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.
vunderba · 1h ago
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.
coldfoundry · 1h ago
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!
There used to be an entire finishing process with this yellow and blue bottled smooth-cast resin and sanding before painting, but they always stayed paper for me.
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.
srean · 2h ago
I 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.
olooney · 1h ago
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):
It's more powerful than compass and straight-edge constructions, but not by much. It essentially gives you cube roots in addition to square roots. You still need a completely different point of view to make the quantum leap the the real numbers, calculus, and limits:
So ultimately I don't know if it would have changed the course of history that much.
srean · 2m ago
Sure, it makes sense to isolate the minimal sets of primitives needed for an operation. Greeks experimented quite a bit with nuesis before focusing on straight edge and compass. Folding, as you noted, was not part of their mix.
BTW nuesis can also trisect angles.
Yes one would not reach the reals (that's not the ultimate goal) but the geometry would certainly would have been richer.
By no means is the area of folding a mathematical dead end as new theorems still get discovered.
WillAdams · 1h ago
Akira Yoshizawa actually used origami in a factory setting to communicate geometric and engineering concepts.
WillAdams · 1h ago
As a person who wonders where the paper X-15 model he had vanished to after he joined the service, this resonates with me.
While there are a lot of models available for purchase/download, the classic tool for this sort of thing is
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.
Stevvo · 1h ago
"3D Rendering with Paper" might have been a more accurate title. The modelling process is very similar to regular 3D modelling. In theory, with perfect paper and cutting and gluing skills you could print any UV map and cut, fold and glue it into a paper model using this method.
RodgerTheGreat · 1h ago
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.
meindnoch · 52m ago
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.
zaphar · 40m ago
He specifically set a constraint for now curved surfaces. Using cylindrical and conical surfaces would have violated that constraint.
pupppet · 2h ago
The final build looks great, I thought I was looking at a 3D render.
xnx · 2h ago
Very cool. Would probably get even more attention with the title "3D Modeling the SR-71 Blackbird with Paper".
aleph_minus_one · 2h ago
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".
dieggsy · 2h ago
While that would certainly be a factor, I think I'd argue it's less about where you're from and more about what your interests or experience are.
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".
Which would be kind of a shame, since I think the post has some nice points to make regardless of whether you're into the SR-71 Blackbird or planes; that's just the example chosen to paint the broader picture.
the_af · 2h ago
I love this!
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.
There used to be an entire finishing process with this yellow and blue bottled smooth-cast resin and sanding before painting, but they always stayed paper for me.
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.
Folds are powerful. One can trisect or n-sect any angle for finite n. One still needs the compass though for circle.
Makes for a very powerful tool set.https://en.wikipedia.org/wiki/Neusis_construction
https://en.wikipedia.org/wiki/Conic_section
https://en.wikipedia.org/wiki/Quadrature_(mathematics)
https://en.wikipedia.org/wiki/Quadrature_of_the_Parabola
They just preferred the simpler axioms on grounds of aesthetic parsimony.
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
It can be used to trisecting an angle, an impossible construction with straightedge and compass:
https://www.youtube.com/watch?v=SL2lYcggGpc&t=185s
It's more powerful than compass and straight-edge constructions, but not by much. It essentially gives you cube roots in addition to square roots. You still need a completely different point of view to make the quantum leap the the real numbers, calculus, and limits:
https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_t...
https://en.wikipedia.org/wiki/Dedekind_cut
So ultimately I don't know if it would have changed the course of history that much.
BTW nuesis can also trisect angles.
Yes one would not reach the reals (that's not the ultimate goal) but the geometry would certainly would have been richer.
By no means is the area of folding a mathematical dead end as new theorems still get discovered.
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.
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.
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".
Which would be kind of a shame, since I think the post has some nice points to make regardless of whether you're into the SR-71 Blackbird or planes; that's just the example chosen to paint the broader picture.
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.