Wolfram Cloud Document

In[]:=

UsingRuledSurfacePlot5::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 z = 2, x = 0 and the circumference

2

x

+

2

y

= 4, z = 0. 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 is the directrix curve and

c

2

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

In[]:=

Manipulate[

ζ

1

[u_]:={0,2Sin[u],2};

ζ

2

[u_]:={2Cos[u],0,-2};

ζ

3

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

ζ

1

[u],

ζ

2

[u],{u,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],0.03]}],Graphics3D[{Red,Ball[

ζ

3

[k1],0.03]}],ParametricPlot3D[

ζ

3

[u],{u,0,2π}],ParametricPlot3D[

ζ

1

[u],{u,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,ImageSize700,ViewPoint{5,-10,5}],{k1,0.00001,2π,0.00001},SaveDefinitionsTrue,ControlPlacementTop,SaveDefinitions->True]

Out[]=

k1