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Properly combine RevolutionPlot3D graphics?

GROUPS:

I am planning to graph a Solid of Constant width, more specifically, a rotated Reuleaux Pentagon. Due to the limitation of my mathematical understanding, I can only plot them using three functions and use RevolutionPlot3D to create graph. However, I don't really know how to combine them. The following code for two of the three parts don't seem to work:

Show[RevolutionPlot3D[{Sqrt[
    1 - (t - Sin[\[Pi]/5]/(2 Sin[(3 \[Pi])/10]))^2] - 1/2}, {t, 
   Sin[\[Pi]/5]/(2 Sin[(3 \[Pi])/10]), Sin[(72 \[Pi])/180]}, 
  RevolutionAxis -> "X"], 
 RevolutionPlot3D[{Sqrt[1 - t^2]}, {t, Sin[(72 \[Pi])/180], 1}, 
  RevolutionAxis -> "X"]]

If you try and plot them one by one, it is quite easy to see how the graph created with the "Show" function doesn't work. Graphs one by one:

RevolutionPlot3D[{Sqrt[
        1 - (t - Sin[\[Pi]/5]/(2 Sin[(3 \[Pi])/10]))^2] - 1/2}, {t, 
       Sin[\[Pi]/5]/(2 Sin[(3 \[Pi])/10]), Sin[(72 \[Pi])/180]}, 
      RevolutionAxis -> "X"]

 RevolutionPlot3D[{Sqrt[1 - t^2]}, {t, Sin[(72 \[Pi])/180], 1}, 
      RevolutionAxis -> "X"]

If done properly, I think they should line up seamlessly. Does any one have any idea about it?

POSTED BY: Chao Peter Yang
Answer
13 days ago

Hi Chao Peter Yang,

I guess the default plot range is not wide enough. Simply add the option PlotRange -> All like so:

Show[RevolutionPlot3D[{Sqrt[1 - (t - Sin[\[Pi]/5]/(2 Sin[(3 \[Pi])/10]))^2] - 1/2}, {t, 
   Sin[\[Pi]/5]/(2 Sin[(3 \[Pi])/10]), Sin[(72 \[Pi])/180]}, RevolutionAxis -> "X"], 
 RevolutionPlot3D[{Sqrt[1 - t^2]}, {t, Sin[(72 \[Pi])/180], 1}, RevolutionAxis -> "X"], PlotRange -> All]

Regards -- Henrik

POSTED BY: Henrik Schachner
Answer
13 days ago

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