Making High Quality 3D Prints

Math 250 - Math with Mathematica
Christopher Hanusa

Comprehension Questions

12-1. Export to STL one of the models you created in Tutorials 10 or 11.  Did it export correctly?

12-2. Use PolyhedronData to create a 3D model of a polyhedron of your choice.  (If you can’t find one you like, may I suggest my favorite polyhedron, the Snub Cube?)  Export it to an STL file.  Upload it to Sketchfab or Shapeways.

12-3.  See what the difference is when you export an STL file for a ParametricPlot3D curve when
(a) You use PlotPoints ONLY as an option in ParametricPlot3D but NOT in the PlotStyle->Tube option.
(b) You use PlotPoints ONLY in the PlotStyle->Tube option but NOT as an option in ParametricPlot3D.

12-4. A fascinating surface you see in multivariable calculus is the function f(x,y)=xy/(x^2+y^2).  This surface is not continuous at (x,y)=(0,0).  Create a block with this upper surface similar to the one in Tutorial 11.  Adjust the PlotPoints option so that the block has a good enough resolution to see the structure of the discontinuity.

12-5. Create a 3D model of the surface given by
x(u,v)=Cos[u] (Sin[2v]^2+Sin[v])
y(u,v)=Sin[u] (Sin[2v]^2+Sin[v])
z(u,v)=                  Cos[v]

12-6.  Create a sphere or torus that is the opposite of smooth --- having extremely POOR resolution.  (Remember to import and export so that you can see the result.)

12-7. The Cube and the Octahedron are two dual polyhedra.  Use PolyhedronData and DiscretizeGraphics to import both of them as meshes.  Then create the union of these two shapes so that you can see all 6 vertices of the octahedron poking through the faces of the cube, and all 8 vertices of the cube poking through the faces of the octahedron.  You may wish to use RegionResize to change the relative sizes of these shapes.

12-8. Extract the edges of one of the models you have already exported.  Then use the Map function to create a wireframe of the object like this for the sphere:

Challenge Questions

12-X1. Use a Table Command and TransformedRegion/TranslationTransform to create an army of hundreds of octahedra and cubes.

12-X2. Create three overlapping tori that form a globe, like this:

12-X3. Create two interlocking tori that loop through one another, like this:.

12-X4. Create a function oriented torus that has an additional parameter that programs the torus to be parallel to the xy-plane, yz-plane, or xz-plane.