A while ago, I was in a bookstore and spotted Pasta by Design, a book featuring a pasta catalog and the corresponding parametric equations to plot them in 3D space.
This book by George L. Legendre started a small obsession with me wanting to apply these parametric equations within Cinema4D. It took quite a bit of research to find a way to bring these equations into C4D, but I eventually found a way (more detail below).
While some of these shapes would’ve been easy to generate using simple primitive splines, I was keen on the idea of having mathematical formulas generate all the geometry. The idea that there would be no modeling or spline-based geometry is really interesting; the beauty was in the process of generating the geometry based on the purity of formulas. Of course, the lighting and shading help a lot in the aesthetic sense.
The Formula Spline object in C4D plots in the only 2D and allows for one variable, when the 3D formulas included in the book required a slightly more complicated setup.
I stumbled on a multi-platform 3D Graphing Calculator by the guys over at Runiter, which not only allowed me to graph in 3D properly but allowed for OBJ export and choose the amount of detail/subdivisions for the generated geometry.
In C4D, I’d import the pasta geometry and give it a bit of thickness (the graphing calculator has the option to add thickness, but I ignored it, wanting to do aesthetic modifications within C4D). After that, I’d UV Unwrap it and start adding some custom shaders that would give a pasta-like feel.
I was particularly happy with the way that the 3D Graphing Calculator generated a surprisingly clean topology, which made thickening and UV Unwrapping of the geometry considerably easier.