Built-in Mathematica Symbol

RevolutionPlot3D

RevolutionPlot3D[f_z, {t, t_min, t_max}]
generates a plot of the surface of revolution with height f_z at radius t.

RevolutionPlot3D[f_z, {t, t_min, t_max}, {

,

_min,

_max}]
takes the azimuthal angle

to vary between

_min and

_max.

RevolutionPlot3D[{f_x, f_z}, {t, t_min, t_max}]
generates a plot of the surface obtained by rotating the parametric curve with x, z coordinates {f_x, f_z} around the z axis.

RevolutionPlot3D[{f_x, f_z}, {t, t_min, t_max}, {

,

_min,

_max}]
takes the azimuthal angle

to vary from

_min to

_max.

RevolutionPlot3D[{f_x, f_y, f_z}, {t, t_min, t_max}, ...]
plots the surface obtained by rotating the parametric curve with x, y, z coordinates {f_x, f_y, f_z}.

MORE INFORMATION

RevolutionPlot3D[f_z, {t, ...}] is equivalent to RevolutionPlot3D[{t, 0, f_z}, {t, ...}].

RevolutionPlot3D[f_z, {t, t_min, t_max}, {, _min, _max}] corresponds to plotting the f_z in cylindrical coordinates as a function of radius t and angle .

The angle is measured in radians, counterclockwise from the positive x axis when viewed from above.

RevolutionPlot3D[{{f}, {g}, ...}, ...] plots surfaces corresponding to all the functions f, g, ....

Holes are left at positions where f etc. evaluate to None, or anything other than real numbers.

RevolutionPlot3D treats the variables r, t and as local, effectively using Block.

RevolutionPlot3D has attribute HoldAll, and evaluates f only after assigning specific numerical values to variables.

In some cases it may be more efficient to use Evaluate to evaluate f symbolically before specific numerical values are assigned to variables.

RevolutionPlot3D has the same options as Graphics3D, with the following additions and changes:

Axes	True	whether to draw axes
BoundaryStyle	Automatic	how to draw boundary lines for surfaces
BoxRatios	Automatic	side ratios for the bounding 3D box
ColorFunction	Automatic	how to determine the color of curves and surfaces
ColorFunctionScaling	True	whether to scale arguments to ColorFunction
EvaluationMonitor	None	expression to evaluate at every function evaluation
Exclusions	Automatic	, curves to exclude
ExclusionsStyle	None	what to draw at excluded points or curves
MaxRecursion	Automatic	the maximum number of recursive subdivisions allowed
Mesh	Automatic	how many mesh divisions in each direction to draw
MeshFunctions	{#4&,#5&}	how to determine the placement of mesh divisions
MeshShading	None	how to shade regions between mesh divisions
MeshStyle	Automatic	the style for mesh divisions
Method	Automatic	the method to use for refining surfaces
NormalsFunction	Automatic	how to determine effective surface normals
PerformanceGoal	$PerformanceGoal	aspects of performance to try to optimize
PlotPoints	Automatic	the initial number of sample points in each parameter
PlotStyle	Automatic	graphics directives for the style for each object
RegionFunction	(True&)	how to determine whether a point should be included
WorkingPrecision	MachinePrecision	the precision used in internal computations

Interactive labeling can be specified for surfaces using Tooltip, StatusArea, or Annotation.

RevolutionPlot3D initially evaluates each function at a number of equally spaced sample points specified by PlotPoints. Then it uses an adaptive algorithm to choose additional sample points, subdividing in each parameter at most MaxRecursion times.

You should realize that with the finite number of sample points used, it is possible for RevolutionPlot3D to miss features in your functions. To check your results, you should try increasing the settings for PlotPoints and MaxRecursion.

On[RevolutionPlot3D::accbend] makes RevolutionPlot3D print a message if it is unable to reach a certain smoothness of curve.

With the default setting BoxRatios->Automatic, slices through the final 3D graphic parallel to the z axis give forms that agree with the default aspect ratio used by Plot.

The arguments supplied to functions in MeshFunctions and RegionFunction are x, y, z, t, and r, where . Functions in ColorFunction are by default supplied with scaled versions of these arguments.