Some Types of Ruled Surfaces
Author
Alejandro Latorre Chirot
Title
Some Types of Ruled Surfaces
Description
This animation shows how different cases will be generated from the equation of a ruled surface. The equation of a ruled surface is: X(u, v) = b(u) + v d(u), where b(u) is the base curve (directrix) and d(u) is director curve (generatrix).
Category
Working Material
Keywords
Ruled, surface, directrix, generatrix
URL
http://www.notebookarchive.org/2024-09-7v6usjt/
DOI
https://notebookarchive.org/2024-09-7v6usjt
Date Added
2024-09-17
Date Last Modified
2024-09-17
File Size
447.49 kilobytes
Supplements
Rights
Redistribution rights reserved
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Some Types of Ruled Surfaces
Some Types of Ruled Surfaces
Alejandro Latorre Chirot
AlgunosTiposDeSuperficiesRegladas::usage="Superficie reglada:(u, v) = (u) + v (u)Donde (u) es la curva base (directriz),(u), la curva directora (generatriz).Referencia: Wolfram MathWorld, Ruled Surface. ";
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Hiperboloide de una hoja:
In[]:=
Manipulate[Show[{ParametricPlot3D[{Cos[u],2Sin[u],0}+{-vSin[u],2vCos[u],v},{u,0,t},{v,-5,5},PlotStyle->Opacity[0.6],MeshFalse,BoundaryStyleDirective[Black,Thick],PerformanceGoal"Quality",ColorFunction"BlueGreenYellow"]},AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRangeAll],Style["Hiperboloide de una hoja:",Bold,Medium],{{t,1,"Valor (t)"},0.01,2π,0.01},ControlPlacementLeft]
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Paraboloide hiperbólico:
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Manipulate[Show[{ParametricPlot3D[{u,0,}+v{1,-2,2u},{u,0,t},{v,-1,1},PlotStyle->Opacity[0.6],MeshFalse,BoundaryStyleDirective[Black,Thick],PerformanceGoal"Quality",ColorFunction"BlueGreenYellow"]},AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRangeAll],Style["Paraboloide hiperbólico:",Bold,Medium],{{t,1,"Valor (t)"},0.01,1,0.01},ControlPlacementLeft]
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Conoide de Plücker:
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Manipulate[Show[{ParametricPlot3D[{0,0,2Cos[u]Sin[u]}+v{Cos[u],Sin[u],0},{u,0,t},{v,-5,5},PlotStyle->Opacity[0.6],MeshFalse,BoundaryStyleDirective[Black,Thick],PerformanceGoal"Quality",ColorFunction"BlueGreenYellow"]},AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRangeAll],Style["Conoide de Plücker:",Bold,Medium],{{t,1,"Valor (t)"},0.01,2π,0.01},ControlPlacementLeft]
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In[]:=
gr1=Show[{ParametricPlot3D[{0,0,2Cos[u]Sin[u]}+v{Cos[u],Sin[u],0},{u,0,2π},{v,-5,5},PlotStyle->Opacity[0.6],MeshFalse,BoundaryStyleDirective[Black,Thick],PerformanceGoal"Quality",ColorFunction"BlueGreenYellow"]},AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRangeAll]
Out[]=
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ResourceFunction["SpinShow"][gr1,120]
Out[]=
Banda de Möbius :
ManipulateShowParametricPlot3D{Cos[u],Sin[u],0}+vCosuCos[u],CosuSin[u],Sinu,{u,0,t},{v,-5,5},PlotStyle->Opacity[0.4],MeshFalse,BoundaryStyleDirective[Black,Thick],PerformanceGoal"Quality",ColorFunction"BlueGreenYellow",AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRangeAll,Style["Banda de Möbius :",Bold,Medium],{{t,1,"Valor (t)"},0.01,2π,0.01},ControlPlacementLeft
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In[]:=
gr=ShowParametricPlot3D{Cos[u],Sin[u],0}+vCosuCos[u],CosuSin[u],Sinu,{u,0,2π},{v,-5,5},PlotStyle->Opacity[0.4],MeshFalse,BoundaryStyleDirective[Black,Thick],PerformanceGoal"Quality",ColorFunction"BlueGreenYellow",AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRangeAll
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Out[]=
In[]:=
ResourceFunction["SpinShow"][gr,120]
Out[]=
Cite this as: Alejandro Latorre Chirot, "Some Types of Ruled Surfaces" from the Notebook Archive (2024), https://notebookarchive.org/2024-09-7v6usjt
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