Pensieve header: A collection of 4-dimensional hardware pieces.

SetDirectory["C:\\drorbn\\AcademicPensieve\\2013-12\\4DHardware"]

MakeImage["4DHardware-01",
Graphics3D[{
Opacity[0.85],
Glow[Red],Polygon[{{-10,0,-10},{-10,0,10},{10,0,10},{10,0,-10}}],
Glow[Blue],
Polygon[{{0,-10,-10},{0,-10,10},{0,-1,10},{0,-1,-10}}],
Polygon[{{0,10,-10},{0,10,10},{0,1,10},{0,1,-10}}]
}, Lighting -> None, Boxed -> False],
ImageSize -> 300]

MakeImage["4DHardware-02",
Graphics3D[{
Opacity[0.75],
Glow[Hue[0]],Polygon[{{-10,0,-10},{-10,0,10},{10,0,10},{10,0,-10}}],
Glow[Hue[3/8]],
Polygon[{{0,-10,-10},{0,-10,10},{0,-1,10},{0,-1,-10}}],
Polygon[{{0,10,-10},{0,10,10},{0,1,10},{0,1,-10}}],
Glow[Hue[3/4]],
Polygon[{{1,10,0}, {1,2,0}, {10,2,0}, {10,10,0}}],
Polygon[{{-1,10,0}, {-1,2,0}, {-10,2,0}, {-10,10,0}}],
Polygon[{{-1,-10,0}, {-1,-2,0}, {-10,-2,0}, {-10,-10,0}}],
Polygon[{{1,-10,0}, {1,-2,0}, {10,-2,0}, {10,-10,0}}]
}, Lighting -> None, Boxed -> False],
ImageSize -> 300]

MakeImage["4DHardware-03",
Graphics3D[{
Opacity[0.65],
Glow[Hue[0/4]],Polygon[{{-10,0,-10},{-10,0,10},{10,0,10},{10,0,-10}}],
Glow[Hue[1/4]],
Polygon[{{0,-10,-10},{0,-10,10},{0,10,10},{0,10,-10}}],
Glow[Hue[2/4]],
Polygon[{{-10,10,0}, {-10,-10,0}, {10,-10,0}, {10,10,0}}],
Glow[Hue[3/4]],
Polygon[10{{2,-1,-1}, {-1,2,-1}, {-1,-1,2}}+2{1,1,1}]
},
Boxed->False,ImageSize->{390.`,Automatic},Lighting->None,PlotRange->10,ViewPoint->{24.7,12.5,7.45},ViewVertical->{-0.072,-0.109,0.991}
],
ImageSize -> 300]

MakeImage["4DHardware-04",
Graphics3D[{
Opacity[0.65],
Glow[Hue[0/4]],Polygon[{{-10,0,-10},{-10,0,10},{10,0,10},{10,0,-10}}],
Glow[Hue[1/4]],
Polygon[{{0,-10,-10},{0,-10,10},{0,10,10},{0,10,-10}}],
Glow[Hue[2/4]],
Polygon[{{-10,10,0}, {-10,-10,0}, {10,-10,0}, {10,10,0}}],
Glow[Hue[3/4]],
Polygon[10{{2,-1,-1}, {-1,2,-1}, {-1,-1,2}}-2{1,1,1}]
},
Boxed->False,ImageSize->{390.`,Automatic},Lighting->None,PlotRange->10,ViewPoint->{24.7,12.5,7.45},ViewVertical->{-0.072,-0.109,0.991}
],
ImageSize -> 300]

Column[{
Slider[Dynamic[s], {-2,2}],
Dynamic[Graphics3D[{
Opacity[0.85],
Glow[Hue[0/4]],Polygon[{{-10,0,-10},{-10,0,10},{10,0,10},{10,0,-10}}],
Glow[Hue[1/4]],
Polygon[{{0,-10,-10},{0,-10,10},{0,10,10},{0,10,-10}}],
Glow[Hue[2/4]],
Polygon[{{-10,10,0}, {-10,-10,0}, {10,-10,0}, {10,10,0}}],
Glow[Hue[3/4]],
Polygon[10{{2,-1,-1}, {-1,2,-1}, {-1,-1,2}}+s{1,1,1}]
},
Lighting -> None, Boxed -> False,
PlotRange -> 10, ViewPoint->{25,10,10}
]]
}]

MakeImage["4DHardware-05",
Plot3D[{x y, -0.1-x y}, {x,-2,2}, {y,-2,2},
BoxRatios->{1,1,0.4`},Boxed->False,ImageSize->{315.1729630273366`,260.`},Method->{"RotationControl"->"Globe"},PlotRange->{{-2,2},{-2,2},All},PlotRangePadding->{Scaled[0.02`],Scaled[0.02`],Scaled[0.02`]},ViewPoint->{-2.580627656842925`,-0.9026639334946656`,-1.9938803173473902`},ViewVertical->{0.`,0.`,-1.`}, PlotStyle->{{Opacity[0.8], Red},{Opacity[0.8], Blue}}, Mesh -> False, PlotPoints -> 50, Boxed -> False, Axes->False
],
ImageSize -> 300
]

Column[{
Slider[Dynamic[h], {-2,2}],
Dynamic[Plot3D[{x y, h-x y}, {x,-2,2}, {y,-2,2},
PlotStyle->{{Opacity[0.8], Red},{Opacity[0.8], Blue}}, Mesh -> False, PlotPoints -> 50, Boxed -> False, Axes->False, PlotRange -> All
]]
}]

MakeImage["4DHardware-06",
Graphics3D[{
Opacity[0.75],
Glow[Red],Polygon[{{-10,-10,0},{-10,10,0},{10,10,0},{10,-10,0}}],
Glow[Blue],CapForm[None],
Tube[{{0,0,2},{0,0,10}}, 4],
Tube[{{0,0,-2},{0,0,-10}}, 4]
}, Lighting -> None, Boxed -> False],
ImageSize -> 300]

MakeImage["4DHardware-07",
Graphics3D[{
Opacity[0.75],
Glow[Red],
Polygon[{{-4,-4,0},{-4,4,0},{4,4,0},{4,1,0},{0,0,0},{4,-1,0},{4,-4,0}}],
Glow[Blue],
Polygon[{{-4,0,-3},{-4,0,-1},{0,0,0},{-4,0,1},{-4,0,3},{4,0,3},{4,0,-3}}]
},
Boxed -> False, Axes -> False, PlotRange -> All, Lighting -> None,ViewPoint->{1.94,-2.46,1.25},ViewVertical->{0.17,-0.17,1.29}
],
ImageSize -> 300]

MakeImage["4DHardware-08",
Show[ParametricPlot3D[
{(2+Cos[β])Cos[α], (2+Cos[β])Sin[α], Sin[β]},
{α,(π/10),2π-(π/10)}, {β,(π/10),2π-(π/10)},
Mesh -> False, PlotStyle -> {Glow[Red], Opacity[0.75]}
],
Graphics3D[{
Opacity[0.75],
Glow[Blue],
Polygon[{{-4,-4,0},{-4,4,0},{4,4,0},{4,1,0},{0,0,0},{4,-1,0},{4,-4,0}}],
Glow[Green],
Polygon[{{-4,0,-3},{-4,0,-1},{0,0,0},{-4,0,1},{-4,0,3},{4,0,3},{4,0,-3}}]
}],
Boxed -> False, Axes -> False, PlotRange -> All, Lighting -> None,ViewPoint->{1.94,-2.46,1.25},ViewVertical->{0.17,-0.17,1.29}
],
ImageSize -> 300]

(* Based on Classes/13-Aarhus/Shpagat.nb *)
MakeImage["4DHardware-09",
Graphics3D[{
Polygon[{{1,0,0},{1,0,3},{-1,0,3},{-1,0,0}}],
Polygon[{{1,0,0},{1,1,-2},{0,1,-2}, {0,0,0}}],
Polygon[{{-1,0,0},{-1,-1,-2},{0,-1,-2}, {0,0,0}}]
}, Boxed -> False],
ImageSize -> 300]

(* Based on Projects/WKO/Wen.nb *)
MakeImage["4DHardware-10",
{r0, r1, r2, r3} = {5, 1, 2, 3}; (* the radii of the bends, the narrow, the connect, and the wide *)
p[u_,v_] := Which[
v<0, (* the narrow tube *)
  {-r0+r0*Cos[v], 0, -r0*Sin[v]}+(r1-(r2-r1)2v/Pi)*(-Cos[u]*{-Cos[v],0,Sin[v]}+{0,Sin[u],0}),
v<Pi, (* the bend *)
  {((r1+r3)-(r3-r1)*Cos[v])*Cos[u], ((r1+r3)-(r3-r1)*Cos[v])*Sin[u], -(r1+r3)*Sin[v]}/2,
v<3Pi/2, (* the wide tube *)
  {r0+r0*Cos[v], 0, -r0*Sin[v]}+(r3-2(r3-r2)(v-Pi)/Pi)*(Cos[u]*{-Cos[v],0,Sin[v]}+{0,Sin[u],0})
];
ParametricPlot3D[
p[u,v],
{u, 0, 2Pi}, {v,-Pi/2, 3Pi/2},
 PlotStyle->Opacity[0.75], Axes -> None, Boxed -> False,
ViewPoint->{-0.785,-2.78,-1.74},ViewVertical->{-0.863,-0.595,-0.394}
],
ImageSize -> 300]

(* With formulas from Projects/PlanetHopf/ *)
MakeImage["4DHardware-11",p[z_,w_] := {Re[z], Im[z], Re[z]+Im[w]};
p[z_,w_] := (1/(1-Im[w])){Re[z], Im[z], Re[w]};
p[l_List] := p @@ l;
ParametricPlot3D[
p[((Sqrt[2])/2)(E^(I α)){(E^(I ϕ)),1}],
{ϕ,0,π},{α,0,2π},
Axes -> None, Boxed -> False,
ViewPoint->{3.13364,0.01505,-1.25003},ViewVertical->{0.178547,-0.953207,-0.663175}
],
ImageSize -> 300]

κ[s_] := (Piecewise[{{{0,s+7}, s≤-10}, {{s+10,s+7}, -10<s≤-4}, {{6+3Cos[((π s)/8)], -3Sin[((π s)/8)]}, -4<s≤4}, {{10-s,s-7}, 4<s≤6}, {{10-s,s-7}, 8<s≤10}, {{0,s-7}, 10<s}}])

ParametricPlot[κ[s], {s,-15,15}, Axes -> None]

MakeImage["4DHardware-12",
κκ[s_,t_] := If[t>0,
Append[t κ[15s/t]/9, t],
{0,15s/9,t}
];
ParametricPlot3D[κκ[s,t], {s,-1,1}, {t,-0.5,1},
 PlotRange -> All, PlotPoints -> 50, Mesh -> None, Axes-> None, Boxed -> False,
ViewPoint->{1.66,-2.56,1.46},ViewVertical->{2.81,-0.33,0.93}
],
ImageSize -> 300]

MakeImage["4DHardware-13",
ParametricPlot3D[
{t Cos[α], t Sin[2α]/2,1-t},
{α,(π/2)+(π/24),((5π)/2)-(π/24)}, {t,0,1},
ColorFunction -> Function[{x,y,z,α,t}, Glow[Hue[(3/8)(1+Sin[α])t]]],
ColorFunctionScaling->False, Lighting -> None, Boxed -> False, Axes -> None, Mesh -> False,
PlotStyle->Opacity[0.8], ViewPoint->{-1.078,2.84056,-1.47504},ViewVertical->{-0.875417,0.787683,-0.560478}
],
ImageSize -> 300]

MakeImage["4DHardware-14",
ParametricPlot3D[
{t Cos[α],t Sin[α], Sin[2α]},
{α,0,π/2}, {t,-1,1},
ColorFunction -> Function[{x,y,z,α,t}, Glow[Hue[((3α)/(2π))]]],
ColorFunctionScaling->False, Lighting -> None, Boxed -> False, Axes -> None, Mesh -> False,
PlotStyle->Opacity[0.8], ViewPoint->{2.92229,-1.60047,0.552585},ViewVertical->{0.694529,-0.375278,1.22767}
],
ImageSize -> 300]

MakeImage["4DHardware-15",
Plot3D[{x y, 0.1-x y}, {x,-2,2}, {y,-2,2},
BoxRatios->{1,1,0.4`},Boxed->False,ImageSize->{315.1729630273366`,260.`},Method->{"RotationControl"->"Globe"},PlotRange->{{-2,2},{-2,2},All},PlotRangePadding->{Scaled[0.02`],Scaled[0.02`],Scaled[0.02`]},ViewPoint->{-2.580627656842925`,-0.9026639334946656`,-1.9938803173473902`},ViewVertical->{0.`,0.`,-1.`}, PlotStyle->{{Opacity[0.8], Red},{Opacity[0.8], Blue}}, Mesh -> False, PlotPoints -> 50, Boxed -> False, Axes->False
],
ImageSize -> 300
]

MakeImage["4DHardware-16",
α=0.8;
Plot3D[{1-α(1-(((x^2)+(y^2))/8)), -1+α(1-(((x^2)+(y^2))/8))}, {x,-2,2}, {y,-2,2},
BoxRatios->{1,1,0.4},Boxed->False, PlotRange->{{-2,2},{-2,2},{-1,1}},PlotStyle->{{Opacity[0.8], Red},{Opacity[0.8], Blue}}, Mesh -> False, PlotPoints -> 50, Boxed -> False, Axes->False
],
ImageSize -> 300
]

MakeImage["4DHardware-17",
α=1.2;
Plot3D[{1-α(1-(((x^2)+(y^2))/8)), -1+α(1-(((x^2)+(y^2))/8))}, {x,-2,2}, {y,-2,2},
BoxRatios->{1,1,0.4},Boxed->False, PlotRange->{{-2,2},{-2,2},{-1,1}},PlotStyle->{{Opacity[0.8], Red},{Opacity[0.8], Blue}}, Mesh -> False, PlotPoints -> 50, Boxed -> False, Axes->False
],
ImageSize -> 300
]

Kink[s_,t_] := If[s≤0, {t,0,0}, (* s is size, t is time *)
({{\[Piecewise], ({{{t,0,0}, t<-1.25s}, {{5t+5s,0,-4t-5s}, -1.25s≤t<-s}, {(s/π){-Sin[((π t)/s)],1+Cos[((π t)/s)],((π t)/s)}, -s≤t≤s}, {{5t-5s,0,-4t+5s}, s<t≤1.25s}, {{t,0,0}, t>1.25s}})}})]

Plot[Kink[1,t], {t,-3,3}]

MakeImage["4DHardware-18",
ParametricPlot3D[{s,Kink[s,t][[1]], Kink[s,t][[2]]},
{s,-0.25,1}, {t,-1.75,1.75},
ColorFunction -> Function[{x,y,z,s,t},Hue[((1+Kink[s,t][[3]])/3)]],
ColorFunctionScaling->False, PlotRange -> {{-0.25,1},{-0.75,0.75}, {0,0.75}}, Mesh -> False,  Boxed -> False, Axes->False, PlotStyle->{Opacity[0.7]}, PlotPoints -> 150
],
ImageSize -> 300
]

MakeImage["4DHardware-19",
Graphics3D[{
Opacity[0.85], Glow[Red],
Polygon[{{0,0,-1},{0,0,1},{1,0,1},{1,0,-1}}],
Polygon[{{0,0,-1},{0,0,1},{-(1/2),((Sqrt[3])/2),1},{-(1/2),((Sqrt[3])/2),-1}}],
Polygon[{{0,0,-1},{0,0,1},{-(1/2),-((Sqrt[3])/2),1},{-(1/2),-((Sqrt[3])/2),-1}}]
}, Lighting -> None, Boxed -> False, ViewPoint->{0.174611,-2.89946,1.73569},ViewVertical->{0.00615481,-0.107975,0.995608}],
ImageSize -> 300]

σ[s_, t_] := {s}~Join~Kink[0.75-(s^2),t];
MakeImage["4DHardware-20",
ParametricPlot3D[σ[s,t][[1;;3]],
{s,-1,1}, {t,-1.75,1.75},
ColorFunction -> Function[{x,y,z,s,t},Hue[((2/3+σ[s,t][[4]])/2)]],
ColorFunctionScaling->False, PlotRange -> {{-1,1},{-0.75,0.75}, {0,0.75}}, Mesh -> False,  Boxed -> False, Axes->False, PlotStyle->{Opacity[0.6]}, PlotPoints -> 200, ViewPoint->{-1.9772,-1.66109,2.18665},ViewVertical->{0.0420887,0.0784289,2.65968}
],
ImageSize -> 300
]

σ[s_, t_] := {s}~Join~Kink[0,t];
MakeImage["4DHardware-21",
ParametricPlot3D[σ[s,t][[1;;3]],
{s,-1,1}, {t,-1.75,1.75},
ColorFunction -> Function[{x,y,z,s,t},Hue[((2/3+σ[s,t][[4]])/2)]],
ColorFunctionScaling->False, PlotRange -> {{-1,1},{-0.75,0.75}, {0,0.75}}, Mesh -> False,  Boxed -> False, Axes->False, PlotStyle->{Opacity[0.6]}, PlotPoints -> 200, ViewPoint->{-1.9772,-1.66109,2.18665},ViewVertical->{0.0420887,0.0784289,2.65968}
],
ImageSize -> 300
]

σ[s_, t_] := {s}~Join~Kink[0.25+((s^2)/2),t];
MakeImage["4DHardware-22",
ParametricPlot3D[σ[s,t][[1;;3]],
{s,-1,1}, {t,-1.75,1.75},
ColorFunction -> Function[{x,y,z,s,t},Hue[((2/3+σ[s,t][[4]])/2)]],
ColorFunctionScaling->False, PlotRange -> {{-1,1},{-0.75,0.75}, {0,0.75}}, Mesh -> False,  Boxed -> False, Axes->False, PlotStyle->{Opacity[0.6]}, PlotPoints -> 250, ViewPoint->{-1.9772,-1.66109,2.18665},ViewVertical->{0.0420887,0.0784289,2.65968}
],
ImageSize -> 300
]

σ[s_, t_] := {s}~Join~Kink[0.8(s^2)-0.05,t];
MakeImage["4DHardware-23",
ParametricPlot3D[σ[s,t][[1;;3]],
{s,-1,1}, {t,-1.75,1.75},
ColorFunction -> Function[{x,y,z,s,t},Hue[((2/3+σ[s,t][[4]])/2)]],
ColorFunctionScaling->False, PlotRange -> {{-1,1},{-0.75,0.75}, {0,0.75}}, Mesh -> False,  Boxed -> False, Axes->False, PlotStyle->{Opacity[0.6]}, PlotPoints -> 250, ViewPoint->{-1.9772,-1.66109,2.18665},ViewVertical->{0.0420887,0.0784289,2.65968}
],
ImageSize -> 300
]

MakeImage["4DHardware-24",
Show[
ParametricPlot3D[{s,Kink[s,t][[1]], Kink[s,t][[2]]},
{s,-0.5,1}, {t,-1.75,1.75},
ColorFunction -> Function[{x,y,z,s,t},Hue[((1+Kink[s,t][[3]])/3)]],
ColorFunctionScaling->False, PlotRange -> {{-0.5,1},{-0.75,0.75}, {-0.25,0.75}}, Mesh -> False,  Boxed -> False, Axes->False, PlotStyle->{Opacity[0.7]}, PlotPoints -> 150
],
Graphics3D[{Opacity[0.7], Hue[0.75],
Polygon[{{-0.2,-0.75,-0.25},{-0.2,-0.75,0.75},{-0.2,0.75,0.75},{-0.2,0.75,-0.25}}]
}]
],
ImageSize -> 300
]

MakeImage["4DHardware-25",
Show[
ParametricPlot3D[{s,Kink[s,t][[1]], Kink[s,t][[2]]},
{s,-0.5,1}, {t,-1.75,1.75},
ColorFunction -> Function[{x,y,z,s,t},Hue[((1+Kink[s,t][[3]])/3)]],
ColorFunctionScaling->False, PlotRange -> {{-0.5,1},{-0.75,0.75}, {-0.25,0.75}}, Mesh -> False,  Boxed -> False, Axes->False, PlotStyle->{Opacity[0.7]}, PlotPoints -> 150
],
Graphics3D[{Opacity[0.7], Hue[0.75],
Polygon[{{0.5,-0.75,-0.25},{0.5,-0.75,0.75},{0.5,0.75,0.75},{0.5,0.75,-0.25}}]
}]
],
ImageSize -> 300
]

MakeImage["4DHardware-26",
Show[
ParametricPlot3D[Append[0.2(1-0.5(1-(z^2))){1,0}+t{0,1},z],{t,-1,1}, {z,-1,1},
 Mesh -> False,  Boxed -> False, Axes->False, PlotStyle->{Glow[Hue[0]], Opacity[0.7]}, Lighting -> None],
ParametricPlot3D[Append[0.2(1-0.5(1-(z^2))){-(1/2),((Sqrt[3])/2)}+t{((Sqrt[3])/2),(1/2)},z],{t,-1,1}, {z,-1,1},
 Mesh -> False,  Boxed -> False, Axes->False, PlotStyle->{Glow[Hue[1/3]], Opacity[0.7]}, Lighting -> None],
ParametricPlot3D[Append[0.2(1-0.5(1-(z^2))){-(1/2),-((Sqrt[3])/2)}+t{-((Sqrt[3])/2),(1/2)},z],{t,-1,1}, {z,-1,1},
 Mesh -> False,  Boxed -> False, Axes->False, PlotStyle->{Glow[Hue[2/3]], Opacity[0.7]}, Lighting -> None],
PlotRange -> All, ViewPoint->{1.07475,-2.85045,1.47304},ViewVertical->{0.0785897,-0.166645,0.983457}
],
ImageSize -> 300
]

MakeImage["4DHardware-27",
Show[
ParametricPlot3D[Append[0.2(1-1.5(1-(z^2))){1,0}+t{0,1},z],{t,-1,1}, {z,-1,1},
 Mesh -> False,  Boxed -> False, Axes->False, PlotStyle->{Glow[Hue[0]], Opacity[0.7]}, Lighting -> None],
ParametricPlot3D[Append[0.2(1-1.5(1-(z^2))){-(1/2),((Sqrt[3])/2)}+t{((Sqrt[3])/2),(1/2)},z],{t,-1,1}, {z,-1,1},
 Mesh -> False,  Boxed -> False, Axes->False, PlotStyle->{Glow[Hue[1/3]], Opacity[0.7]}, Lighting -> None],
ParametricPlot3D[Append[0.2(1-1.5(1-(z^2))){-(1/2),-((Sqrt[3])/2)}+t{-((Sqrt[3])/2),(1/2)},z],{t,-1,1}, {z,-1,1},
 Mesh -> False,  Boxed -> False, Axes->False, PlotStyle->{Glow[Hue[2/3]], Opacity[0.7]}, Lighting -> None],
PlotRange -> All, ViewPoint->{1.07475,-2.85045,1.47304},ViewVertical->{0.0785897,-0.166645,0.983457}
],
ImageSize -> 300
]

Kink2[s_,t_] := If[s≤0, {t,-(t^2),0}, (* s is size, t is time *)
({{\[Piecewise], ({{{t,-(t^2),0}, t<-1.25s}, {{5t+5s,-(((5t+5s))^2),-4t-5s}, -1.25s≤t<-s}, {(s/π){-Sin[((π t)/s)],1+Cos[((π t)/s)],((π t)/s)}, -s≤t≤s}, {{5t-5s,-(((5t-5s))^2),-4t+5s}, s<t≤1.25s}, {{t,-(t^2),0}, t>1.25s}})}})]

MakeImage["4DHardware-28",
ParametricPlot3D[{s,Kink2[s,t][[1]], Kink2[s,t][[2]]},
{s,-0.25,1}, {t,-1.75,1.75},
ColorFunction -> Function[{x,y,z,s,t},Hue[((1+Kink2[s,t][[3]])/3)]],
ColorFunctionScaling->False, PlotRange -> {{-0.25,1},{-0.75,0.75}, {-0.5,0.75}}, Mesh -> False,  Boxed -> False, Axes->False, PlotStyle->{Opacity[0.7]}, PlotPoints -> 50, ViewPoint->{2.43635,-2.09609,1.05859},ViewVertical->{0.383393,-0.107315,1.12979}
],
ImageSize -> 300
]

σ[s_, t_] := {s}~Join~Kink2[0.75-(s^2),t];
MakeImage["4DHardware-29",
ParametricPlot3D[σ[s,t][[1;;3]],
{s,-1,1}, {t,-1.75,1.75},
ColorFunction -> Function[{x,y,z,s,t},Hue[((2/3+σ[s,t][[4]])/2)]],
ColorFunctionScaling->False, PlotRange -> {{-1,1},{-0.75,0.75}, {-0.5,0.75}}, Mesh -> False,  Boxed -> False, Axes->False, PlotStyle->{Opacity[0.6]}, PlotPoints -> 200, ViewPoint->{-2.60408,-1.97812,0.869364},ViewVertical->{-0.332387,-0.276651,1.47206}
],
ImageSize -> 300
]

σ[s_, t_] := {s}~Join~Kink2[0,t];
MakeImage["4DHardware-30",
ParametricPlot3D[σ[s,t][[1;;3]],
{s,-1,1}, {t,-1.75,1.75},
ColorFunction -> Function[{x,y,z,s,t},Hue[((2/3+σ[s,t][[4]])/2)]],
ColorFunctionScaling->False, PlotRange -> {{-1,1},{-0.75,0.75}, {-0.5,0.75}}, Mesh -> False,  Boxed -> False, Axes->False, PlotStyle->{Opacity[0.6]}, PlotPoints -> 200, ViewPoint->{-2.60408,-1.97812,0.869364},ViewVertical->{-0.332387,-0.276651,1.47206}
],
ImageSize -> 300
]

σ[s_, t_] := {s}~Join~Kink2[0.25+((s^2)/2),t];
MakeImage["4DHardware-31",
ParametricPlot3D[σ[s,t][[1;;3]],
{s,-1,1}, {t,-1.75,1.75},
ColorFunction -> Function[{x,y,z,s,t},Hue[((2/3+σ[s,t][[4]])/2)]],
ColorFunctionScaling->False, PlotRange -> {{-1,1},{-0.75,0.75}, {-0.5,0.75}}, Mesh -> False,  Boxed -> False, Axes->False, PlotStyle->{Opacity[0.6]}, PlotPoints -> 250, ViewPoint->{-2.60408,-1.97812,0.869364},ViewVertical->{-0.332387,-0.276651,1.47206}
],
ImageSize -> 300
]

σ[s_, t_] := {s}~Join~Kink2[0.8(s^2)-0.05,t];
MakeImage["4DHardware-32",
ParametricPlot3D[σ[s,t][[1;;3]],
{s,-1,1}, {t,-1.75,1.75},
ColorFunction -> Function[{x,y,z,s,t},Hue[((2/3+σ[s,t][[4]])/2)]],
ColorFunctionScaling->False, PlotRange -> {{-1,1},{-0.75,0.75}, {-0.5,0.75}}, Mesh -> False,  Boxed -> False, Axes->False, PlotStyle->{Opacity[0.6]}, PlotPoints -> 250, ViewPoint->{-2.60408,-1.97812,0.869364},ViewVertical->{-0.332387,-0.276651,1.47206}
],
ImageSize -> 300
]

MakeImage["4DHardware-33",
Show[
Graphics3D[{
Opacity[0.25],Yellow,Sphere[{0,0,0},1]
}, Boxed -> False],
ParametricPlot3D[
{r Cos[θ], r Sin[θ],0},
{r,0,1}, {θ,0,2π},
Mesh -> False, PlotStyle -> {Opacity[0.75], Red},  PlotPoints -> 150
],
ParametricPlot3D[
{r Cos[θ], 0, r Sin[θ]},
{r,0,1}, {θ,0,2π},
Mesh -> False, PlotStyle -> {Opacity[0.75], Green},  PlotPoints -> 150,
RegionFunction -> Function[{x,y,z,r,θ}, 8Abs[z]≥1-(x^2)]
],
ParametricPlot3D[
{0,r Cos[θ], r Sin[θ]},
{r,0,1}, {θ,0,2π},
Mesh -> False, PlotStyle -> {Opacity[0.75], Blue}, PlotPoints -> 150,
RegionFunction -> Function[{x,y,z,r,θ}, 4Abs[z]≥1-(y^2) && 8Abs[y]≥1-(z^2)]
],
Lighting -> "Neutral"
],
ImageSize -> 300, ViewPoint->{1.06422,-2.02233,2.49552},ViewVertical->{-0.140349,0.145661,0.979329}]

MakeImage["4DHardware-34",
{v0,v1,v2,v3}={{1,1,1},{1,-1,-1},{-1,1,-1},{-1,-1,1}}//N;
α=ArcCos[((v0.v1)/(Sqrt[(v0.v0)(v1.v1)]))];
CircularSector[v0_,v1_] := Polygon[{{0,0,0}}~Join~#]& /@ Partition[
Table[RotationMatrix[θ, {v0,v1}].v0, {θ,0,α,α/36}],
2,1
];
Graphics3D[{
Opacity[0.25],Yellow,Sphere[{0,0,0},(Sqrt[3])],
Opacity[0.75], Hue[0], EdgeForm[], CircularSector[v0,v1],
Opacity[0.75], Hue[0.15], EdgeForm[], CircularSector[v0,v2],
Opacity[0.75], Hue[0.3], EdgeForm[], CircularSector[v0,v3],
Opacity[0.75], Hue[0.45], EdgeForm[], CircularSector[v2,v3],
Opacity[0.75], Hue[0.6], EdgeForm[], CircularSector[v1,v3],
Opacity[0.75], Hue[0.75], EdgeForm[], CircularSector[v1,v2]
},
Lighting -> "Neutral", Boxed -> False,
ViewPoint->{2.97591,-1.53334,-0.492778},ViewVertical->{0.865466,0.232794,0.443593}
],
ImageSize -> 300
]

MakeImage["4DHardware-35",
h[x_,y_] := (r=(Sqrt[(x^2)+(y^2)]);
Which[
r≤1, (Sqrt[1-(r^2)]),
2≤r≤3,(Sqrt[(r-2)(3-r)]),
(((x-6))^2)+(y^2)≤4, (1/3)(Sqrt[4-(((x-6))^2)-(y^2)]),
True, 0
]);
Plot3D[{h[x,y], -h[x,y]},{x,-5,10}, {y,-5,5},
PlotRange -> All, Boxed -> False, Axes -> None, PlotPoints -> 250, PlotStyle->{Opacity[0.75]}, Mesh -> 8,
ViewPoint->{1.54027,-2.96757,0.520682},ViewVertical->{0.,0.,1.}
],
ImageSize -> 300
]

MakeImage["4DHardware-36",
Show[{
Graphics3D[{
Opacity[0.75],Glow[Blue],CapForm[None],
Tube[{{0,0,-10},{0,0,10}}, 4]
}],
Plot3D[0, {x,-10, 10}, {y,-10,10}, RegionFunction->Function[{x,y}, (x^2)+(y^2)≤(3^2) || (x^2)+(y^2)≥(5^2)],
Mesh -> None, Axes -> None, PlotStyle -> {Opacity[0.75],Glow[Red]}
]
}, Lighting -> None, Boxed -> False],
ImageSize -> 300]

MakeImage["4DHardware-37",
style=Sequence[
PlotStyle -> {Opacity[0.75]},  Mesh ->False, ColorFunctionScaling -> False,
ColorFunction -> Function[{x,y,z,t,h}, Glow[Hue[(3/8)-(3/8)(1-(h^2))]]]
];
Show[{
ParametricPlot3D[h{0,0,1}+t{1,0,0}, {t,0,2}, {h,-1,1},Evaluate[style]],
ParametricPlot3D[h{0,0,1}+t{-(1/2),((Sqrt[3])/2),0}, {t,0,2}, {h,-1,1},Evaluate[style]],
ParametricPlot3D[h{0,0,1}+t{-(1/2),-((Sqrt[3])/2),0}, {t,0,2}, {h,-1,1},Evaluate[style]]
},
Lighting -> None, Axes -> False, Boxed -> False, ViewPoint->{0.174611,-2.89946,1.73569},ViewVertical->{0.00615481,-0.107975,0.995608}, PlotRange -> {{-1,2},{-(Sqrt[3]),2},{-1,1}}],
ImageSize -> 300]

MakeImage["4DHardware-38",
style=Sequence[
PlotStyle -> {Opacity[0.75]},  Mesh ->False, ColorFunctionScaling -> False,
ColorFunction -> Function[{x,y,z,t,h}, Glow[Hue[(3/8)+(3/8)(1-(h^2))]]]
];
Show[{
ParametricPlot3D[h{0,0,1}+t{1,0,0}, {t,0,2}, {h,-1,1},Evaluate[style]],
ParametricPlot3D[h{0,0,1}+t{-(1/2),((Sqrt[3])/2),0}, {t,0,2}, {h,-1,1},Evaluate[style]],
ParametricPlot3D[h{0,0,1}+t{-(1/2),-((Sqrt[3])/2),0}, {t,0,2}, {h,-1,1},Evaluate[style]]
},
Lighting -> None, Axes -> False, Boxed -> False, ViewPoint->{0.174611,-2.89946,1.73569},ViewVertical->{0.00615481,-0.107975,0.995608}, PlotRange -> {{-1,2},{-(Sqrt[3]),2},{-1,1}}],
ImageSize -> 300]

MakeImage["4DHardware-39",
{v0,v1,v2,v3}={{1,1,1},{1,-1,-1},{-1,1,-1},{-1,-1,1}}//N;
Cap[v_, h_]:=Module[{M, α=π/12},
M=Orthogonalize[{v,{1,0,0},{0,1,0}}];
ParametricPlot3D[
{Cos[ϕ]-Cos[α],Sin[ϕ]Cos[θ],Sin[ϕ]Sin[θ]}.M,
{θ,0,2π}, {ϕ,0,α},
PlotStyle -> {Opacity[0.75],Glow@Hue[h]}, Mesh ->None
]
];
Show[
Cap[v0,0/4],Cap[v1,1/4],Cap[v2,2/4],Cap[v3,3/4],
Lighting -> None, Boxed -> False,Axes -> None,
ViewPoint->{1.72505,1.99618,2.24488},ViewVertical->{-0.42126,0.613926,0.67101}
],
ImageSize -> 300
]

MakeImage["4DHardware-40",
{v0,v1,v2,v3}={{1,1,1},{1,-1,-1},{-1,1,-1},{-1,-1,1}}//N;
Cap[v_, h_]:=Module[{M, α=π/12},
M=Orthogonalize[{v,{1,0,0},{0,1,0}}];
ParametricPlot3D[
{Cos[ϕ]-Cos[α],Sin[ϕ]Cos[θ],Sin[ϕ]Sin[θ]}.M,
{θ,0,2π}, {ϕ,0,α},
PlotStyle -> {Opacity[0.75],Glow@Hue[h]}, Mesh ->None
]
];
Show[
Cap[-v0,0/4],Cap[-v1,1/4],Cap[-v2,2/4],Cap[-v3,3/4],
Lighting -> None, Boxed -> False,Axes -> None,
ViewPoint->{1.72505,1.99618,2.24488},ViewVertical->{-0.42126,0.613926,0.67101}
],
ImageSize -> 300
]

MakeImage["4DHardware-41",
{v0,v1,v2,v3}={{1,1,1},{1,-1,-1},{-1,1,-1},{-1,-1,1}}//N;
Cap[v_, h_]:=Module[{M, α=π/8},
M=Orthogonalize[{v,{1,0,0},{0,1,0}}];
ParametricPlot3D[
{Cos[ϕ]-Cos[α],Sin[ϕ]Cos[θ],Sin[ϕ]Sin[θ]}.M,
{θ,0,2π}, {ϕ,0,α},
PlotStyle -> {Opacity[0.85],Glow@Hue[h]}, Mesh ->None, PlotPoints -> 50
]
];
Show[
Cap[v0,0/4],Cap[v1,1/4],Cap[v2,2/4],Cap[v3,3/4],
Lighting -> None, Boxed -> False,Axes -> None, PlotRange->{{-1,1}, {-1,1}, {-1,1}}/4,
ViewPoint->{-2.10548,-1.77719,2.09966},ViewVertical->{0.296139,-0.653224,0.69685}
],
ImageSize -> 300
]

MakeImage["4DHardware-42",
{v0,v1,v2,v3}={{1,1,1},{1,-1,-1},{-1,1,-1},{-1,-1,1}}//N;
Cap[v_, h_]:=Module[{M, α=π/8},
M=Orthogonalize[{v,{1,0,0},{0,1,0}}];
ParametricPlot3D[
{Cos[ϕ]-Cos[α],Sin[ϕ]Cos[θ],Sin[ϕ]Sin[θ]}.M,
{θ,0,2π}, {ϕ,0,α},
PlotStyle -> {Opacity[0.85],Glow@Hue[h]}, Mesh ->None, PlotPoints -> 50
]
];
Show[
Cap[-v0,0/4],Cap[-v1,1/4],Cap[-v2,2/4],Cap[-v3,3/4],
Lighting -> None, Boxed -> False,Axes -> None, PlotRange->{{-1,1}, {-1,1}, {-1,1}}/4,
ViewPoint->{-2.10548,-1.77719,2.09966},ViewVertical->{0.296139,-0.653224,0.69685}
],
ImageSize -> 300
]

MakeImage["4DHardware-43",
Graphics3D[{
Opacity[0.75],Dashed, Thick,
Glow[Red],Polygon[{{-10,0,-10},{-10,0,10},{10,0,10},{10,0,-10}}],
Glow[Blue],
Polygon[{{0,-10,-10},{0,-10,10},{0,-2,10},{0,-2,-10}}],
Polygon[{{0,10,-10},{0,10,10},{0,2,10},{0,2,-10}}],
Line[{{0,0,-10},{0,0,10}}]
}, Lighting -> None, Boxed -> False],
ImageSize -> 300]

MakeImage["4DHardware-44",
Graphics3D[{
Opacity[0.75],Dashed, Thick,
Glow[Hue[0]],Polygon[{{-10,0,-10},{-10,0,10},{10,0,10},{10,0,-10}}],
Glow[Hue[3/8]],
Polygon[{{0,-10,-10},{0,-10,10},{0,-2,10},{0,-2,-10}}],
Polygon[{{0,10,-10},{0,10,10},{0,2,10},{0,2,-10}}],
Line[{{0,0,-10},{0,0,10}}],
Glow[Hue[3/4]],
Polygon[{{2,10,0}, {2,3,0}, {10,3,0}, {10,10,0}}],
Polygon[{{-2,10,0}, {-2,3,0}, {-10,3,0}, {-10,10,0}}],
Polygon[{{-2,-10,0}, {-2,-3,0}, {-10,-3,0}, {-10,-10,0}}],
Polygon[{{2,-10,0}, {2,-3,0}, {10,-3,0}, {10,-10,0}}],
Line[{{-10,0,0},{-3,0,0}}], Line[{{3,0,0},{10,0,0}}],
Line[{{0,-10, 0},{0,-2,0}}], Line[{{0,2, 0},{0,10,0}}]
}, Lighting -> None, Boxed -> False],
ImageSize -> 300]

MakeImage["4DHardware-45",
ParametricPlot3D[
{t Cos[α],t Sin[α], Sin[2α]},
{α,0,π/2}, {t,-1,1},
ColorFunction -> Function[{x,y,z,α,t}, Glow[Hue[((3α)/(2π))]]],
RegionFunction -> Function[{x,y,z,α,t} , α<π/4∨Abs[t]>0.15(1-Sin[2α])],
ColorFunctionScaling->False, Lighting -> None, Boxed -> False, Axes -> None, Mesh -> False,
PlotStyle->Opacity[0.8],
ViewPoint->{3.04409,-1.04426,1.02454},ViewVertical->{0.656036,-0.224113,1.44137}
],
ImageSize -> 300]

MakeImage["4DHardware-46",
ParametricPlot3D[
{t Cos[α],t Sin[α], Sin[2α]},
{α,0,π/2}, {t,-1,1},
RegionFunction -> Function[{x,y,z,α,t} , α<π/4∨Abs[t]>0.15(1-Sin[2α])],
Boxed -> False, Axes -> None, Mesh -> False,
PlotStyle-> Directive[Red, Opacity[0.8]],
ViewPoint->{3.04409,-1.04426,1.02454},ViewVertical->{0.656036,-0.224113,1.44137}
],
ImageSize -> 300]

MakeImage["4DHardware-47",Graphics3D[{
Opacity[0.85],
Glow[Red],Polygon[{{-10,0,-10},{-10,0,10},{10,0,10},{10,0,-10}}],
Glow[Green],
Polygon[{{0,-10,-10},{0,-10,10},{0,-1,10},{0,-1,-10}}],
Polygon[{{0,10,-10},{0,10,10},{0,1,10},{0,1,-10}}],
Opacity[1], Blue,
Arrow[{{-6,8,0},{6,8,0}}], Arrow[{{-6,-8,0},{6,-8,0}}],
Arrow[{{8,-6,0},{8,6,0}}], Arrow[{{-8,-6,0},{-8,6,0}}]
, Black,
Text[Style[x, 16],{3,9,1}], Text[Style[y, 16],{4,-6.5,1}],
Text[Style[z, 16], {7,-4,1}], Text[Style[z, 16], {-6.5,-4,1}]
}, Lighting -> None, Boxed -> False,
ViewPoint->{0.90007,-1.05231,3.08748},ViewVertical->{-0.232159,0.442406,0.866244}
], ImageSize -> 300]