RevolutionSurfaceAgnesiCurve::usage="The surface of revolution is based on the Agnesi curve with cartesian equation:y =
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​; 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: {3, -2, 4} + t {1, 0, 0}.And the envelope will have the shape of the revoution surface based on the Agnesi curve obtained in example 1.Reference: Personal.";
Example 1:
Animation:
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ManipulateShowa=
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;RevolutionPlot3Dx,
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,0,{x,-3,3},{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,-5,5},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 the Agnesi curve:",Bold,Large],{{θ1,1,"Value (θ)"},0.1,2π,0.1},ControlPlacementTop
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Revolution surface based on the Agnesi curve:
Value (θ)
Example 2:
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