Oliver’s Computer Algebra Project, Workshop, 11/16/2017

this was done live during the workshop.

Problem 1

Volume[ImplicitRegion[x^2+y^2+z^2<1,{x,y,z}]]

Problem 2

Problem 3

Macaroni=ParametricPlot3D[ {(3+Cos[2t])Cos[s],(3+Cos[t])Sin[s],Sin[t]},{t,0,2Pi},{s,0,Pi},Boxed->False,Axes->False,PlotStyle->{RGBColor[1,0.6,0],Thickness[0.2]},Mesh->False];
Graphics3D[ Table[ Translate[Rotate[Scale[First[Macaroni],Random[]],2Pi Random[],{Random[],Random[],Random[]}],10{Random[],Random[],Random[]}],{8}],Boxed->False]

Problem 4 (Swiss Cheese)

RegionPlot3D[ Sin[10 x]+Sin[10 y]+Sin[10 z]<0.6 && x^2<1 && y^2<1 &&z^2<1 && z<x+y, {x,-2,2},{y,-2,2},{z,-2,2},PlotPoints->100,Mesh->False,ColorFunction->Hue]

Problem 5

ContourPlot3D[ x^2+y^2+z^2-z^4==1 ,{x,-2,2},{y,-2,2},{z,-2,2}]

Problem 6   Sea Urchin

r[t_,s_]:={Cos[t] Sin[s],Sin[t] Sin[s],Cos[s]};R:=2Random[]-1;
S1=ParametricPlot3D[  r[t,s],{t,0,2Pi},{s,Pi/4,Pi},PlotStyle->Red,Mesh->False,Boxed->False];
thorn[t_,s_]:={RGBColor[0,0,0.4],Tube[ {r[t,s],1.5 r[t,s]+{R,R,R}/3},{0.02,0.001}]};
S2=Graphics3D[ Table[thorn[t,s],{t,0,2Pi,2Pi/30},{s,Pi/4+0.2,Pi,2Pi/30}]];
S3=ParametricPlot3D[0.6{r Cos[t],r Sin[t],1+Sin[t r]},{r,0,1},{t,0,2Pi},Mesh->False,PlotStyle->Green];
Show[{S1,S2,S3},Boxed->False,Axes->False,PlotRange->All]