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February 23, 2016 / or4green

3D Printing an LP Feasible Region

A colleague of mine in the mechanical engineering department, Professor Ron Adrezin, has been getting very active with 3D printers.  Along with his colleagues, he has outfitted their labs with numerous 3D printers for use by students and faculty.  He was written up last fall in the local newspaper for his work with a 3D printer onboard a Coast Guard Arctic Icebreaker.  So when I saw Ron at an in-service day before this semester began, I asked him if he could print a polytope and offered to send him more specifics on the shape I was talking about.  I referred him to my greenOR blog post from 2014 “Visualizing LPs in Mathematica“.  This email conversation followed:

Ron:  Can you save it as an stl file?

Me:   never heard of that, but Mathematica can – https://reference.wolfram.com/language/ref/format/STL.html …  i exported the polytope as an .stl file – please see attached … thanks!

Ron:  Thanks, I will take a look.

A couple of days later Ron let me know his colleague Tom printed it!  They used a Makerbot 5th generation 3D printer and the Makerbot software.

Here are a couple of 2D photos of this 3D polytope:

 

3D printed polyhedral feasible regionspolyhedron2

Here is the source in Mathematica:

feasible region in Mathematica

feasible region in Mathematica

It was a pleasant surprise to learn that the file type the Makerbot software took as input, the .stl file, was something Mathematica could export.  See the link above for how to do it.

It’s been fun showing it off to colleagues and using it as a visual aid in Linear Optimization class that students can hold.  We’re planning to give students in the class the chance to have theirs printed.

Some google searching digs up a lot of activity on 3D printing mathematical objects.  Here are a few I found interesting:

http://www.georgehart.com/rp/rp.html

https://plus.maths.org/content/3d-printing

https://www.simonsfoundation.org/multimedia/3-d-printing-of-mathematical-models/#    At 3:37 of video, he shows Mathematica with something that looks like it could be used for an IP feasible region with objective.  There’s also mention of the program “stella” which is useful for polyhedra.

3D printers are fairly common at MakerSpaces.  Our city of New London has a few at its brand new “Spark” MakerSpace.   I am looking forward to more 3D printing to come…

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