Meshagons : The Brief Story

Meshagons are fully manifold and 3-D printed finite element (FE, force-optimized) tetrahedral structures. To my knowledge the first ever. 

I have been writing code for 3-D automated multi-domain tetrahedral meshing for the last 12+ years, mostly for bioengineering applications. Recently, I had a novel idea (yes, it's rare), "What if I could actually print a force-optimized FE mesh... that would be interesting!!" 3-D printing technologies were (and are) rapidly evolving and 'printing' a solid FE mesh might be possible.  

At first I thought, "This will be easy..." 

Well, it turned out to be a difficult problem. The basic idea was to 'thicken' a mesh (nodes-elements) into a 3-D printable solid surface. I explored many concepts and softwares such as 'skinning' in Blender3D, Grasshopper, and molecular modeling (see below) but the results were not manifold or suitable for printing. Also any method must result in a water-tight printable solid. After much effort (and another 2+ years work as of now), I have developed manifold, printable mesh structures for both artistic and engineering applications. 

There is still a lot of exciting work to do. Generating a meshagon is currently computationally intensive. A larger (~1M) mesh can take a week  to compute on my (somewhat dated) Intel Quad Q6600 4-core system. The method, however, is parallel-friendly and there are plenty of room(s) for improvement. Currently, a resulting meshagon is 99% manifold. I still have to manually resolve some non-manifold joints (two or at most ten for a mid-size mesh). Ultimately, I am certain that this can be automated. Please feel free to email me if there is interest, collaboration, or any questions (tcd@tcdoe.com).

<UPDATE, 4-16>  Site under re-construction, please pardon.

<UPDATE> Selected meshagons are now available. Please email me as the ETSY store is under development.
For custom work and any questions/inquiries email me at  tcd@tcdoe.com.
New lighting sculptures  are also available.

The Alpha

The Organic Cuboid v.3

The new meshagon lamp design, ready to print.

First try: Sphere FE mesh rendered as a 'molecule'.

The 'infinity' mesh in Blender3D rendered in a molecular fashion as 'sticks-and-balls'.

Actual 3-D printed 'infitity' mesh in white plastic. Conversion to 'stl' was challenging.

'Pi' mesh solidified (skinned) in Blender3D. Looks good so far in this render...

But upon further inspection there are many non-manifold joints (highlighted orange). It's impossible. There are too many.

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When there are too many edges intersecting at the 'joint' (node) the Blender (and other) skinning algorithms fail to create manifold. There is no 'fix'. Above is highlighted some of the hundreds of 'non-manifold' edges...

Above and Below; is the new 'Pi' meshagon, which is one of the most difficult objects that I have attempted.  The shape has both thick and also very thin regions. At left (below) is the original mesh which looks rough and jagged. Middle (below) is after 1 smoothing iteration with my in-house programmed Taubin-based smoothing algorithm; ready for 3-D printing. Below right is after 50% decimation and 3x further smoothing steps to produce a more organic (and still manifold) structure.

Initial 'rough' meshagon. Detail below.

Analysis with Meshlab (left) shows that this  "Pi" meshagon is fully manifold and oriented. Which means it is 3-D printable.

I have confirmed that this is indeed printable via Shapeways and NetFabb analyses. This 'Pi' meshagon is approximately 220mm high, and is printable in white or black poly, alumide, and other materials (bronze is expensive but amazing). With some further processing this could also be printed in sandstone (i'm very interested in that material). Email me for questions or further information (tcd@tcdoe.com).

Engineering/Bioengineering applications

I'm quite excited about the potential for 'meshagon sculptures' and also for applications in Engineering, Biomedical, and Architectural designs. I'm working on some new challenging meshes; implants and prosthetic designs, a large elliptical toroid, large 'wall panels', and 'monolithic' cylinder shapes. I am also working on smaller meshes for lighting (and  inexpensive 'tea lights'). Another problem I'm working on is how best to control the meshagon parameters so that it has a defined solid outer surface with controllable thickness. This is essential for creating accurate parts/components for engineering (and potentially bioengineering) applications.

See my Sci/Eng page for more info about applications.

Finally here is the latest 'Pi' mesh (ready/confirmed) and a the first meshagon lamp design. I can't wait to see these sculptures in ceramic, alumide, sandstone, and chrome plated (working on that process now).

Further exciting work is ongoing for engineering and bioengineering structures !