Oliver Computer Algebra Project 2014

Problem 1

S=RegionPlot3D[ Sin[x] Sin[y] Sin[z]<0.2 && Cos[x] Cos[y] Cos[z] <0.3 ,{x,-5.2,5.2},{y,-5.2,5.2},{z,-5.2,5.2},PlotPoints->40,Boxed->False,PlotStyle->Hue,Mesh->False,Axes->1];
Export["cheese.3ds",S,"3DS"]

Import["cheese.3ds"]

Problem 2

picture=Import["http://www.math.harvard.edu/archive/21a_fall_11/donald.jpg"];
ParametricPlot3D[(2+Sin[t]) {Cos[t] Sin[s],Sin[t] Sin[s],Cos[s]},{s,0,Pi},{t,0,2Pi},Lighting->"Neutral",Mesh->False,PlotPoints->40,TextureCoordinateFunction->({#5,#4}&),PlotStyle->{Texture[picture]},ViewPoint->{-3.25,-0.9,-0.2},ViewVertical->{-0.64,-0.05,-0.9},Axes->False,Boxed->False,PlotRange->All]

S=ParametricPlot3D[ {(2+Sin[s +t]+Cos[s])Cos[t],(2+Sin[s+t]+Cos[s])Sin[t],Sin[s]},{t,0,2Pi},{s,0,2Pi},TextureCoordinateFunction->({#5+3Pi,#4+Pi}&),PlotStyle->{Yellow},Mesh->False,Boxed->False,Axes->False];
Export["goldenegg.ply",S,"PLY"]

Import["goldenegg.ply"]

Problem 3

S1={Yellow,Sphere[{0,0,0},1]};
S2={Orange,Sphere[{0,0,-1.5},0.6]};
S3={Blue,Tube[Table[{0.5,0,-1.4}+{t,0,t^2},{t,0,1,0.1}],0.1]};
S4={Blue,Tube[Table[{-0.5,0,-1.4}+{-t,0,+t^2},{t,0,1,0.1}],0.1]};
S=Graphics3D[{S1,S2,S3,S4}];
Export["s.stl",S,"STL"]

Problem 4

Import["desktop/pavan.ply"]

Assignment

Be creative. If you use inspiration beyond these templates, give credit. Use the above templates to do the following: 

1) (3 points) A region plot of a solid of your choice.
2) (3 points) A surface of your choice. (this can also use textures)
3) (4 points) An arbitrary three dimensional object of your choice. Try to make something printable. 

Submit your notebook after removing all the graphics in the above menu Cell -> Delete All Output. If you should use additional resources like textures 
or scanned objects, send them too or provide a link to a download page.

Oliver Knill, November 10 , 2014, email: knill@math.harvard.edu