Graphics`SurfaceOfRevolution`

A surface of revolution is generated by rotating a curve about a given line. SurfaceOfRevolution plots the surface of revolution generated by rotating about any axis the graph of a function in the - plane or a curve described parametrically.

Surface of revolution of a curve.

This loads the package.

In[1]:= <<Graphics`SurfaceOfRevolution`

The curve is rotated about the axis.

In[2]:= SurfaceOfRevolution[
Sin[x], {x, 0, 2 Pi}]

Out[2]=

Any options you give are passed directly to the built-in ParametricPlot3D.

In[3]:= SurfaceOfRevolution[ Sin[x], {x, 0, 2 Pi},
ViewVertical -> {1, 0, 0},
Ticks -> {Automatic, Automatic,
{-1., 0, 1.}}]

Out[3]=

This gives the surface of revolution of a curve in the - plane described parametrically with the variable .

In[4]:= SurfaceOfRevolution[{1.1 Sin[u], u^2},
{u, 0, 3 Pi/2}, BoxRatios -> {1, 1, 2}]

Out[4]=

Surface of revolution of a curve over a reduced angle.

Here is the same curve rotated from to .

In[5]:= SurfaceOfRevolution[{1.1 Sin[u], u^2},
{u, 0, 3 Pi/2}, {t, 0, Pi},
BoxRatios -> {1, 1, 2}]

Out[5]=

Specifying the axis of revolution.

Here is a curve rotated about a different axis in three-dimensional space.

In[6]:= SurfaceOfRevolution[x^2, {x, 0, 1},
RevolutionAxis -> {1, 1, 1}]

Out[6]=

Surfaces of revolution from a list of data points.

We can also generate a surface of revolution from a curve specified by a list of data points. The points can lie in the - plane or in three-dimensional space.

Here is a list of data in the - plane.

In[7]:= dat = Table[{n, n^3}, {n, 0, 1, .1}];

This gives the surface of revolution of dat about the axis connecting the origin to point {1, -1, 1} .

In[8]:= ListSurfaceOfRevolution[dat, {t, 0, Pi/2},
RevolutionAxis -> {1, -1, 1},
PlotRange -> All]

Out[8]=