RevolutionSurfaceAstroid::usage="The surface of revolution is based on the astroid with parametric equations:​27 Cost
3
]
​, 27 Sin[t
3​
]
​, 0} and cartesian equation:
2
3
x
+ y
2
3
​
= 9; z = 0. And it will be rotated around the X axis in the first example.In the second example you will see the envelope of a family of spheres with center on the axis:ℒ: {-8, 5, -1} + t {5, 4, -3}.And the envelope will have the shape of the revoution surface based on the astroid obtained in example 1.But only half of the surface of revolution will be observed (by the nature of this curve. Most of the time the complete surface is observed as happened in the notebooks of cuadrics that circumscribed the family of spheres). Reference: Personal.";
Example 1:
Animation:
In[]:=
Manipulate[Show[{RevolutionPlot3D[{27
3
Cos[t]
,27
3
Sin[t]
,0},{t,0,2π},{θ,0,θ1},RevolutionAxis{1,0,0},PlotStyle->Opacity[0.6],MeshFalse,BoundaryStyleDirective[Black,Thick],PerformanceGoal"Quality",ColorFunction"BlueGreenYellow",PlotPoints->60],​​ParametricPlot3D[t{1,0,0},{t,-30,30},ColorFunction->"BlueGreenYellow",PlotStyleThick]},AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRangeAll,ViewPoint{1.3,-2.4,2.},ImageSize700],Style["Revolution surface based on an astroid:",Bold,Large],{{θ1,1,"Value (θ)"},0.1,2π,0.1},ControlPlacementTop]
Out[]=
​
Revolution surface based on an astroid:
Value (θ)
Example 2:
In[]:=
Out[]=