Mathematica Project, Math 21a, Fall, 2012

The project

This creative project asks you to produce an art object in Mathematica which can be printed on a 3D printer.
The project is due Sunday December 9, 2012 but you can submit anytime unitl then. Submit the project electronically to knill@math.harvard.edu after deleting all output (Choose Cell->DeleteAllOutput in the menu to the top of this window. You will get a confirmation that your project is accepted). We will print the printable submissions using a 5000 dollar grant from the Elson Family Arts initiative. We try to print as many projects as possible until the money is gone.

Example: A bumpy sphere

Grab the bracket to the right of the following yellow cell with the cursor. Click on it, then hold the Shift key and hit Return to evaluate the cell. A graphic showing the parametrized surface should appear below.

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The simplest export, which a 3D printer understands is in STL format, but this does not use the color:

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It will look as follows:

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If we want to print in color, we have to export in WRL (virtual world reality modelling language) format as follows:

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When this object is uploaded to http://www.shapeways.com using millimeters as unit and printed in Full Color Sandstone, it costs 17 dollars. The cost of the printing very much depends on the material as well as the size. You get full credit if you submit an original object which can be printed for less than 20 dollars. Original means that it should be something new. Submitting a bare sphere for example is not original. Here is how the above project looks on Shapeways:

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In the rest of this notebook, we give you more examples and ideas to get started.

Tips

-Watch the size.
-Minimal wall thickness: 1mm.
-Surfaces need to be closed.
-The object should be connected. One piece only
- Not too many polygons (1 Million).
-Increase the resolution like PlotPoints0->100 to make the object smoother.
-Watch the dimension of the object so that the prize is reasonable
-Submit the WRL or STL file to Shapeways to see whether it prints.

Example: A Sculpture

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Example: The perfect Euler brick

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Example: A form

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Example: A ring

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The translation and rotation and scaling things do not work unfortunately:

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Example: A  wire form

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Example: A polyhedron

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Example: A surface

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Example: A statue

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We will have a workshop during the last week, which will give you more ideas and answer any questions. Feel free to email Oliver if you have questions.

Oliver Knill, November 22, 2012