UsingRuledSurfacePlot4::usage=" A ruled surface is generated by a straight line that moves in such a way that it always remains parallel to the YZ plane and cuts to the straight line: x + z = 1, y = 0 and to the parabola
2
y
= x, 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 line 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.418,2003;​ Personal. ";
In[]:=
​​Manipulate[Show[
ζ
1
[u_]:={
2
u
,0,1-
2
u
};
ζ
2
[u_]:={0,u,
2
u
-1};​​
ζ
3
[u_]:={
2
u
,u,0};ResourceFunction["RuledSurfacePlot"][
ζ
1
[u],
ζ
2
[u],{u,-1,k1},{v,-1,1},PerformanceGoal"Quality",MeshStyleDirective[AbsoluteThickness[0.5],Opacity[0.2]],PlotStyleOpacity[0.1]],Graphics3D[{Red,Ball[
ζ
1
[k1],0.015]}],Graphics3D[{Red,Ball[
ζ
3
[k1],0.015]}],Graphics3D[{Red,Thick,InfiniteLine[{
ζ
1
[k1],
ζ
3
[k1]}]}],ParametricPlot3D[
ζ
1
[u],{u,-1,1}],ParametricPlot3D[
ζ
3
[u],{u,-1,1}],AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,PlotRangeAll,ViewPoint{15,-10,8},ImageSize700​​],{k1,-1.0+0.00001,1,0.00001},SaveDefinitionsTrue,ControlPlacementTop]
Out[]=
​
k1