Diagonal shift variant
For the past couple months I have been exploring various designs using a diagonal shift element, working up from simple test models and crease patterns to more complex designs. Now I’m exploring a new variation of the same theme.
In this test model, I am using the same basic diagonal shift element but also changing the width of the tube above and below the shift. This gives the design a bit more flexibility in how I can use it. The change in width only adds a little complexity to the crease pattern, but it makes the model a bit more challenging to collapse.
Double diagonal shift vase 2
This model is a continuation of my diagonal shift series. In this piece, I pushed the off-balance look I started exploring earlier in the series to its limit. As before, I put small rocks in the bottom of the model to keep it balanced. Since the paper is so light, the little bit of extra weight allows me to create shapes that would be nearly impossible in other sculptural media. Just like I’ve been doing throughout this series, I enjoy combining simple, elegant forms with unexpected elements.
The double diagonal shift is challenging to collapse. This version where the two shifts are going in the same direction is more challenging than my last version where the shifts went in opposite directions.
For this design, I incorporated a gradient of metallic paint, from silver at the top to copper at the bottom, and left the black paper exposed on the planes of the diagonal shift. As always, I painted the paper before folding it.
Double diagonal shift vase
This piece builds on my recent test models and copper vase using a diagonal shift element. This is my first model incorporating more than one diagonal shift into the same model. It’s certainly more challenging to collapse the model – I almost had to wrestle the paper into shape. It’s also particularly difficult to do any sort of shaping to the middle tier since there’s no way to reach inside of it to manipulate the paper.
As always, I painted the paper before folding it. Since the folds created strong diagonals, I used the paint to incorporate additional diagonal design elements.
As was pointed out to me on Flickr several months ago, these sorts of designs have a bit of a surrealist twist. I had the original idea for this series shortly after visiting the Magritte Museum in Brussels, which probably influenced me subconsciously. My origami has always had a contrast between simple, elegant forms and an engineering aspect of analyzing how the shape is constructed from one uncut rectangle of paper. This series takes that analysis aspect and makes it more explicitly part of the shape itself.
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:
Diagonal shift crease pattern 1 – small shift (click to enlarge)
Diagonal shift crease pattern 2 – medium shift (click to enlarge)
Diagonal shift crease pattern 3 – large shift (click to enlarge)
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.
Copper diagonal shift vase
After folding several test models with a diagonal shift, I was finally able to incorporate that design element into a more complex model. For this model, I used black Elephant Hide paper and painted all of the paper except for the diagonal shift element with gold and copper acrylic paint. Because the top half of the model is shifted so far to one side, the vase normally would be very unstable and prone to tipping over. I put a few pebbles in the bottom of the vase to weigh it down. Since the paper is so light, it doesn’t take much extra weight to make it stable.
I recently folded an initial test model with a diagonal shift. At that point, there were still quite a few problems with my test model, including a combination of mathematical complications and folding difficulties. Since then, I have made several changes that help solve those problems without significantly changing the appearance of the final models:
Diagonal shift test models
To make the math easier, I created an Excel spreadsheet that automates most of the calculations based on the distances and angles between each fold. This is the first of my models where I have relied on the computer to help figure out the dimensions. I also made a change to the crease pattern that simplified both the folding process and the math.
In my new folding process, the diagonal shift creates a half-twist in the paper, so the paper on the far left above the diagonal shift ends up on the far right on the bottom half of the model. The amount the top and bottom halves are shifted along the diagonal is related to how steep the diagonal is. When the diagonal is close to horizontal, there is very little shift. As the diagonal gets steeper, the amount of shift increases.
I am planning on incorporating this design element into more complex models and hopefully posting some crease patterns soon.
In my recent oval models, I have been combining segments of different sizes of circles. Here I’ve taken the same idea of combining portions of circles in a different direction. This corrugation is based on three equally sized semicircles that alternate directions like in the letter S. As the outer circles get larger, the inner circle gets smaller, and vice versa.
S-curve corrugation (back)
In this model, the outer edges were challenging to fold because there is not much tension to hold the paper in place. This design could be extended indefinitely as a series of repeating curves, or it could be combined with circles of other sizes to create a closed form like in my oval forms.
Building on my recent oval test model, I folded this bowl based on an oval. Again, the oval is made of portions of circles of two sizes. Here, the radius of the small circle is 2″ at the widest point, and the radius of the large circle is 6″ at the widest point. The collapse of the bottom half of the form was fairly straightforward, but the top part was more challenging because the form wanted to become more circular. Overall, I think ovals will work fairly well for relatively short, simple forms but will be challenging for taller forms and more complex forms. Even though I think a lot of interesting things could be done with ovals, I’m using the ovals mostly as a building block toward some of my other ideas that are in the works.
My article “Designing and Folding Curved-Crease Pleated Forms” was recently published in The Fold, OrigamiUSA’s online publication.
You have to be a member of OrigamiUSA to access the article. If you’re not a member and want to know what the article is about, most of the content overlaps with my three recent tutorials on the concepts, math, and folding techniques behind pleated origami forms.
Seed pod bowl
The seed pod bowl is one of my most popular models, and I’ve gotten more requests for its crease pattern than for any of my other models. I finally drew the crease pattern:
Crease pattern for seed pod bowl (click to enlarge)
As with all my crease patterns, the red lines are mountain folds and the blue lines are valley folds. The top side of the paper will become the inside of the form.
A few notes:
- The mountain/valley pattern on this model is the opposite as it is for most of my models. Viewed from the inside of the final form, the straight folds are mountains and the curved folds are valleys.
- Since this model does not have a flat base and is not a tube, the collapse process is a bit different that my other models. Briefly, I used a combination of tape and glue to hold the creases in place at the two ends of the form, and wet-folded to create the curved form.
- Given the crease pattern as drawn, the model will be curved all the way around and not sit flat. I fixed that problem by making a small dent where I wanted the base (not shown on the crease pattern).