Parametric Pasta

A while back ago I was in a bookstore and spotted Pasta by Design, a book featuring a catalogue of pastas 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 really easy to generate using simple primitive splines, I was keen on the idea of having all the geometry be generated by mathematical formulas. The idea that there would be no modelling 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 helps a lot in the aesthetic sense.

SaccottiniFusilliGnocchi

The Formula Spline object in C4D plots in 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 properly graph in 3D, but allowed for OBJ export and choosing 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.

Castellane Cappelletti Agnolotti BuccoliI was particularly happy with the way that the 3D Graphing Calculator generated surprisingly clean topology, which made thickening and UV Unwrapping of the geometry considerably easier.

The biggest challenge was changing the mathematical formula to computational notation, and while I remembered most of my order of operations, I tended to over-complicate the formulas and would make the graphing calculator bug out. Thankfully, long-time collaborator and Cornell graduate Alex Marin was kind enough to proof-read and correct my embarrassingly complicated adaptations.

Here’s an example of the 3D Graphing Calculator UI (left), an example of how the data is presented in the Pasta By Design Book (top-right), and a result of the Castellane formula (bottom-right).

pastelera An early test using displacement maps in VRAYforC4D.

castellaneAn early shading test using VRAYforC4D’s Subsurface Scattering layered in a Blend Material.

pasta_SSS

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7 comments

  1. Great pasta! A friend of mine has this book, it’s great to see the equations brought to life as it were. Can I ask what font you use for the captions?

  2. Pingback: Cuisilinear | these things i work on

  3. HI, I was so amazed that I ordered the book! just received it and I was hoping to open into the the Graph calculator software type whats in the book and jobs were done! Could you help?? I would like to be able to try out this amazing technique you came out with! Thanks, Michelangelo

    • Hey Michelangelo, glad you liked it! There’s a link in the actual blog post to the graphic calculator software I used to generate the geometry based on the formulas – after getting that geometry I brought it into C4D as an OBJ object. Hope that helps!

      I saw your tweet – yeah it’s not as easy as it sounds, I know I struggled for a while before being able to get it right. These links should help you figure it out:

      https://en.wikipedia.org/wiki/Order_of_operations

      http://www.purplemath.com/modules/mathtext.htm

      Basically just convert the formulas into computer notation, and remember that some of those formulas have variables which you need to specify (the graphic calculator allows you to determine variables and inputs for them).

      Have fun!

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