This is going to be one of those origami posts where I talk way too much about math. But before I get to the math, I will explain how you can make one of these things entirely with ordinary arts and craft tools.
“Ordinary tools” is the relevant bit here, since my understanding is that experts in curved-crease origami don’t use ordinary tools, they use things like vinyl cutters. When I first tried making these, I could not find any instructions for how to make these models using ordinary tools (I later found an article by Ekaterina Lukasheva), so when I finally figured out a method, I wanted to share it.
Making a template
Before we draw the creases directly on the paper, we need to make a template. The template ensures that each of the four curves are identical to each other.