#### Fold/Unfold

###### Computational folding/unfolding for zero-waste fashion

It takes up to 20,000 litres of water to produce enough cotton for a t-shirt and a pair of jeans, with up to 60% of it lost before reaching the cotton fields due to infrastructural inefficiency. Pesticide Action Network UK reports that 21,000 cotton farmers - many of whom are children cotton pickers in developing countries - die every year due to pesticide poisoning. Despite such heavy costs, on average, 15% of materials produced is simply discarded as offcut.

Fold/Unfold is a two-part project investigating zero-waste aesthetic possibilities from, first, 2D to 3D angle, then, from 3D to 2D angle.

## Part 1: Fold

The Metabolism movement formed in Japan in 1960 and was based on an ambitious vision of accelerated urbanism and advanced technology existing in parallel with an untainted nature, i.e. a selfsufficient techno-utopia. The key element to the movement was the use of identical modular units for the construction of whole cities.

The complexity of the set-up of Metabolist megastructures to be selfsufficient is apparent, yet, the simplicity of the idea of modular units that can make up whole cities provides a somewhat contrasting viewpoint to the concept. Interestingly, a new kind of science that specifically deals with this idea of a simple rule that generates complexity is Stephen Wolfram’s cellular automaton (Wolfram 2002, p. 23).

Cellular Automaton

The cellular automaton refers to a simple program with very few set of explicit rules and the behaviour of which can be instantly visualised for analysis. It consists of a row of cells, each row referring to a specific step in the programming and each cell coloured either black or white. Using this anomaly of a simple rule that is able to generate complexity, this project investigates the design possibilities of a zerowaste garment for which the patterns were generated by a cellular automaton.

Several patterns generated by cellular automata were translated into laser-cutting templates and cut into heavyweight wool suiting. The final fabric sheets with the laser-cut designs were used to generate interesting drape on the body as an alternative to traditional patterncutting methods without producing waste during the entire process.

The original Fractal Trees cellular automaton pattern generated via Wolfram Demonstrations Project

A section of the original Fractal Trees pattern was used as laser-cutting template. Cut in a piece of square material without creating any waste in the process.

The original Arc Form Design cellular automaton pattern generated via Wolfram Demonstrations Project

A laser ready pattern derived from the original cellular automaton pattern . Each line is cut with laser without creating waste.

The original pattern generated using the ContourPlot[] function on Wolfram Mathematica

A two-tone simplified version of pattern on the left. Yellow lines indicate lines for lasercutting. Colour blocking used to add design interest for when draping the material.

The original pattern generated using the ContourPlot[] function on Wolfram Mathematica

A two-tone simplified version of pattern on the left. Yellow lines indicate lines for lasercutting. Colour blocking used to add design interest for when draping the material.

The original pattern generated using the ContourPlot[] function on Wolfram Mathematica

A two-tone simplified version of pattern on the left. Yellow lines indicate lines for lasercutting. Colour blocking used to add design interest for when draping the material.

## Part 2: Unfold

Can a 3D-to-2D approach supplemented with computational accuracy be a better alternative to traditional patternmaking, which is inherently a 2D-to-3D approach?

Unfold is an ongoing project that employs computational geometry in the patternmaking (or more precisely, pattern generation) process. Where traditional patternmaking takes a flat piece of fabric and cuts it into different shapes that are then stitched together to make 3D forms, Unfold explores the opposite, whereby a 3D mesh is cut where needed to turn it into one, or several, flat piece/s on a single plane. Doing this computationally allows the patternmaker to also incorporate zero-waste property into the final result by letting the computer to decide on the most optimal way to cut that will result in as few cuts as possible while making as efficient use of the given material as possible.

The inputs for the program would be: 1. the size of the material available (i.e. how efficiently it needs to use the material), and 2. maximum number of separate flat pieces that can result from the unfolding process. The output is the final shape of the cut pieces.

Further work is to include a generative function that will allow the program to make decisions on how the 3D form (i.e. the drape on the body) could look in order to optimise for the criteria described above. Naturally, once this stage is completed, there are possibilities to extend on the criteria to include more functional properties into the final garment such as having extra layers in certain areas on the garment to give better durability or protection from the elements.

The principles of Unfold can eventually be adapted for zero-waste tailored clothing with the help of 3D body scanning.

###### Example unfolding of a simple pyramid mesh (a network of the polygons in the pyramid is shown next to each step)

###### 00:34 Demo of the unfolding stages

Unfold process

(work in progress)

The mesh representation of the target 3D object gets unfolded into 2D space by flattening the “creases” (edges connecting pair of adjacent polygons) in an iterative manner until all polygons of the 3D mesh end up in the same plane. In the process, we invariably end up “cutting” the object along some “creases” while simultaneously rotating the polygons into co-planar arrangement until the initial 3D shape is completely flattened. We do this:

• by searching for a single edge which when cut along would split the object into 2 disconnected “modules” (collection of polygons). If none exists, we create such a “hinge” edge by cutting minimal number of other edges. We do not cut along the “hinge”, but rotate one of the “modules” around it instead.

• Then in the unfolding step we look for the angle of relative rotation of 2 “modules” connected by the “hinge” edge that brings the 2 polygons connected by the “hinge” (“base” polygon and “flap” polygon) into the same plane and carry out the rotation. This rotates the entire smaller half of the object to bring “base” and “flap” into the same plane.

• Once the rotation is done, we join the vertices of the “base” and “flap” polygons to produce one large polygon by having “base” absorb “flap’s” vertices.

• We repeat the process until only 2 large polygons are left and rotate them into the same plane, making the entire 3D object unfold into 2D space.

• In complex shapes of many mesh elements, we run into the problem of unfolded, in-plane shapes having to overlap on top of each other. We solve the problem late in the unfolding process to eliminate the overlap with minimal number of additional cuts, further optimizing the 3D to 2D translation.

• In case of an octahedron, our procedure would severe 3 of the 4 edges connecting the 2 pyramids the octahedron is made of and unfold at the edge left. This would join the 2 triangular sides, one from each pyramid into a single quadrilateral. Then it would proceed to join it with the rest of the triangles in an iterative fashion.