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Mathematica

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Standard Packages

Graphics

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.

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

The curve is rotated about the

axis.

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

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

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}]

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}]

Specifying the axis of revolution.

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

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}];

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