## CURVED CREASING

##### How could one go about thinking of making processes that are like nature?

#### Ford Foundation

###### Graduation Thesis Project

Curved creasing transforms a flat piece of flimsy material into a much stronger material with the ability to resist force. I created an algorithm that allows for the creation of radiolarian type structures. The algorithm directly outputs a CAD file that can be used to laser cut and assemble the structure.

#### Computing Creases

Each individual shape has unique geometry and curves that join together to form the larger structure. These curvatures are calculated geometrically. The parts are numbered and the 3D visualization provides the instruction on which part to connect where.

Given a mesh, the length of each segment is easy to calculate. The challenge is with the in-plane angle. What the in-plane angle defines is the angle of the segment when projected into a plane that is perfectly tangent to the surface. There were certain mathematical techniques used to derive this, but once it was figured out, all the pieces came together. Another thing that I had to be careful of was chirality. So the orientation of each piece had to be carefully put and accounted for all throughout the making.

##### Curving lines help form the most basic element through which we can reach other dimensions.

#### Computing Creases

One of the key insights came from the fact that when the paper is folded in the 3-segment hub-like manner, the dihedral angle can be controlled by simply folding the paper at the crease. The more the paper gets folded, the larger the dihedral angle. This basically makes it such that the computation for the dihedral angle doesn’t even need to be accounted for! The material and the crease pattern will automatically take care of it. This leaves just 2 parameters that need to be calculated - the length of each segment and the inplane angle.

#### Failures to Success

The first few paper trials didn't end up working out. There were errors in calculations and the algorithms. Through iterations I was able to solve the errors and generate simple polyhedral shapes. It was interesting working out the geometry for these.

Eventually, I used the algorithm to build something more complex. The egg was the first step that while making it for the first time I wasn't sure how it would turn out.