RevolutionSurfaceDeltoid::usage="The surface of revolution is based on the Deltoid with cartesian equation:​(​
2
x
+
2
y
2
)
- 8 a x(​
2
x
- 3
2
y
​) + 18
2
a
​(​
2
x
+
2
y
​) - 27
4
a
= 0; 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: {0, 2, 2} + t {1, 0, 0}.And the envelope will have the shape of the revoution surface based on the deltoid obtained in example 1.Reference: Personal.";
Example 1
Animation:
In[]:=
ManipulateShowa=3;RevolutionPlot3Dx,
-9
2
a
-12ax-
2
x
-2
a
3
(3a+2x)
,0,x,
-9
2
a
-12ax-
2
x
+2
a
3
(3a+2x)
,0,x,-
9
2
,9,{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,-10,10},ColorFunction->"BlueGreenYellow",PlotStyleThick],AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRangeAll,ViewPoint{-2,-2.4,2.},ImageSize700,Style["Revolution surface based on the Deltoid:",Bold,Large],{{θ1,1,"Value (θ)"},0.1,2π,0.1},ControlPlacementTop
Out[]=
​
Revolution surface based on the Deltoid:
Value (θ)
Example 2:
In[]:=
Out[]=