Wolfram Cloud Document

In[]:=

UsingRuledSurfacePlot3::usage=" A ruled surface is generated by a line that moves in such a way that it always remains parallel to the XZ plane and cuts to the line x = 3, z = 0 and the ellipse

2

y

+ 4

2

z

= 4, x = 0. To the use 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 is the directrix curve and

c

2

the director curve. The generatrix line go through the two curves. References: Wolfram MathWorld: ResourceFunction, RuledSurfacePlot. Lehman, Charles H. Geometría Analítica. Ed. Limusa: p.419, 2003; Personal ";

In[]:=

Manipulate[

ζ

1

[θ_]:={3,2Cos[θ],0};

ζ

2

[θ_]:={-3,0,Sin[θ]};

ζ

3

[θ_]:={0,2Cos[θ],Sin[θ]};Show[ResourceFunction["RuledSurfacePlot"][

ζ

1

[θ],

ζ

2

[θ],{θ,0,k1},{v,-1,1},PerformanceGoal"Quality",MeshStyleDirective[AbsoluteThickness[0.5],Opacity[0.2]],PlotStyleOpacity[0.1]],Graphics3D[{Red,Ball[

ζ

1

[k1],0.06]}],Graphics3D[{Red,Ball[

ζ

3

[k1],0.06]}],ParametricPlot3D[

ζ

3

[θ],{θ,0,2π}],ParametricPlot3D[

ζ

1

[θ],{θ,0,2π}],Graphics3D[{Red,Thick,InfiniteLine[{

ζ

1

[k1],

ζ

3

[k1]}]}],AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,PlotRangeAll,ViewPoint{5,-10,5},ImageSize700],{k1,0.00001,2π,0.00001},SaveDefinitionsTrue,ControlPlacementTop,SaveDefinitions->True]

Out[]=

k1