Any ideas how to model this origami piece?

It is a square piece of paper that ends up looking like a hyperbolic paraboloid, but my math teacher says it is not one. As the number of folds approaches infinity, I guess someone has already proved that it is not one. Thanks, Chris

Attachments:

origami1.3dm, 68 KB

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Permalink Reply by Chris K. Palmer on February 10, 2010 at 9:19pm

Chris,

To start when it folds there are triangular faces being created that you need to model. You may try to play with Tachi-san's Origamizer to see it in action but that is not to discourage you from reinventing his wheel in grasshopper land.

Good luck and drop me an email: chris@shadowfolds.com when you want to chat,

Chris K. Palmer

Permalink Reply by Evan C on February 11, 2010 at 2:17am

seems pretty straightforward... but are you trying to really model the physical sheet of paper (conserving area), or just get the general form?

Permalink Reply by Evan C on February 11, 2010 at 3:41am

basically, take any surface and subdivide it concentrically, rebuild as straight lines, move half the lines vertically, loft between lines.

the def is a little messy.

Attachments:

origami test.ghx, 464 KB

Permalink Reply by Chris Wilkins on February 11, 2010 at 5:52am

I've put no prior research into folding paper, so I don't even know the basics, but I do have the model in hand to help figure it out. You said "are you trying to really model the physical sheet of paper (conserving area), or just get the general form?" - Yes, I'm trying to model the physical sheet (almost). I do know that as the piece folds, that the faces become non-planar, and twist 90 degrees by the end of the fold. I enjoyed studying how you did that definition, but unfortunately, since it won't fold into a flat square of paper, its not exactly what I need to do.

So I'm just ignoring the paper in between the folds at the moment. For now, I'm just trying to model the movement of the straight lines along the folds. I think that if we take the paper as zero-thickness, then those can stay straight. Not sure though. Thanks!

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