Pensieve header: Images for the BF2C talk.

SetDirectory["C:\\drorbn\\AcademicPensieve\\2014-02\\BF2C"]

Kink0[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}})}})];
Kink[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["Ingredient1",
Graphics3D[{
Opacity[0.85],
Glow[Green],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["Ingredient2",
Graphics3D[{
Opacity[0.75],
Glow[Hue[0]],Polygon[{{-10,0,-10},{-10,0,10},{10,0,10},{10,0,-10}}],
Glow[Hue[1/3]],
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[2/3]],
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["Ingredient3",
ParametricPlot3D[{s,Kink0[s,t][[1]], Kink0[s,t][[2]]},
{s,-0.25,1}, {t,-1.75,1.75},
ColorFunction -> Function[{x,y,z,s,t},Hue[((1+Kink0[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["Roseman1a",
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["Roseman1b",
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
]

MakeImage["Roseman2a",
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["Roseman2b",
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
]

σ[s_, t_] := {s}~Join~Kink[0.75-(s^2),t];
MakeImage["Roseman3a",
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~Kink[0,t];
MakeImage["Roseman3b",
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~Kink[0.25+((s^2)/2),t];
MakeImage["Roseman4a",
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~Kink[0.8(s^2)-0.05,t];
MakeImage["Roseman4b",
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["Roseman5a",
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["Roseman5b",
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
]

MakeImage["Roseman6a",
Show[
ParametricPlot3D[{s,Kink0[s,t][[1]], Kink0[s,t][[2]]},
{s,-0.5,1}, {t,-1.75,1.75},
ColorFunction -> Function[{x,y,z,s,t},Hue[((1+Kink0[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["Roseman6b",
Show[
ParametricPlot3D[{s,Kink0[s,t][[1]], Kink0[s,t][[2]]},
{s,-0.5,1}, {t,-1.75,1.75},
ColorFunction -> Function[{x,y,z,s,t},Hue[((1+Kink0[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["Roseman7a",
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]

$Image["Roseman7a"]

MakeImage["Roseman7b",
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["VeeAtom",
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]

MakeImage["DoublePoint",
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["Xp",
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["Xm",
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["BubbleWrap",
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 -> 600
]

MakeImage["ShieldedTriplePoint",
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 -> 450, ViewPoint->{1.06422,-2.02233,2.49552},ViewVertical->{-0.140349,0.145661,0.979329}]

MakeImage["ShieldedVertex",
{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/72}],
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 -> 450
]

MakeImage["ColourWheel",
s="rggbrb";
ImageCrop[PieChart3D[
Table[1, {StringLength[s]}],
ChartStyle :> (Characters[s] /. {"r"->Red, "g"->Green, "b"->Blue}),
SectorOrigin->{{RandomReal[{0,2π}],"Counterclockwise"},1},
ChartBaseStyle->EdgeForm[{Thickness[0.03],Black}],
ChartElementFunction->"ProfileSector3D",
ImagePadding -> 0, ImageMargins -> 0, PlotRangePadding->0
]],
ImageSize -> 300]