Superellipsoid

Author

Eric W. Weisstein
January 30, 2022

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Surfaces/Superellipsoid.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Superellipsoid.html.

©2022 Wolfram Research, Inc. except for portions noted otherwise

Pictures

V5

ImplicitPlot3D

<<Utilities`Typesetting`
<<ImplicitPlot3D`

With[{a=1,b=1.5,c=2},
Show[GraphicsArray[
Graphics3D[
{
EdgeForm[],ImplicitPlot3D[Abs[x/a]^#+Abs[y/b]^#+Abs[z/c]^#==1,{x,-2,2},{y,-2,2},{z,-2,2},
DisplayFunction->Identity,
Contours->{0},
PlotPoints->20][[1]]
},
Boxed->False,
PlotRange->All,
PlotLabel->TraditionalForm[n==#]
]&/@Range[4]
],GraphicsSpacing->-.15]
]//Timing

ContourPlot3D

<<Graphics`ContourPlot3D`

With[{a=1,b=1.5,c=2},
Show[GraphicsArray[
ContourPlot3D[Abs[x/a]^#+Abs[y/b]^#+Abs[z/c]^#,
{x,-2,2},{y,-2,2},{z,-2,2},
DisplayFunction->Identity,
Contours->{1},
PlotPoints->5,
Boxed->False,
PlotRange->All,
PlotLabel->TraditionalForm[n==#]
]&/@Range[4]
],GraphicsSpacing->-.15]
]//Timing

V6

With[{a=1,b=1.5,c=2},
GraphicsGrid[{
ContourPlot3D[Abs[x/a]^#+Abs[y/b]^#+Abs[z/c]^#==1,
{x,-2,2},{y,-2,2},{z,-2,2},
Boxed->False,Axes->False,Mesh->False,
PlotLabel->TraditionalForm[n==#]
]&/@Range[4]},Spacings->-170,ImageSize->500
]]