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UsingRuledSurfacePlot::usage=" A parabolic ciclid of Dupin is represented. To use the ResourceFunction, the RuledSurfacePlot[

c

1

,

c

2

,u] it should be considered so:



χ

(u,v) =

c

1

(u) + v

c

2

(u),

c

1

it's the directrix and

c

2

the director curve. The generatrix line passes through the two curves.. References: Wolfram MathWorld: ResourceFunction, RuledSurfacePlot; Personal. ";

In[]:=

p=1;Manipulate

ζ

1

[u_]:=

2

p

-

2

u

2p

,u,0;

ζ

2

[u_]:=

2

u

2p

,0,u;Show[ResourceFunction["RuledSurfacePlot"][

ζ

1

[u],

ζ

2

[u],{u,-5,k},{v,-5,5},PerformanceGoal"Quality",MeshStyleDirective[AbsoluteThickness[0.5],Opacity[0.2]],PlotStyleOpacity[0.1]],Graphics3D[{Red,Ball[

ζ

1

[k],0.2]}],Graphics3D[{Red,Ball[

ζ

2

[k],0.2]}],ParametricPlot3D[

ζ

1

[u],{u,-5,5}],ParametricPlot3D[

ζ

2

[u],{u,-5,5}],Graphics3D[{Red,Thick,InfiniteLine[{

ζ

1

[k],

ζ

2

[k]}]}],AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,PlotRange15,ImageSize900,ViewPoint{1.3,-2.4,2.}],{k,-5+0.00001,5,0.00001},SaveDefinitionsTrue,ControlPlacementTop

Out[]=

k