- Problem 12.1 Create a Space curve
r={Cos[t],Sin[3t],Cos[t]}+{Cos[17t],Sin[17t],0}/10;
S=Graphics3D[{Red,Tube[Table[r,{t,-Pi/2,Pi/2,0.01}],0.04]},
ViewPoint->{-2.0522,-0.854289,2.5511},
ViewVertical->{-0.541,-0.22644,2.032},Boxed->False,Axes->False]
- Problem 12.2 Create a surface
r={(3+Cos[3s])Cos[t],(3+Cos[3s])Sin[2t], 4 Sin[s]};
ParametricPlot3D[r,{s,0,2Pi},{t,0,2Pi}, Mesh->False,
PlotPoints->40,PlotStyle->{Directive->Specularity["Red",100],Yellow},
Boxed->False,Axes->False]
- A surface with texture
picture=Import["https://www.ibiblio.org/wm/paint/auth/pollock/pollock.key.jpg"];
r=(Sin[2t]+Cos[3s]){Cos[t]Sin[s],Sin[t]Sin[s],Cos[s]};
ParametricPlot3D[r,{s,0,Pi},{t,0,2Pi},
Lighting->"Neutral",Mesh->False,PlotPoints->40,
TextureCoordinateFunction->({#5,#4}&),
PlotStyle->{Directive->Specularity["White",100],
Texture[picture]},Boxed->False,Axes->False,
ViewPoint -> {2.78, 1.58, -1.05},ViewVertical -> {-0.47, -0.22, -0.88}]
- Problem 12.3 ContourSurface
ContourPlot3D[x^4 y^2+y^4 z^2+z^4 x^2==0.03,{x,-2,2},{y,-2,2},{z,-2, 2},
PlotPoints->30,MeshStyle->{Yellow},
ContourStyle->{Directive->Specularity["Yellow",100],Orange},
Boxed->False,Axes->False]
- Problem 12.4 Coordinates
f={x+Sin[y*z]/10,y+Sin[x*z]/3,z+Sin[x*y]/10};rad=0.02;
X=Table[{Red,Tube[Table[f,{x,-2,2,0.1}],rad]},{y,-2,2,1},{z,-2,2,1}];
Y=Table[{Green,Tube[Table[f,{y,-2,2,0.1}],rad]},{x,-2,2,1},{z,-2,2,1}];
Z=Table[{Blue,Tube[Table[f,{z,-2,2,0.1}],rad]},{x,-2,2,1},{y,-2,2,1}];
Graphics3D[{X,Y,Z},Boxed->False]
DistortionFactor=Det[{D[f,x],D[f,y],D[f,z]}]/.x->0.5/.y->0.7/.z->0.8
- A 2D coordinate system
f={x+Sin[4y]/10,y+Sin[4x]/10};rad=0.01;
X=Table[{Red,Thickness->rad,Line[Table[f,{x,-2,2,0.1}]]},{y,-2,2,1}];
Y=Table[{Green,Thickness->rad,Line[Table[f,{y,-2,2,0.1}]]},{x,-2,2,1}];
Graphics[{X,Y}]
DistortionFactor=Det[{D[f,x],D[f,y]}]/.x->0.5/.y->0.6
- An other example close to spherical
Clear[r,s,t];f={r Sin[s] Cos[t],r Sin[s] Sin[t],r Cos[s]+0.1 Sin[s]}; rad = 0.01;
X=Table[{Red, Tube[Table[f,{r,0,1,0.1}],rad]}, {s,0,Pi,Pi/3},{t,0,2 Pi,Pi/3}];
Y=Table[{Green, Tube[Table[f,{t,0,2Pi,0.1}],rad]},{r,0,1,0.2},{s,0,Pi,Pi/3}];
Z=Table[{Blue, Tube[Table[f,{s,0,Pi,0.1}],rad]}, {r,0,1,0.2},{t,0,2 Pi,Pi/3}];
Graphics3D[{X, Y, Z}, Boxed -> False]
DistortionFactor = Simplify[Det[{D[f, r], D[f, s], D[f, t]}] ]
- An other example close to polar coordinates
Clear[r, t]; f = {r Cos[t], r Sin[t] +1.4 Sin[4t]/10}; rad = 0.01;
X=Table[{Red,Thickness->rad, Line[Table[f,{r,0,1,0.1}]]},{t,0,2 Pi,Pi/6}];
Y=Table[{Green,Thickness->rad,Line[Table[f,{t,0,2Pi,0.1}]]},{r,0,1,0.2}];
Graphics[{X, Y}]
DistortionFactor = Simplify[Det[{D[f, r], D[f, t]}] ]