Introduction: 3D Printing With Mathematica

Picture of 3D Printing With Mathematica

Mathematica is a software program from Wolfram Research. Similar to something like processing, you can quickly see visual outcomes from typed commands. This program is mostly used for computation and creating graphs in the fields of math, science and engineering, but it can also be used as a graphic design and modeling tool. Unfortunately, it's slightly pricey, but if you already have a copy, using Mathematica for 3D models is certainly a way to get more bang for your buck!

Thanks to Mathematica's Export function, you can create geometric and complex 3D graphics and save them as .STLs for printing. With a little editing in Tinkercad and gentle finishing, resin prints from the Autodesk Ember can beautifully reflect light and color thanks to intricate polygons!

Let's get started. For this process, you'll need:

  • Mathematica
  • A Log-in to TinkerCad
  • Meshmixer
  • SLA 3D printer of your choice. I used the Autodesk Ember, which printed quite nicely due to great machine resolution!

Step 1: Render in Mathematica

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Open up your version of Mathematica and create a new notebook. We'll be using a simple script* that creates series of cuboids that are rotated around a core axis. By switching up degrees of rotation, we can get unique outcomes. To make things simple, I have included my notebook in the attachments. Download and open this to both play with models and understand the script.

When you're ready to download, Mathematica has an Export function that you can access from below your graphic in the GUI, or type in as a command (Export[filepath,"STL"]);

Useful tips for navigating in Mathematica:

  • Down arrow key - new cell
  • New subsection - command 5
  • Double Click a cell bracket to expand or contract it.
  • Free-form input // shift + enter will submit
  • capital letters on all command names [] for all command arguments {} for lists and ranges

Useful reference on 3D primitives

*This script is taken from a textbook, but unfortunately I have lost the reference link. I will upload it once it emerges!

Step 2: Edit in TinkerCad

Picture of Edit in TinkerCad

To avoid using supports that may disrupt the surface of the model, I simply uploaded my geometry into Tinkercad and removed the bottom half of the mesh. This way, it could print flat onto the build head, resulting in a clean and reflective surface!

Step 3: Place in Meshmixer and Upload to Ember

To prep this file for the Ember printer, I followed these steps:

1.) Import into MeshMixer

2.) Size to 35mm x 35mm

3.) Move to platform

4.) Export

5.) Upload to Emberprinter.com

6.) Slice and Print!

The Autodesk Ember user manual should have everything you need for getting your file ready to print on Ember.

Step 4: PRINT

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One you've checked for enough Resin and calibrated the print head, you can go ahead and print your Mathematica file*!

*See Katy Perry's infamous left shark standing victoriously on the print as a base. Printed by Daniel Porter.

Step 5: FINISHING

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I've found that nail polish acts as a great finish for prints. For this one, I painted the base red and the upper portion with clear nailpolish. The clear nailpolish creates a clear and reflective surface and the colored base makes for a print that's optically different depending on which angle it's held.

Step 6: More Fun in Mathematica

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The possibilities are near endless in Mathematica. Above are a few other files I tried rendering for other graphics oriented projects.

To play with any of my experimental notebooks, head on over to github.

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