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June 12, 2014 AT 6:00 am

Meshagons – tetrahedral finite element (FE) mesh sculptures #3DThursday #3DPrinting

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Check out Todd Doehring fascinating journey to solve a process for generating “Meshagons” using tools he uses more typically for creating models from MRI and CT scans! Meshagons – tetrahedral finite element (FE) mesh sculptures. Via Fabbalo.

Meshagons are tetrahedral finite element (FE) mesh sculptures, to my knowledge, the first ever.  For the last 15+ years I have been writing and developing code to mesh tissues and structures mostly from 3-D MRI and CT scans.  Then I had an idea (it’s rare), “What if I could actually print a 3-D FE mesh… that would be interesting!” 3-D printing technologies were then (and certainly are now) rapidly evolving and it looked like printing a mesh might actually be possible.

At first, I thought “this will be easy…” but it turned out to be a difficult problem. The basic idea was to convert my wire-frame meshes (nodes, elements) by ‘thickening’ to suit for 3-D printing.

I explored many concepts such as molecular modeling (see below for details). The early results were not satisfying from an artistic standpoint. Instead of just ‘balls-and-sticks’ what I really wanted was a more organic structure with parametric control of edge and joint thicknesses.  Also, any method must produce the water-tight manifold surface required for 3-D printing. After much effort (about 2 years work!) I have finally developed a solution using alpha-shapes. It works. I can now generate force-optimized, smooth-manifold FE mesh ‘sculpture’ for 3-D printing of pretty much any shape (also from fonts) with further applications in engineering, bioengineering, and architecture.

There are still some issues. Generating a meshagon is very computationally intensive (see details below). A larger mesh can take a week  to compute on my (somewhat dated) Intel Quad Q6600 4-core system. However, the current code is quite parallel-friendly and there is plenty of room for improvements and new ideas. If you are interested feel free to email me….

Read the whole saga for how he explored and solved this challenge on his site here.

Meshagons history tcdoe com

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