Origami, TreeMaker and ReferenceFinder
Bryan Bishop
http://www.codinghorror.com/blog/archives/000792.html
.. which linked me over to some interesting finds.
http://jorigami.sf.net/
"This is an open source java implementation for the fold and cut
problem (a pretty old problem). It can be stated as this: cosidering a
polygon as the input, can we fold a paper in such way that with an
straight cut it will generate the given polygon? The fantastic answer
here is YES, for any polygon. And here we have implemented one
solution for this problem. The generated origamis can be really hard
to fold. "
http://www.langorigami.com/science/treemaker/treemaker5.php4
"TreeMaker is a program for the design of origami bases. You draw a
stick figure of the base on the screen; each stick in the stick figure
(the "tree") will be represented by a flap on the base. You can also
place various constraints on the flaps, forcing them to be corner,
edge, or middle flaps, and/or setting up various symmetry
relationships (forcing pairs of flaps to be symmetric about a line of
symmetry of the paper, for example). Once you have defined the tree,
TreeMaker computes the full crease pattern for a base which, when
folded, will have a projection (roughly speaking, its "shadow")
equivalent to that specified by the defining tree. The crease pattern
can be printed out, or copied and pasted into another graphics program
for further processing. Crease assignment (mountain or valley) are not
computed, but with a few simple rules and some exploration by hand,
the proper crease assignment can usually easily be found. "
http://www.langorigami.com/science/reffinder/reffinder.php4
"After program initialization (which takes about 30 seconds to build
the database of folding sequences), you type in a numerical or
algebraic expression for the coordinates of a point or a line.
ReferenceFinder immediately returns the 5 "best" short folding
sequences that approximates that point or line. The approximations are
very good, often better than 1 part in 1000, which, in my experience,
is about the limit of human folding precision. ReferenceFinder can
parse simple algebraic expressions (thanks to a contribution from
Carlos Furuti). The default paper shape is a unit square, but you can
change the dimensions for any rectangle (e.g., a silver rectangle or
currency). For each solution, ReferenceFinder reports the absolute
error in distance, the rank (the number of folds needed), and the
sequence of actions needed to construct the desired reference mark.
For more details, read the README.txt file that accompanies each of
the download packages. "
" ... And that opens up another question: if you are an origami
composer (or wish to be), do you need to use TreeMaker? The answer is:
absolutely not. The vast majority of the world's composers of
technical origami don't use it; in fact, I don't use it for the
majority of my own designs. What I do use it for is for what you might
call "rapid prototyping"; quickly examining 3 or 4 (or 5 or 10)
different general arrangements of flaps in a base before settling on
one particular configuration as the focus of my design. For that
purpose, it's an invaluable tool in my arsenal. And for several of my
designs, notably the Scorpion varileg, opus 379, Mule Deer, opus 421,
and Maine Lobster, opus 447, I couldn't have designed them without it
..."
Examples of Lang's folds:
http://www.langorigami.com/art/gallery/gallery.php4?name=maine_lobster
http://www.langorigami.com/art/gallery/gallery.php4?name=squirrel
I'm still processing in awe.
Bryan Bishop
> While browsing the web I found this article:
> http://www.codinghorror.com/blog/archives/000792.html
> .. which linked me over to some interesting finds.
Turns out Robert J. Lang, over at NASA, doing that origami work, has
done a TED talk:
http://www.ted.com/index.php/talks/robert_lang_folds_way_new_origami.html