The surfaces below are parametric surfaces of revolution and rotational sweeps generated by FEAview. All of the surfaces have a corresponding modeling file that can be read by FEAview.

Astroid of Revolution:

File:    /Gallery/astroid_revolution.model
 

Cardioid of Revolution:

File:    /Gallery/cardioid_of_revolution.model

Note:  For parametric surfaces of revolution, specify an odd number of stacks if you wish the figure to be symmetrical about its equator.

Circular plate or disk:

File:    /Gallery/plate1.model

File:    /Gallery/plate2.model

Cissoid of Diocles of Revolution:

File:    /Gallery/cissoid_of_revolution.model

 

Cycloid of Revolution:

File:    /Gallery/cycloid_of_revolution.model

Epicyloid of Revolution:

File:    /Gallery/epicyloid_of_revolution.model

In the animation produced by using the "a", "b", and "c" spin-buttons, in the Edit Curve Dialog, the epicyloid (the curve in the center) produces some amazing patterns.  Not to be out-done, the epicyloid surface of revolution acts like a sausage extruder when the spin-buttons are used in the Edit Surface Dialog.

Hypocycloid of Revolution:

File:    /Gallery/hypocycloid_of_revolution.model

This may another breakdown of the "standard parameterization" of a surface of revolution. On close inspection, the surface looks much more complicated than the curve that produced it.
 

Limaçon of Revolution:

File:    /Gallery/limacon_of_revolution.model

The figure on the bottom is a surface of revolution from a limaçon using the standard parameterization formula. This may be an error or a limitation of the formula; the interior of the surface doesn't reflect the loop in the limaçon curve.

The rotational sweep function, that produced the figure on the top, does it right.

Figure Eight of Revolution:

File:    /Gallery/figure8_revolution.model
 

Hyperbola of Revolution:

File:    /Gallery/hyperbola_of_revolution.model

Nephroid of Revolution:

File:    /Gallery/nephroid_of_revolution.model
 

Parabola of Revolution:

File:    /Gallery/parabola_of_revolution.model

Pseudosphere = Tractrix of Revolution:

File:    /Gallery/pseudosphere.model

Rotational Sweep:

The rotational sweep is a more dependable modeling function than the standard equation of a surface of revolution from Calculus.

File:    /Gallery/Rotational_Sweep.model     

Left: start with a curve and an arbitrary line to rotate about	Right: The rotational sweep produced by a 360 degree rotation, with 40 divisions, of the ellipse around the line: