Crease Pattern

This piece is one I designed for my show at Furman University in 2014. This is the widest piece I’ve folded: I used one sheet of Elephant Hide cut and re-glued to make a total circumference of 126 cm (diameter of 40 cm, or 16 inches). Here’s the crease pattern, showing the painted areas on the paper:

I recently posted the crease pattern for another piece from my Intersections series. Here’s another from the same series.

This design from 2013 is one of my early pieces from the diagonal shift series. The crease pattern is below:

I folded a variation in 2014 with the same crease pattern. The only difference between these two pieces is the painted pattern.

The four-part intersections bowl is a model I designed in 2014, and I posted some photos in progress when I was folding it. I drew the crease pattern before my solo show at Furman University and displayed actual-size printouts of the crease pattern on the walls there, but somehow it never made my blog. So now it’s time to rectify that!

The crease patterns for all four pieces are below, from the tallest piece to the shortest one. Click any of the images to get a higher-resolution version.

I designed a variation to my crimp-bends last spring, and here is the crease pattern. The concept is similar, but instead of being based on two sine waves, this version is based on one sine wave and one straight horizontal line. In this variation, part of the flat plane joining the top and bottom tubes is exposed. So far I haven’t figured out a mathematically correct way to place the central line such that the joining plane folds flat, but it comes close enough to work in practice.

I posted a photo of a test model of the downhill diagonal shift earlier this year. Here is the crease pattern for that model. The central part of the crease pattern is exactly the same as the standard uphill diagonal shift I’ve posted crease patterns of before. The top and bottom sections are the crimp-bends I recently posted and build on the sine waves used in the central diagonal shift. Since each portion of the crease pattern is a distortion of a tube, it’s fairly straightforward to stack these in all sorts of interesting combinations.

I previously posted images of these crimp-bent tubes that I designed earlier this year, and here are the crease patterns. The top and bottom edge of each bend are based on sine waves. The angles of the internal crimps on each vertical gore use the same math as the diagonal shifts, where each diagonal fold is angled toward one convergence point.

I recently posted photos of several large-scale origami pieces I folded. These pieces incorporate painted diagonal elements, but the folded patterns are not much more complicated than the ones from the series of tutorials I wrote a while back.

Here are the crease patterns for two of those pieces (and a few more comments below):

In both of these pieces the painted regions have sinusoidally curved edges that in the folded form create the illusion of flat planes. This is all based on geometry: a plane that cuts through a cylinder at an angle creates a sine wave when the cylinder is unrolled. My forms are more complicated than just cylinders and there are places where the paper overlaps. That means a sine wave doesn’t create a perfect plane, but it’s close enough for the eye to follow.

The crease pattern for the turquoise vase is exactly the type of pattern I described in my earlier tutorials. The purple vase is similar – the top section follows the same type of pattern, and the bottom part is a simple corrugated pattern I previously used in my diamond vases. The corrugation requires some extra glue at the base, but it’s a similar level of difficulty to fold as the curved-crease pleats.

I’ve previously posted several crease patterns for my diagonal shift designs. Since posting those crease patterns, I designed a diagonal shift variant where the top and bottom halves of the paper form tubes of different widths and folded several models based on that design. Here are some crease patterns for a couple versions of diagonal shift variants. The dimensions on these don’t quite match any of the models I’ve folded, but they at least show the approach I used.

First, the single diagonal shift variant:

The bottom half of this crease pattern is identical to the crease patterns I posted before. Just above the middle, the diagonal lines only go partway past the middle of each gore, and the top section forms a narrower tube. This crease pattern gives something similar to the central part of this model.

These designs can also be combined in a couple ways. One option is to mirror the diagonal shift element vertically, giving a double diagonal shift pattern like the one in this vase:

Another other option is to also shift the top diagonal shift section over by 8 gores (half the width of the paper, excluding the overlap), which gives something like this model:

The math behind these designs is a good bit more complicated than I enjoy doing by hand, so I’ve set up spreadsheets to automatically do most of the math for me. I haven’t written about that aspect yet, but I might do that at some point when I have time.

Recently I have folded several test pieces and a finished model incorporating a diagonal shift element. Here are several crease patterns showing how that element works, along with some notes and folding hints below:

For each design, the “curves” marking the top and bottom of the diagonal shift are based on sine curves. The sine curves are offset by one gore (the top curve is shifted one gore right relative to the bottom gore). This allows all the mountain folds to cross the centers of their gores at exactly the same height. Without this offset, the crease pattern will not collapse correctly.

One of the biggest challenges in designing these forms is figuring out how far apart the two sine curves need to be. I wrote an Excel spreadsheet to automatically calculate the correct distance based on the angles and distances in the crease pattern.

Of course, this element can be incorporated into more complex models, like I did recently. I’m working on folding more models of this sort.