RevolutionSurfaceBicorn::usage="The surface of revolution is based on the Bicorn with cartesian equation:( - ) = ( + 2 a z - ; y = 0. And it will be rotated around the Z 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: {-2, 1, 3} + t {1, -4, 2}.And the envelope will have the shape of the revoution surface based on the bicorn obtained in example 1.Reference: Personal.";
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Example 1
Animation:
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ManipulateShowa=3;RevolutionPlot3Dx,0,,x,0,,{x,-3,3},{θ,0,θ1},RevolutionAxis{0,0,1},PlotStyle->Opacity[0.6],MeshFalse,BoundaryStyleDirective[Black,Thick],PerformanceGoal"Quality",ColorFunction"BlueGreenYellow",PlotPoints->60,ParametricPlot3D[t{0,0,1},{t,-2,5},ColorFunction->"BlueGreenYellow",PlotStyleThick],AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRangeAll,ViewPoint{-2,-2.4,-1.},ImageSize700,Style["Revolution surface based on the Bicorn:",Bold,Large],{{θ1,1,"Value (θ)"},0.1,2π,0.1},ControlPlacementTop
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Example 2:
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