InversePedalNegativePedalTwistedSurface::usage="In this notebook for the twisted surface, its inversion will be made with respect to a sphere with center at the origin and radius 4. Once you have the inverse you will get its pedal and negative-pedal surfaces. Reference: Personal.";
Animation of Pedal Surface
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SwatchLegend[{Yellow,Green,Gray},{"Twisted surface","Inversion surface","Pedal surface of inversion surface"}]Manipulate[σ[u_,v_]:={Cos[v]Cos[u],-Sin[v]Cos[u],v+Sin[u]};α=ResourceFunction["InversionSurface"][{0,0,0},4,σ[u,v],{u,v}];=ResourceFunction["PedalSurface"][α,{0,0,0},{u,v}];Show[{ParametricPlot3D[σ[u,v],{u,0,2π},{v,0,2π},PlotStyle{Yellow,Opacity[1]},PerformanceGoal->"Quality",PlotPoints60],ParametricPlot3D[α,{u,0,2π},{v,0,2π},PlotStyle{Green,Opacity[0.3]},MaxRecursion->3],ParametricPlot3D[,{u,0,t1},{v,0,2π},PlotStyle{Gray,Opacity[0.2]},MaxRecursion->3]},AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,ViewPoint{1.3,-2.4,1},PlotRange10,ImageSize700],{t1,0.00001,2π,0.00001},SaveDefinitions->True,ControlPlacement->Top]
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Animation of Negative Pedal Surface
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σ[u_,v_]:={Cos[v]Cos[u],-Sin[v]Cos[u],v+Sin[u]};α=ResourceFunction["InversionSurface"][{0,0,0},4,σ[u,v],{u,v}]
++,-++,++;
16Cos[u]Cos[v]
2
Cos[u]
2
Cos[v]
2
(v+Sin[u])
2
Cos[u]
2
Sin[v]
16Cos[u]Sin[v]
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Cos[u]
2
Cos[v]
2
(v+Sin[u])
2
Cos[u]
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Sin[v]
16(v+Sin[u])
2
Cos[u]
2
Cos[v]
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(v+Sin[u])
2
Cos[u]
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Sin[v]
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α=++,-++,++;=D[α,u];=D[α,v];=Nα-()
16Cos[u]Cos[v]
2
Cos[u]
2
Cos[v]
2
(v+Sin[u])
2
Cos[u]
2
Sin[v]
16Cos[u]Sin[v]
2
Cos[u]
2
Cos[v]
2
(v+Sin[u])
2
Cos[u]
2
Sin[v]
16(v+Sin[u])
2
Cos[u]
2
Cos[v]
2
(v+Sin[u])
2
Cos[u]
2
Sin[v]
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σ
NP
α.()
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2
Norm[]
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