Making High Quality 3D Prints

Challenge Questions

Math 250 - Math with Mathematica
Christopher Hanusa

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 orientedtorus that has an additional parameter that programs the torus to be parallel to the xy-plane, yz-plane, or xz-plane.

12-X5. Create a shape that is an interpolation between a circle and a square.  (Expand to see hints)

Hint 1

You’ll have to use ParametricPlot3D instead of Plot3D.

Hint 2

Create a one-parameter function for the boundary of each both the circle and the square.

Hint 3

For the boundary of the square use a piecewise-defined function.

Hint 4

For the boundary of the circle use {cos(theta),sin(theta)}

Selected Solutions

Solution to Question 12-X2

ParametricPlot3D[{
{(10+Cos[v]) Cos[u],(10+Cos[v]) Sin[u],Sin[v]},
{(10+Cos[v]) Cos[u],Sin[v],(10+Cos[v]) Sin[u]},
{Sin[v],(10+Cos[v]) Cos[u],(10+Cos[v]) Sin[u]}},{u,0,2Pi},{v,0,2Pi},PlotStyle->{Red,Green,Blue},Mesh->None,PlotPoints->30,Boxed->False,Axes->False]

Solution to Question 12-X3

ParametricPlot3D[{{(3+Cos[v]) Cos[u],(3+Cos[v]) Sin[u],Sin[v]},{(3+Cos[v]) Cos[u]+3,Sin[v],(3+Cos[v]) Sin[u]}},{u,0,2Pi},{v,0,2Pi},PlotStyle->{Yellow,Purple},Mesh->None,PlotPoints->{70,70},Boxed->False,Axes->False]