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plotting - RevolutionPlot3D: but NOT revolving about the z axis


I want to demonstrate generating a solid of revolution by revolving a planar region about, say, a horizontal axis. However, RevolutionPlot3D doesn't seem to have an option for revolving a curve about something other than the z axis. I'm curious how you all would handle this.


Here's a simple example:


theta0 = Pi;
Manipulate[

  GraphicsRow[{
    Plot[x^2, {x, 0, 1}, PlotStyle -> {Thick, Black}, Filling -> Axis],
    Rotate[RevolutionPlot3D[Sqrt[x], {x, 0, 1}, {t, theta0 - .001, T},
    PlotRange -> {{-1, 1}, {-1, 1}, {0, 1}}, BoxRatios -> 1, 
    Boxed -> False, Axes -> False, ViewPoint -> {0, -2, 1}], -Pi/2]
  }],
{T, theta0, theta0 + 2 Pi}]

enter image description here


My questions:





  1. Is there a "better" way to showcase revolving about a horizontal axis of revolution than what I've done with Rotate?




  2. Is it possible to generate the higher quality, finished surface of revolution while the slider bar is moving instead of only when the slider is released?




  3. How do I prevent the vertical tick labels on the far left edge as well as the graphic on the far right edge from being clipped? (I tried Spacings and ImagePadding.)





  4. How do I vertically align the horizontal axis of revolution of the right graphic with the horizontal axis of the left graphic?




Edit: I had a follow up question but I will spin that off as a separate question.



Answer



Answers:



  1. RevolutionAxis, set to either "X" or {1,0,0}. (This also required adjustments to the PlotRange and ViewPoint options.)

  2. PerformanceGoal -> "Quality"


  3. I switched from GraphicsRow to Row, which I like much better. (I then also set ImageSize -> Small to make the plots a bit bigger than they'd naturally be in Row.)

  4. I was able to align the plots pretty well by setting BaselinePosition for each of the plots.


I also turned off the Mesh since I felt it was distracting, especially at the beginning of the sequence.


theta0 = Pi;
Manipulate[Row[{
   Plot[x^2, {x, 0, 1}, PlotStyle -> {Thick, Black}, 
       Filling -> Axis, BaselinePosition -> Axis, ImageSize -> Small], 
   RevolutionPlot3D[x^2, {x, 0, 1}, {t, theta0 - .001, T}, 
       PlotRange -> {{0, 1}, {-1, 1}, {-1, 1}}, BoxRatios -> 1, 

       Boxed -> False, Axes -> False, ViewPoint -> {1, -2, 0}, 
       Mesh -> None, RevolutionAxis -> "X", PerformanceGoal -> "Quality",
       BaselinePosition -> Center, ImageSize -> Small]
   }], {T, theta0, theta0 + 2 Pi}]

enter image description here


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