Diagrams for geometric folds

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slope of 4 to 1

Postby EricGjerde » August 11th, 2005, 1:17 pm

what program are you using to make the grids?

I use adobe illustrator CS (really just learning!) but it has "smart guides" which allow you to snap lines to arbitrary angles that you can set.

so for my triangle/hex diagrams, I set it to snap at 30, 60, 90, 120, 150, etc.

you can do the same for any arbitrary set of angles- and furthermore, you can set the intial angle that it aligns to (meaning you can make 0 degrees actually be, say, 27.5 degrees rotated clockwise, so the whole diagram is offset).

I find this particular feature set to be extremely valuable for diagramming tessellations. each time I create a new diagram I look back over my previous efforts and get irritated at how bad they are, so I figure for someone else who actually has graphic skills it must be a fabulous program! I'm content to muddle through.

-Eric
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Postby mleonard » August 12th, 2005, 9:41 pm

The grids in my last posting were all made with good ol' Microsoft Paint. Yes, it's a terrible program in many ways, but it was free...

For offset grids, or anything involving triangles/hexagons/etc, I have found Cabri Geometry to be very useful. This is primarily an educational geometry program, rather than a graphics program, but I like that - it means it isn't cluttered up with lots of fancy tools that I don't need. It's very easy to create grids at arbitrary angles, regular polygons with any number of sides, and lots more besides. I'm still using the limited free version (I believe the full version costs around $150) which doesn't allow you to save your work. However you can do a screen capture, and then edit the resulting image in any graphics program - I'm using (yup) Microsoft Paint.
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Postby JMcK » August 17th, 2005, 11:28 am

I used Microsoft Word to draw the crease pattern for the Dome of Squares. Once you draw one line at the correct offset angle you can tick the "Lock Aspect Ratio" box to make it stay at that angle as you move it about and lengthen or shorten it. Then you can copy and paste it to create a range of equally spaced parallel lines. Group those lines together, copy them, paste them, rotate them through 90 degrees and you have an offset grid.
(An alternate method would be to draw the grid lines at the normal 0 degree and 90 degree angles and offset the angles of the edges of the square instead.)
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Postby gila o » August 18th, 2005, 5:20 am

I can't contribute to the discussion much about how to make the crease pattern,so I just fold ....


Thanks for any crease pattern that you are publishing!
http://www.flickr.com/photos/87477835@N00/34987037/
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Postby mleonard » August 21st, 2005, 8:33 pm

mleonard wrote:The last pattern should really be at a slope of 4 to 1, but I haven't worked out a neat way of doing this yet.


Hmm... it seems the reason I was having trouble doing this neatly is because the slope should be 9 to 2, not 4 to 1. I don't fully understand this...
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Postby JMcK » August 28th, 2005, 12:08 pm

mleonard wrote:
mleonard wrote:The last pattern should really be at a slope of 4 to 1, but I haven't worked out a neat way of doing this yet.


Hmm... it seems the reason I was having trouble doing this neatly is because the slope should be 9 to 2, not 4 to 1. I don't fully understand this...


Are you sure? I tried a slope of 4 to 1 and it seemed to work OK:
Leonard Tessellation

It occurred to me after seeing Mark's last pattern that you could use the same principle to create a tessellation of Kawasaki roses of different sizes. Instead of using 3x2 sawhorse molecules* to separate the 2x2 and 1x1 squares I folded a tessellation with 8x7 sawhorses. Then I "Kawasakied" it to get this:
Large and small roses

(It would be possible to do a tessellation of 2x2 and 3x3 roses as well, but I think the sawhorse molecules would need to be at least 11x10 to get a decent amount of curl on the roses, so you would need a very dense precreased grid.)

* A sawhorse molecule is sort of like a rectangular waterbomb base. The term was coined by Robert Lang, I think.
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Postby origami_8 » August 28th, 2005, 12:26 pm

JMcK wrote:It occurred to me after seeing Mark's last pattern that you could use the same principle to create a tessellation of Kawasaki roses of different sizes. Instead of using 3x2 sawhorse molecules* to separate the 2x2 and 1x1 squares I folded a tessellation with 8x7 sawhorses. Then I "Kawasakied" it to get this:
Large and small roses


Fascinating! That´s really great looking.
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Postby mleonard » August 30th, 2005, 9:28 pm

I was trying to make the squares line up with the edges of the paper, like this:
Image
I'm pretty sure that you need a slope of 9 to 2 to do this. 4 to 1 still leaves them a bit twisted, so you wind up with an extra triangle of paper on all the outside squares.

I like the large and small K-rose tessellation. I sort of knew that these tessellations were related to K-rose tessellations, but I've never actually tried making one out of the other. It now seems clear that you could tessellate K-roses at any number of different sizes.

I've been working on something slightly different - I call this the "Transformadome":
Image
There's lots of paper left over at the edges of this pattern - if you wrap all this paper round and tuck it up inside, I hope that you will find out where the name Transformadome comes from.
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thanks for providing an answer!

Postby EricGjerde » August 30th, 2005, 11:05 pm

I've been tumbling around a design that involves multiple sizes of squares together, and I wasn't sure if I could fold them in a fashion that I desired without causing unnecessary pleating.

your 2x2 and 1x1 tessellation here gives me some food for thought, and I greatly appreciate it.

-Eric Gjerde
("I'm sure that there's an answer, somehow involving triangles...")
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