# Algorithmic Origami: an Exploration of Expressive Form in Sheet Metal

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## Introduction: Algorithmic Origami: an Exploration of Expressive Form in Sheet Metal

Origami, from ori meaning "folding", and kami meaning "paper" has traditionally been the art of paper folding. The idea is that you start with a sheet paper that fold into sculptures without cutting or gluing it.

This is a piece I did with a single piece of uncut paper.

Today with the help of math and other computational tools origami has evolved into an artform that opens new avenues of complexity and expressiveness. By understanding how the rules and connections between the placement of the folds as well as gaining the ability to visually simulate the final sculpture, the artform has evolved becoming increasingly diverse.

Kirigami is a variation of origami that includes cutting of the paper (from Japanese kiri "cut," kami "paper"), rather than solely folding the paper as in the case with origami.

There are essentially two types of folds in origami:

Mountain fold: where the crease goes up to form a mountain, this type of fold is often represented in Red

Valley fold: where the crease goes down to form a valley, this type of fold is often represented in Blue

Another piece of terminology that you'll hear is Crease Pattern.

Crease Pattern: This is the pattern of creases that you need to fold to reach the desired form.

Having a mathematical and an artistic disposition me and my good friend Udit Datta embarked on an exploration of form focusing mostly in the medium of metal to see how far we could we could take a single sheet of metal by folding and forming it.

In this instructable you'll see how we used a systematic design thinking approach to attain an artistic goal and also learn how to use computational tools to help you create these forms.

## Step 1: Examples

Here are some of the projects that we did using the tools and techniques learnt in this instructable.

## Step 2: More Examples!

Here are some of the projects that we did using the tools and techniques learnt in this instructable.

## Step 3: FreeForm Origami

In the these following steps we'll check out a software called Free Form Origami and Autodesk's Maya and explore various features and workflows moving between the two software to create awesome forms!

http://www.tsg.ne.jp/TT/software/

Extract the zip file, you can use any zip file extractor for this for example:

Once extracted you can simply open the FreeformOrigiami.exe file (no need to install it!).

Before we jump in here's a quick overview and walk through of the setup.

All of the tools are in the toolbar on the upper-left.

Start by going to Constraints > Simulation Mode and make sure this option is not activated.

Also check to make sure the option NonDev is also checked before opening a file.

Free Form Origami accepts two kinds of files: DXF and OBJ.

DXF is a 2D vector format that can contain lines, curves and polylines. To convert a file to this format from other vector formats like .ia, .svg, .eps, etc. you can use Adobe Illustrator's or Inkscape's 'Export As' option.

OBJ is a 3D Mesh file format so it contains 3D objects either in a triangular or quad based mesh. To convert to this format from other 3D formats like .stl, .amf, etc. use Autodesk's Remake or Repetier Host's 'Export As' option.

Now that we know how to convert files it's time to open one up!

We can ease in by opening one of the example files that come with the software.
Go to File > Open and navigate to the model-demo folder.

Open the file called 60grid-triang-small.

## Step 4: Software 2

Once you open the file, it's ready to be 'origamized'.

To navigate the view angle, use right-click drag and middle-mouse drag to 3D rotate and pan around the model.

Navigate to Apply to model > Origamize

You will be prompted with the following window.

The four buttons on the right are four different algorithms that give you different patterns on the surface, for fabrication in any material other than paper we found that the most suitable ones are star and truncated.

On the left of these buttons you'll see a slider, this slider defines the scale of the pattern which directly relates to it's the extent of the projection out of the 2D sheet, this could be described as its factor of bumpiness .

In most cases we found that moving the slider two clicks to right gave us forms that would be fabricate-able and aesthetic.

Next to the slider are some check boxes: the Nega checkbox tells the software to flip the orientation of the pattern along the surface.

Once you have selected the setting you want hit ok and watch the magic happen.

These are settings we used but please feel free to experiment and try all the other options.

While exploring the settings if you see that the model changes into a crazy amorphous and excited digital mess, then this means that the software was unable to resolve the surface. To recover you can either hit Ctrl+Z and try again with different settings or often what we found was that closing the software and trying the very same settings on the freshly opened software yields better results.

## Step 5: Software 3

Now that you have an origamized surface you need to add some constraints.

These constraints enable you to take the form from the computer and actually make it.

The constraints are in the Constraints submenu.

We'll go through the important ones from the top:

The first thing is to click on the Dev+No Overlap option. this makes sure that the form can be unfolded flat and fabricated.

Next click on the Avoid Collision option, this makes sure that none of the faces cut through each other and that the laws of physics remain active.

Next is the Avoid Thin option, this makes sure that none of the angles on the faces of the object are too small, which would make fabrication difficult.

After this add the Planer Facets constraints, this ensures that each facet remains planar.

The last two settings are Thin Limit and Flat Limit:

Thin limit controls the minimum sector angle on a facet, and flat limit controls the maximum folding angle for the valley and the mountain folds. For both of these settings we found that increasing these sliders incrementally allowed the algorithm to resolve without crashing. Do attempt to push the flat limit till 90 degrees as it is very hard to fabricate the object and reach the planned shape if you do not do this. Our recommended setting for the thin limit is atleast 20 degrees.

## Step 6: Software 4

This step is all about manipulating the origamized and fabricatable form, you can however apply these same steps to the form before it is origamized.

The changes you make at this point might crash the software so make sure to save incrementally! And remember that you can always undo the last change using Ctrl + Z.

Navigate to the Tool Submenu, in here we found 3 tools to be very useful forour workflow.

Move: This tool allows you to select any point or edge and move it to where you want it to be. Shift select to select multiple points to move them together.

Magnet Move: This tool allows you to move a region instead of a single point.

Stitch Vertices: This tool allows to have two vertices touch, this is often useful as a reference if you need your folded form to be accurate to what you have designed.

Using the tools and methods described above and in the previous steps you now have the ability to origamize an object into a fabricate able object.

## Step 7: Maya, Creating Base Surfaces

In this step we'll learn how to use maya and its polygon modelling tools to create base surfaces to origamize into sculptures.

There are two main approaches that we took to create our base surfaces: Creating base surfaces completely from scratch and creating a surface onto a 3d scan and.

We'll first go trough making a surface from scratch:

If you don't already have Autodesk's Maya, go to:

Once you have Maya open, we'll first learn the basic navigation:

Use Alt + left mouse to 3D rotate, Scroll wheel to zoom and Alt + Middle mouse to Pan.

Use the Space bar to go into multiview mode, hover the mouse over any view and hit Space again to maximize that view.

Let's create a primitive shape that we can modify: Navigate to Create > Plane

You should now see plane surface in the middle of your workspace. Use the navigation commands to look around it and get a feel of using those commands.

Next go over to the right and click on Polyplane1, you'll see some atrributes that you can change to modify this plane.

Make sure you don't add too many subdivisions as this complicates the origamize step that you learnt about earlier, we recommend not having more than 5 x 5 subdivision if you intend to work with metal. Change the scale to a proportion you like.

Next, right click and drag onto vertex and release the click. You are now in Vertex mode, here you can scale move and rotate individual or groups of vertexes. Using the same right click method you can enter into edge and face mode to manipulate those things respectively.

Once you are in vertex mode click on a vertex and hit W,E or R to move, rotate or scale the vertex, the same applies to edges and faces.

If you need to move the entire object you can go back to object mode by right clicking and hovering over it.

This is how you modify an existing shape to a shape you like. now let's see how to make shapes from scratch.

On the top right click on the little hammer icon .

Click on the quad- draw tool and then click on the work space 4 times, then hover between them and shift + click, you have now created a quad polygon! You can continue to add points and make a network of quads.

Polygon modelling in maya.

Multicut, QuadDraw, Live surfaces, moving vertices, edges and planes

View modes, Creating primitives and editing them.

## Step 8: Lets Talk Metal Fabrication

Now that we have the crease pattern, we can start actually making what we want.

In our research we explored several fabrication methods and materials.

In the following steps we'll discuss about the metal fabrication strategies that we tried.

There are 2 main ways to fold metal to get a sharp corner: Etching/Scoring the metal so that at the fold line the metal is actually thin enough to be folded. And the second method involves creating dashed lines where you actually remove material completely and alternate from meterial to no material.

Another important factor is the kind of metal and the thickness of the metal.

We carried out our exploration mostly in mild steel and aluminium, and tried out many different thicknesses ranging from 0.015 in to 0.04 in. What we found to be the ideal was mild steel at 0.02 in thickness.

Metal sheet thickness is often measured in gauge, here's a handy conversion table: http://www.firemountaingems.com/resources/encyclob...

Being at Autodesk's Pier 9 Workshop gave us the amazing opportunity to try out all the strategies we came up with.

We started our exploration with the scoring method, for this we used a water-jet to etch away most of the metal at the fold lines. We also tried the dashed line cuts on the water jet. We quickly ran into several problems that made us consider other fabrication strategies. Here's what we found: Every time the water jet starts and finishes a cut, there is a a delay of around 10 seconds, this doesnt sound like much but when you add up the time it actually takes to make the cut and then this delay multiplied by several hundred little dashed lines it ends up being an unsustainable approach to continue exploration. Another problem we ran into with the tool pathing software for the water jet was that it was unable to generate a toolpath for these complex network of lines , we had to break each file down into several layers making sure the layers lined up perfectly. For this we referred to Josh's wonderful instructable: https://www.instructables.com/id/How-to-Register-O...

Yet another problem that we faced with the waterjet approach was that when you cut large thin sheets of metal, it is very hard to effectively clamp it down. One work-around for this is to use a plywood spoiler board and to tape your work-piece down with double sided carpet tape. Even tough the tape is strong, at some point during the cut we found that the piece lifted up a bit and started oscillating and this caused the water jet to clog up which made the whole process even slower than it already was.

Using the water jet to score the lines does have it's advantages though, because you are scoring and not completely removing material at the crease lines, the overall object is completely opaque. There is something visually pleasing about seeing these facets subtly folded without having cuts going through their edges.

Weighing all of the advantages and disadvantages that we discovered from using the water jet led us to steer away from this amazing tool. We then shifted our efforts to try out fabrication techniques with laser cutting.

Although it is possible to etch metal with a laser cutter we found that the continuous heat on the fold lines makes the creases work hardened and this makes the metal brittle. This is why we used the laser cutter with the dashed lines approach.

## Step 9: Optional Parametric Dashed Line Algorithm.

To create the dashed lines we first used Illustrator to replace the solid lines with dashed ones.

To this open the dxf file from FreeForm origami in Illustrator.

As we tried our first Dashed line cuts on the laser cutter we found there was a lot of things we wanted to change but other than manually changing every single line to fit our needs we could not continue to use Illustrator to do what we wanted.

We needed to create an algorithm to parametrically do the dashing according to our parameters. To do this we first needed to define what our ideal line dashing algorithm was.

This is what we came up with:

Every crease line needs a tab at it's end and at it's beginning, and any crease line that was longer than 10 cm needed two addtional tabs dividing the crease line evenly. Every intersection should have a circle cutout to allow for enough space for the tabs not to be too close to each other.

With this general idea of what we needed we proceeded to use Grasshopper to create our ooptimized tab spacing algorithm.

First we imported our Dxf

Approach + definition.

## Step 10: Laser Cut!

Recovering from a crash

Cleaning out slack and sharp corners.

## Step 11: Folding Strategy

Now that you have your piece cut-out and ready to be folded, let's walk-through some folding strategies so that you'll be able to successfully fold your piece.

Start by looking at the 3D model on your computer, and get a general idea of what the piece looks like in your head. Then carefully look at the folds around the boundary of your piece.

Start by lightly trying to make the boundary creases in the direction that they are supposed to go in ( mountain fold or valley fold), remember to only start the fold and not completely finish the fold to where it is supposed to go.

Follow the boundary until you've got all those creases in, then go in one level and tackle the ones on the inside closest to the boundary. As you do this level you'll notice that parts of the model begin to snap into place. Continue in this manner going from the outside to the inside of the sheet until you have all the creases in the right direction. Now you can begin making the fold more prominent, start from the out side and go inward.

At the inner most section of your model use your thumbs to snap the model, if this doesn't work you can try use a screwdriver to concentrate the pressure.

It should take around 5 passes to complete depending on the complexity of your model. Be patient! If you don't fold your model by doing these passes you risk putting too much stress on some tabs and breaking them.

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