The Origami Forum

Christian, you are now saying complete nonsense. A crease-pattern DOES NOT, CANNOT, and WILL NOT contain any information as to the convexity of a vertex. If two half-creases intersect, they could be folded either as if their intersection is convex or concave. No "infinitisimal" mountain/valley creases.

AND even if you do not accept the above, Eileen's example of a single crease that can be opened and closed as necessary is perfect.

We have not come with "funny definitions". The definition of "convex" is something that existed WAY before our discussion started.

I also do not agree with your remarks on curved surfaces and bending the paper. You are the one the defined "very soft creases" there...

I also gave an example above, so not only Wolf gave one.

As for examples that contain only one or two creases: a nice thing about disproving something is that it is sufficient to find a single example to disprove a conjencture. Usually these examples are very very simple, such as my overlapping edges example. It is obvious from my example that the same phenomenon holds for very complex models as well. Say you have a human figure with hands that cross. Change the order of hands. This changes the model without changing the CP.

[Edited by saj to remove profanity - 18/11/2004 @ 19:28]

bshuval wrote:Christian, you are now saying complete bullshit. A crease-pattern DOES NOT, CANNOT, and WILL NOT contain any information as to the convexity of a vertex.

Come on Boaz, don't be so harsh - at least he's identified one of the major limitations of CPs as they are currently drawn! Imagine how much easier doing a CP would be if the sense of each vertex were given as well. In fact, I think I'd rather have a CP containing information about each vertex, but no mountain-valley (MV) assignment, than the other way around. Singularities are sooooooo much fun to deal with...NOT!

Regarding "funny definitions" and "trivial examples", well, that's exactly how mathematics and science works - isn't origami just mathematics anyway? . It's amazing how many hypotheses have been toppled just because of that one little trivial example...
It's also not very useful to have a hypothesis that works only if certain complex conditions are met (50 creases? 100 creases? at least 50% of them intersect?)

Anyhow, at least we're now stuck at the definition of what makes a flat-fold distinct - particularly when it comes to handling overlaps. I don't have a rigorous way of defining that yet, but the handwaving one would be if you could turn one overlap state to another overlap state without opening up creases too much. Sort of like a topological transformation, but with a lot of added constraints (such as where the flaps hinge, etc).

wolf wrote:

bshuval wrote: Imagine how much easier doing a CP would be if the sense of each vertex were given as well. In fact, I think I'd rather have a CP containing information about each vertex, but no mountain-valley (MV) assignment, than the other way around.

Hi my first post here although I have been reading the boards for over 2 months I just registered today.

Has anyone ever seen a CP with this vertex indication? If so please provide the URL

Thanks in advance

I got really interested in this vertex assigning method and I had been folding a model someone had requested help for on another topic so I just joined the 2 topics into one assigned CP. For simplicity I only noted the convex vertexes with the ^ sign. The ones that are not noted should be assumed as concave.

If someone wants to try it and let me know their experience, the vertex assigned CP is located at:
http://www.angelfire.com/co/cubo/Rabbitcp.html

The images of the finished model and the original CP are at: http://www.h5.dion.ne.jp/~origami/e/rabbit.html

I would have included the image directly into the post but Angelfire does not allow direct linking

TheRealChris wrote: it's impossible to change a model without changing something. and in the moment you change ANYTHING, it will produce a different crease pattern (even if it would only be a very little crease somewhere in another crease.

so why don't you just give a concrete expample instead of a loose indication?

I will give a concrete example of a loose indication!
The same base, the same M/V is used for Ronald Koh's rhino and Another Creator(cant remember the name)'s Wolf. Understand?

If we consider a crease pattern made of three types of creases, mountain, valley and neutral hinge creases, and we add them all to a crease pattern in the final shape of the model we will have precisely one model and not any others.
If the neutral creases are not clearly marked we will have to make a decision about whether the buttons will be concave or convex.
As for chris´ discussion it is true that a fully M/V/N assigned crese pattern will only make a single model you would have to carry the crease pattern to the full finish instead of the base, and take into account the precise folding of neutral creases.
CP´s are usually only drawn out to the base of a model, upon which the final shaping will be applied, eaven a finished crane will become difficult if you diagramm the creases of all the finishing steps, and furthermore if for example you change the shape of the head from the simple traditional, or a yoshizawa style, or add a beak the crease pattern will change making it a different model according to chris.
What I´m going after is:
If you have a fully assigned crease pattern with moutains, valleys and neutral creases you can only have a single model.
If instead you add vertex orientation to a crease pattern you will only have a single model.
This only holds if the crease pattern is totally finished and shaping is not allowed, and the models are flat folded.

X

This is actually not true. Layers, locks and pockets are one example. They often add nothing to a crease pattern.

Take this CP:


There are five different ways to fold it. This is an example of layers/pockets

Or for one that's an actual design, check out my pyramid CP:
http://www.flickr.com/photos/oriholic/4958288168/

That CP contains every single necessary crease, but there are at least three ways to fold it (actually, there are 2 x 3 x 2 = 12 ways!) There are actually two pocket-locks, one which is not as obvious.

Hope this helps.

Also, hinge creases aren't neutral. They have to have a certain orientation, based on the creases around them.

All crease patterns can be collapsed into normally one base, normally with several ways to do so. Most complex models will have one base, though the more simple ones may have several deviations of the designated base.

dude i thought were dead! im glad your not