BicornSurfaceRevolution::usage="The bicorn  - 2
2
Cos[t]
(2+Cos[t])
3+
2
Sin[t]
​, 2 Sin[t]​, -4
2
Cos[t]
(2+Cos[t])
3+
2
Sin[t]
 it is located on the plane z = 2x. It will be rotated around the straight line t{1, 0, 2}. Reference: Personal. ";
In[]:=
ShowParametricPlot3D-2
2
Cos[t]
(2+Cos[t])
3+
2
Sin[t]
,2Sin[t],-4
2
Cos[t]
(2+Cos[t])
3+
2
Sin[t]
,{t,-π,π},ContourPlot3D[z==2x,{x,-5,5},{y,-5,5},{z,-5,5},ContourStyle->Opacity[0.2]],ParametricPlot3D[{t,0,2t},{t,-2.5,1}],AxesLabel->{x,y,z},AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRangeAll,ViewPoint{6,-2.4,1.}
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In[]:=
ManipulateShowRevolutionPlot3D-2
2
Cos[t]
(2+Cos[t])
3+
2
Sin[t]
,2Sin[t],-4
2
Cos[t]
(2+Cos[t])
3+
2
Sin[t]
,{t,0,2π},{θ,0,θ1},RevolutionAxis{1,0,2},PlotStyle->Opacity[0.6],MeshFalse,BoundaryStyleDirective[Black,Thick],PerformanceGoal"Quality",ColorFunction"BlueGreenYellow",PlotPoints->60,​​ParametricPlot3D[t{1,0,2},{t,-2.5,1},ColorFunction->"BlueGreenYellow",PlotStyleThick],AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRangeAll,ViewPoint{6,-2.4,1.},ImageSize700,Style["Surface of revolution:",Bold,Large],{{θ1,1,"Value (θ)"},0.00001,2π,0.00001},ControlPlacementTop
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​
Surface of revolution:
Value (θ)