionist' models are in full swing - being as close as possible to original. That plane has 160 pieces (a lot of them also subdivided), and every part that has size about 10cm in real life, has been modelled. In two weeks I was still in cockpit. Here is paper model of SR-71: https://www.sklep.model-kom.pl/sr-71-model-samolotu-rozpozna... From drawings it looks like it is more than 167+, not including subparts."

Mathematical and Historical Implications of Paper Folding

A fascinating thread explored the mathematical power of paper folding, connecting it to ancient geometric constructions and modern mathematical concepts.

Paper folding as a primitive geometric tool: "srean: Folds are powerful. One can trisect or n-sect any angle for finite n. You still need the compass though for circle.
```
Straight edge
    Compass
    Nuesis
    Paper folding
```
Makes for a very powerful tool set."
Historical use of origami in education: "WillAdams: Akira Yoshizawa actually used origami in a factory setting to communicate geometric and engineering concepts."
Ancient Greek mathematics and paper folding: "olooney: The Greeks were not adverse to studying topics outside of the classic axioms, for example neusis, conic sections, or Archimedes work on quadrature (which presaged calculus)... As far as I know, the ancient Greeks never thought to fold the paper. It has, however, been studied since the 1980's by modern mathematicians: https://en.wikipedia.org/wiki/Huzita%E2%80%93Hatori_axioms"
Power of origami in geometric constructions: "srean: Origami folding is more powerful than the closure of rationale by square and cube roots. They were extended to the quintic roots by Robert Lang using a type of folding called multifold. Now it's known that with multifolds all of the algebraic numbers can be constructed with origami https://arxiv.org/abs/0808.1517"
Heptagon construction with folding: "Terr_: 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."
Confirmation and explanation of heptagon construction: "avhon1: 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."
Distinction between approximation and proof: "Terr_: 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."
Idealized vs. physical folding: "srean: 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."
Origami SR-71 by Toshikazu Kawasaki: "cousin_it: Btw, 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."
Angular designs and origami: "vunderba: That's pretty awesome. I'd love to see the Lockheed F-117 Nighthawk get the same treatment. Seems like its angular design would lend itself well towards an origami version."

Constraints and Design Philosophy

The discussion also touched upon the self-imposed constraints in the original author's design process and the philosophical debate around them.

Critique of constraints: "aj7: This 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."
Defense of constraints: "Revisional_Sin: "These are self-imposed limitations that fit my preferred-style for model design... I find that these constraints encourage a better designed model that can be assembled easily and predictably, including by others." Seems reasonable." and "the_af: What a bizarre objection. ... This is actually answered in TFA: > Constraints: Let's set some constraints for how we're allowed to model our creation. These are self-imposed limitations that fit my preferred-style for model design: _ > _Why constraints? It may feel weird to impose constraints on an art. However, I find that these constraints encourage a better designed model that can be assembled easily and predictably, including by others. It's ok if you disagree with this because you enjoy your model-making in a different way. The author explained why they chose this path, and it makes sense: a lot of art is about constrains ("don't do digital", "use only 2 colors", "origami without any cuts", etc)."
Author's explanation of stylistic choices: "arvinpoddar: 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."
The nature of developable surfaces: "mk_stjames: 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.... feels very NP-hard to me. This is a subset of the problem in the 3d-scan-to-CAD industry where you have a point cloud/mesh and you need to detect flat planes, cylinders, fillets, etc of a 3d scan and best-fit primitive surfaces to those areas and then join them into a manifold while respecting a bunch of other geometric and tolerance constraints. There is a reason why there are only a few software packages that even attempt to do this, and it is almost always human-guided in some way. It's a fascinating problem."
Suggestion for optimization and future tools: "syntaxing: This is super cool. In theory, a lot of this could have been automated. Quad remesher would probably get you close enough to import to the paper software and Cricut like machine for the cutting and scoring(?)."
Paper model exporters in Blender: "avhon1: 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..."
Preference for Pepakura: "alanbernstein: They mentioned it, seem to prefer pepakura."
Optimization idea for 3D modelers: "maxlin: Interesting. Optimization idea: Make your 3D modellers make their models first out of paper. Bet they'll be more cognizant about extra triangles!"

General Appreciation and Discussion of Paper

Comments also included general appreciation for the Post and related topics, such as the author's stylistic choices and the potential for automation.

General positive sentiment: "the_af: I love this!"
Curiosity about paper properties: "meindnoch: You 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."
Constraint clarification: "zaphar: He specifically set a constraint for now curved surfaces. Using cylindrical and conical surfaces would have violated that constraint."
Arbitrary vs. inherent constraints: "mkl: But that's an arbitrary constraint choice that didn't need to be there. It's not inherent to the medium. He has a justification for it (curves are "flimsy and introduce variances") but that is easy to get around with perpendicular reinforcing pieces inside that constrain the curve."
Nostalgia for old paper model books: "TehCorwiz: I used to have books of models like these. Space stations, trains, wild west diorama sets, cars, etc. I wish I could find copies of the older ones."