RevolutionPlot3D

RevolutionPlot3D[fz, {t, tmin, tmax}] generates a plot of the surface of revolution with height fz at radius t.

• RevolutionPlot3D[fz, {t, tmin, tmax}, {θ, θmin, θmax}] takes the azimuthal angle θ to vary between θmin and θmax.
• RevolutionPlot3D[{fx, fz}, {t, tmin, tmax}] generates a plot of the surface obtained by rotating the parametric curve with x, z coordinates {fx, fz} around the z axis.
• RevolutionPlot3D[{fx, fz}, {t, tmin, tmax}, {θ, θmin, θmax}] takes the azimuthal angle θ to vary from θmin to θmax.
• RevolutionPlot3D[{fx, fy, fz}, {t, tmin, tmax}, ...] plots the surface obtained by rotating the parametric curve with x, y, z coordinates {fx, fy, fz}.

Examples

Create a simple surface of revolution:

RevolutionPlot3D[Sin[t], {t, 0, Pi}]

Create a torus-like shape:

RevolutionPlot3D[{2 + Cos[t], Sin[t]}, {t, 0, 2 Pi}]

Partial revolution (half surface):

RevolutionPlot3D[t^2, {t, 0, 1}, {θ, 0, Pi}]

Please visit the official Wolfram Language Reference for more details.