best way to design models based on 22.5 angles?

General discussion about Origami, Papers, Diagramming, ...
Post Reply
User avatar
origamifreak_1.6180339889
Senior Member
Posts: 260
Joined: April 9th, 2009, 1:10 am
Location: midgar
Contact:

best way to design models based on 22.5 angles?

Post by origamifreak_1.6180339889 »

hello
ive been design my models for over 2 years. i started out by just starting with a traditional base and modify it to look like my design subject. it worked for a while, but after a bit, i ran out of ideas. i started using design techniques in origami design secrets. but i just cant figure out how to get my models to be based on 22.5 angles from those methods. any design method suggestions?
User avatar
orislater
Buddha
Posts: 1211
Joined: November 5th, 2009, 3:57 am
Location: somewhere with a piece of paper in my hand
Contact:

Post by orislater »

i think you could use circle packing with the circles fixed to 22.5
my flickr tissue foil is for noobs! mc FTW!!!!
garrasdecaiman
Junior Member
Posts: 106
Joined: February 17th, 2010, 9:54 am
Location: Xalapa mexico

Post by garrasdecaiman »

Fixing the circles to 22.5° is not really the way circle packing works
circle packing is not very good at achieving Any fixed angles.
Since the circles are arbitrary in their radiuses and their position is a compromise between various arbitrary circles and the edge of the paper, you will probably end up with any other angle exept in the 5 equal length pointed base case which is the bird base, aside from that case you can observe eaven in design secrets that some similar equiradii bases are in fact not related to the 22.5° angle eaven if you are willing to ovserve the seemingly simplistic binary division of the original 90° angle of the square corner.
In the first and most simple case of one maximized circle meaning one single point there are no constraints to which angle you might want to take to thin the corner in to a point since there are no other circles with which you must satisfy the active paths between the centers.
With two such circles you will have a fishbase-like construction which in principle will be easier to solve using binary divisions of 90°but may as well be managed with 15° angles or similar tertiary (eaven more) divisions of the original 90°
With the next eaqually lengthed circles you are forced to use a 60° angle or multiples of 90°/3 be it 60° or 30 or 15, if you insist in using a 22.5° constraint in this case you will be forced to add a river to the circle packing and lose a very large percentage of effectiveness in the distribution of paper compared to the maximum length of points attainable.
in the 5 point case you have the bird base as I have mentioned and
In the 6 point case you are forced once again to resort to 90°/3 divisions.


So as we have seen up to this, we have only encountered a 22.5° perfect circle packing yet, and we have analyzed 6 cases. As complexity increases the precise division of angles like the nice 90/4 or 90/3 and their multiples becomes less common.
In contemporary complex cicle packings when we want to achieve miltiple lenghts or ratios of points we seldom encounter precise angles like the ones we would like to work with.
To overcome this barrier as origamists we have to find middle ground by:

Allowing a point to become longer or shorter by small amounts to obtain convenience in finding their reference points.

Finding the exact reference points for the centers of the circles.

Forcing precise angles on the circle packing (which is what you were thinking of), but jeopardizing the effectiveness of the whole structure making the whole model smaller compared to the original size of the paper and gaining exess paper in the thickness of the points.

Finding a middle ground in all of this to obtain a compromise between the optimum length of points and ease of foldin.

But ultimately the most simple answer would be the best as occam would say

Get away from circle packing and: GET INTO BOX PLEATING!!

Circle packing is a very different animal from box pleating. Box pleating is your best bet, and although it is tedious and labor intensive before you actually beguin modifying your square in to the base, it almost always uses 22.5° angles or it's multiples, and if not you allways have the nice grid to help you.

Anyway although verbose (and I suppose very badly written since english is not my mothertongue) I hope this helps.

criticism and comments are welcome !

X
User avatar
DavidW
Senior Member
Posts: 261
Joined: July 16th, 2005, 10:44 pm
Location: South Carolina

Post by DavidW »

Get away from circle packing and: GET INTO BOX PLEATING!!
Going back to box pleating is not the answer (though many have done it) because it is abandoning decades of progress in design to retreat back to the 70s where people box pleated using foil (since many box pleated designs are not possible to fold using regular paper). Box pleating is not economical by any stretch of the imagination, and has really only found its niche for elegant design in human figures where the extra layers are put to good use extracting detail that otherwise would not be present.

The strength of circle packing design is the opposite of box pleating-- it makes such economical use of the paper that more often than not it is foldable with any thin, strong paper. I think that the most obvious example where that rule is broken is in insects where Lang has you use repeated sinks to narrow flaps.
User avatar
origamimasterjared
Buddha
Posts: 1670
Joined: August 13th, 2004, 6:25 pm
Contact:

Post by origamimasterjared »

Um David, box-pleating has experienced a HUGE rebirth, and improved by leaps and bounds since. It seems your perception of box-pleating is what's stuck back in the 1970s. You realize Robert Lang is now using box-pleating almost exclusively, right? Circle-packing may be most efficient in terms of paper usage (and even then it is often not, as it may require lots of pleat sinking to achieve the desired effect, which wastes a ton of paper), but there are other efficiencies to take into account, such as foldability/ease of folding and the shapes of the flaps themselves. This is where a true 22.5˚ design can be far nicer. Look at Satoshi Kamiya's work, and see how remarkably efficient it tends to be in terms of paper usage. Hideo Komatsu's too (though his design style is very different).

If you want to get into 22.5, box-pleating (or if you prefer, square-packing) actually is a good way to start, sort of. Any grid-based design can easily be converted to 22.5˚ angles. It's not true 22.5˚ design, but at least the angles are nice. Look at some of Brian Chan's CPs to get an idea. Also, Sipho Mabona's Crab is a fantastic example of a diagonal-box-pleated design with 22.5˚ angles.
User avatar
DavidW
Senior Member
Posts: 261
Joined: July 16th, 2005, 10:44 pm
Location: South Carolina

Post by DavidW »

But Jared you're NOT talking about box-pleating. Lang's more recent efforts are mostly in hybrid approaches that combine elements of circle packing with box-pleating. That is a genuinely new modern approach to design. And I believe Chan and Mabona take a similar approach.

Lang's approach is in stark contrast withe the amateur efforts that have not been focused on the way that Lang does it, but instead on classical box-pleating, no different at all from how it was done in the 70s.

All it does is emphasize again the divide between a few expert masters and the handful of would be designers that eagerly devoured ODS but found they could only apply the chapter on box pleating.
garrasdecaiman
Junior Member
Posts: 106
Joined: February 17th, 2010, 9:54 am
Location: Xalapa mexico

Post by garrasdecaiman »

Actually I can observe that Mr lang has occupied many styles and is at the breaking point in many different disciplines, for example in pure circle packing and precise reference finding he has made the scorpion from insects 2 which is a very strange model since you take a long time finding the circle references but once they are found and the active paths found the whole model is practically finished from the base in very simple thinnings.
In box pleating he has the longhorn beetle, the butterfly.
and some very interesting tasselations, the american flag for example, some volumetric folding like the numbers for wired, and the vases.
Furthermore he has done some breaktrhoughs in new styles like the hexagon pleated scorpion.

22.5° are a good place to start designing because of the easyness of finding the reference lines but constrains the creativity to birdbaselike molecules and box pleating molecules, these two combined techniques are in fact very powerful but as Mr. Brill would say they constrain your creativity. And although some very impressive new models have been achieved by these techniques they usually seem dated and inefficient, for example Mr. Sirgo's "papiroinsectos" or "imaginado en papel" relies very hevily in 22.5° angles and some are a constant fight against the paper to force long lines from birdbases.

And sorry but it's not easy being a would-be designer hidden in a room in the south of mexico, compared to Mr.Lang's being able to go to many conventions, seeing great origamists and theorists and being allowed to play with state of the art laser cutters.
I'm not a real fan of box pleating but I do recognize that some wonderful works have been done from that technique.
newbpcpfolder
Senior Member
Posts: 372
Joined: June 7th, 2010, 5:37 pm
Location: India
Contact:

Post by newbpcpfolder »

@ garrasdecaiman
I agree with you on every point - I am a circle packer myself, but still I'm trying to learn it. I fix the angles based on the diameter/radius of the circle, and usually, my circle packing models are also based on grids. The grids also help me fix the angles.
I do not agree with you on 1 point however - that box pleating uses 22.5 AND its multiples. Not ALL multiples, however. if it even uses 22.5, 67.5, 11.25, etc., it cannot be considered BP. It does not ALMOST ALWAYS use 22.5, though it uses some of its multiples:0, 45, 90 and 180. only models with these angles are considered BP. If 22.5 is used for thinning the flaps, it can still be considered BP, as you thin the flaps with it, and not use it as a part of the design itself. For example, you can take either Sipho Mabona's mantis or Lang's Bull moose.
I never used 22.5 as a design part in any of my BP models - I only used the 4 angles mentioned above. I used 22.5 for thinning certain flaps.
User avatar
orislater
Buddha
Posts: 1211
Joined: November 5th, 2009, 3:57 am
Location: somewhere with a piece of paper in my hand
Contact:

Post by orislater »

i thought you were a boxpleater?!
my flickr tissue foil is for noobs! mc FTW!!!!
garrasdecaiman
Junior Member
Posts: 106
Joined: February 17th, 2010, 9:54 am
Location: Xalapa mexico

Post by garrasdecaiman »

Yes but, as you have explained 22.5° multiples implies that angles like 22.5*0=0°, 22.5*2=45°, 22.5*=90° and 22.5*8=180° and because you use binary divisions in the thinning it means that you occupied these instead of, for example 15° multiples in which 15*3=45° and the other angles can be attained.
So in fact you have used the 22.5° angle as a starting point for your model eaven if you have not actively used it by designing reference points stemming from the angle.
And since we have established the whole useful angles as a system it does not make a difference if you have used one or the other since they are all related. I could also make a case for 11.25° angles or to make it clearer direct binary divisions of a 360° base circle. Or similarly 2PI/4=1/2PI=45° so you have used PI, Pi/2, PI/4 and for thinning PI/8 and possibly PI/16.
I hope this makes clearer what I was talking (well writing) about
X
newbpcpfolder
Senior Member
Posts: 372
Joined: June 7th, 2010, 5:37 pm
Location: India
Contact:

Post by newbpcpfolder »

the point is, you can redesign any grid based model using a 22.5 degree geometry. for example, Sipho Mabona redesigned his flying locust in 22.5, though it is a box-pleated model. he used 22.5 degree fo thinning the flaps in the head(antenna, mouthparts, etc.), but from a structural point of ciew, it is strictly BP. In the 22.5 version, the basis of that structure is still based on BP, isn't it?
http://www.mabonaorigami.com/blog/2009/10/07/locust-cp/
User avatar
origamipete
Forum Sensei
Posts: 544
Joined: August 3rd, 2010, 4:28 pm
Location: the heart of europe, that's my home, my castle =D
Contact:

Re:

Post by origamipete »

garrasdecaiman wrote:you will probably end up with any other angle exept in the 5 equal length pointed base case which is the bird base
last time i checked, the center flap on a bird base is noticably shorter than the remaining four. you have your bases confused :wink:
Post Reply