# Why is this RevolutionPlot3D empty in the middle around x = 0.5?

Why is this RevolutionPlot3D empty in the middle around x = 0.5 like this?

RevolutionPlot3D[Min[x^2, x^2 - 2 x + 1], {x, 0, 1},
RevolutionAxis -> "X", BoxRatios -> {1, 1, 1}]


• Please write an INFORMATIVE title... one that deals with the content of your question more specifically. After all, what do YOU think the average reader understands from your title alone? Commented Apr 14, 2022 at 3:13
• @DavidG.Stork sorry for that. I didn't notice much as it was the only thing in my mind.
– hana
Commented Apr 14, 2022 at 5:20

## 1 Answer

Original answer

RevolutionPlot3D[Min[x^2, x^2 - 2 x + 1], {x, 0, 1},
RevolutionAxis -> "X", BoxRatios -> {1, 1, 1}, Exclusions -> None]


Edit: many thanks to @Bob Hanlon for suggesting the use of MaxRecursion

RevolutionPlot3D[Min[x^2, x^2 - 2 x + 1], {x, 0, 1},
RevolutionAxis -> "X", BoxRatios -> {1, 1, 1}, Exclusions -> None,
MaxRecursion -> 6]


• +1 MaxRecursion -> 6 is useful Commented Apr 13, 2022 at 23:30
• rgn = ImplicitRegion[(y^2 + z^2 <= x^4 && 0 <= x <= 1/2) || (y^2 + z^2 <= (x^2 - 2 x + 1)^2 && 1/2 < x <= 1), {x, y, z}]; Then Volume[rgn] evaluates to Pi/80 Commented Apr 14, 2022 at 0:28
• I found an old thread and this works too. ImplicitRegion[ z^2 + y^2 <= Min[x^2, x^2 - 2 x + 1]^2 && 0 <= x <= 1, {x, y, z}]
– hana
Commented Apr 14, 2022 at 1:05
• @hana I think that the main idea -which was initially demonstrated by Bob here- is to use $x,y,z$ as variables such that Volume is well-defined. Great suggestions by both!!!
– bmf
Commented Apr 14, 2022 at 1:11
• Thanks for the update and the MaxRecursion -> 6 looks much nicer!
– hana
Commented Apr 14, 2022 at 5:22