Some 3D folding

Over the past couple days (finals week lol) I found myself extremely motivated to make things, particularly in 3D. So I started trying to convert parts of my first big Mathematica/Wolfram Language project into 3D.

Most of the changes are cosmetic. I quickly familiarized myself with the rotation transform functions and got to work. This time around I was too unfamiliar/intimidated with the huge matrices so I just shelved it for at least a month or two. But it did inspire to start looking at some Linear Algebra material so hopefully a more direct implementation of rotation matrices can come soon?

Anyways to familiarize myself with the 3D graphics tools I glanced through the documentation and found some useful code to pick up.
First off was a quick test with creating polygons in 3space.

Then I moved on to rotating around an arbitrary vector v (In this case <1,0,0>, the x axis)

An hour or so of messing around, and I finally got the hang of the 3D folding:

Now, when I turned to revising my original code for 3D I actually noticed several things:
Firstly,  my original code was super messy and disorganized and poorly documented (oops)
I was trying to bring over some of my old functions to 3D but I was having trouble figuring out what functions did what exactly. I think a good Saturday afternoon exercise would be to cleanly rewrite the entire original program from scratch.

I was writing most of this during my TA period in school (finals week doesn't really leave much help/work for us to do around here :o) so I didn't really feel like updating most of the code or fixing it. I really only changed two functions by adding a z component and super lazily but quickly fixed the others on the fly.

With an arbitrary point I had chosen I just directly implemented the last bit of the rotation matrices (some quick coordinate geometry resolved the question of what vector to rotate around etc.)

I was having some trouble constructing the top polygon for now as the shape folds so I've left it out for now. (My struggle is to do with the way Mathematica stores points versus ordered pairs in their 3D graphics directives)

The actual code for the finished graphic isn't published yet. I probably want to clean it up a bit but that should come soon.

Here are some pictures of my graphic so far for an arbitrary Kawasaki obeying point (the top polygon is missing, see above)

It's still missing the top polygon but you can see the resemblance to some a 2d relative of a similar figure (the opacities are not accurate in 2d, the 3d is correct, because the polygon ordering wasn't considered when the demonstration was originally made, another problem I really should resolve when I find time).

As from my Wolfram Demonstration
http://demonstrations.wolfram.com/OneVertexOrigamiFolding/

Have a nice day

Tis The Season

 I bought the Czech Origami Convention book from 2014 from Origami Shop last week. I was immediately impressed by the deer designed by Yasushi Miyashita  and was surprised that it was only around 70 steps (such a nice design and so quick too!)

This all started with a test fold from a piece of red Mulberry that I had attempted to make with white glue a long time ago.

The color was really nice, but I wasn't expecting much, so I didn't take any in between pictures.

The paper I had used was kind of brittle and weak (white glue doesn't work for sizing, oops). Nevertheless, this deer came out really well and made for a neat ornament so I decided to give it another try.
I selected a rather nice piece of pagoda blue mulberry from World Market and sized it with MC

And then got started folding...

The base was already pretty good without any embellishments, but I wanted to give it as a gift so I needed to make it a little more sturdy. I added a little bit of glue to the legs to help it stand without support. Everything else (including the head and antlers)was done without any glue, and the glue used in the legs didn't actually affect the appearance.

A couple hours of work after I started, I had my final finished deer!

 And I took a picture with my first deer. The colors of both are so beautiful!

Spinosaurus-Shuki Kato

I've wanted to try this one for years (probably since I first saw the diagrams some years ago), and only now have realized this dream.

This is the Spinosaurus, designed by Shuki Kato. Almost a decade ago (wow) the staff of Origami Weekly produced hand-drawn diagrams for it:
https://www.flickr.com/photos/origamiweekly/4079269103
The download no longer works, but I had a printed copy floating around my house which I used.

Starting with an 18 inch square, some waterbomb like folds yield a structure that little resembles a dinosaur

I have to admit that when I originally got to this part I had also noticed that my paper was not a square, and considered giving up, worried that my references would be too far off the mark for me to be able to complete the fold. Luckily, I persevered.

That picture on the bottom right is me folding during lunch, not at home.

And at last, after some hours worth of total folding, the finished product!
I like the detailed toes and fingers, but I do kind of feel like the forelegs are too short. But otherwise this is definitely a cool design. It also stands on its own!

 Here's a quick comparison with the Carnotaurus from last week:

A poorly taken outside picture,

And of course, battle time!

Some Crease Pattern Discussion

I was exploring some design ideas this weekend. Here's some of what I came up with

First off is a deer. I generally try to stick with small grids and simple references. The tree for a basic deer is actually pretty simple provided you are okay with spending a lot of time shaping.

I didn't spend a lot of time thinking about the tree and just created some flaps and messed around for a little. After a couple minutes this is what I got. The neck still seems too short though... Let's try increasing the grid

Left:
Aha, now this could be interesting. There are still some problems though. Now there are extra units on the right leg, and there's not much going on at the head, which is a bit disappointing for the larger grid.
Right:
Shifting some units around results in this. It's promising, but the extra space near the top suggests some possibilities.

Maybe by adding units at the top (folding with a rectangle instead, we could get antlers and a more detailed head)

This is an interesting result, I used some more complex structures to widen the torso portions, but it's still not incredible. Also apparently I messed up counting the units and made the torso too long. oops. But the neck is longer, the front legs are shorter (which is important as they won't be crimped in the same way), and we now have ears and antlers!. What we have is still a success. And also something to be tussled with at a later date. Right now, the grid is 20x40, but if I correct the length of the torso it might down to 20x 38, which is not that different from 20x 40, it just involves folding over some units at the end.

Well I had planned on posting more of my discoveries from this weekend tonight, but I still have homework to finish, so I'll write those up at a later date.

Cheers.

Update: 12/11/18
I shifted the body down one unit to make the torso more reasonable, and added some stuff to widen the head:

The weird intersections in the mouth area aren't actually correct, but they're meant to show generally what's going on. Here's a little fold to show what they actually fold like:

Carnotaurus-Satoshi Kamiya

Over the past two years I've become more and more busy, and my new schedule makes it more difficult for me to make polished and practiced final folds for my Flickr Gallery. Nowadays after folding a test fold from test paper, I usually move on to the next design I've happened upon. But these test folds don't seem like they really belong on my Flickr gallery, so I've decided to create this blog for me to post all the little things I work on or fold in little updates (although most likely nobody except me will bother reading it).  At any rate, it will certainly be something interesting to look back on in a couple years.

So I recently found some time to attempt the Carnotaurus diagrammed in Works of Satoshi Kamiya (Vol. 1). I have attempted it once before, out of 6-inch tant (not ideal, I know), but the result wasn't exactly pretty. This time around I chose a much more suitable paper:  an 18 inch square of Masking Paper. This paper is a really good all  round test paper, and I'll probably write about it later.

This attempt started off much more promising than the last. I was careful to  make each crease as accurate as possible.

I forgot to take more in between pictures though (oops, I'll probably get to that next time) until I got to an almost completed base:

There was a little hiccup in the arms; I could not figure out how the arms were being swiveled into position, but I just applied a technique from shaping to get it done a different way with similar (I hope results)

This point was really exciting. The fold was coming along really cleanly despite the significant number of steps involving folding through layers that adds onto paper creep inaccuracy.
Maybe 30 minutes later, I was (mostly) finished:

This is the product I obtained without any embellishments or glue. I was pretty pleased with the result and impressed that Kamiya had designed it to stand up without supports. Things like that require very careful management of layers/paper usage and are a testament to his skill.

But the paper was still thin, and there was a crease going through the upper thigh  that was causing the legs to splay and fall so I decided to  add a little glue for display longevity

The final product is now sitting on my desk and I will update this page when I photograph it.

Edit (10/10/18)
Here's a photo (a little poorly lit :(  )