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
RevolutionAxis	{0,0,1}	rotates around the specified axis
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.

The functions are evaluated all over each surface.

By default, surfaces are treated as uniform white diffuse reflectors, corresponding to ColorFunction->(White&).

RevolutionPlot3D returns Graphics3D[GraphicsComplex[data]].

EXAMPLES

CLOSE ALL

Basic Examples (3)

Revolve a function curve around the

axis:

Revolve a parametric curve around the

axis:

Revolve a parametric curve halfway around the

axis:

Revolve a function curve around the

axis:

In[1]:=

Out[1]=

Revolve a parametric curve around the

axis:

In[1]:=

Out[1]=

Revolve a parametric curve halfway around the

axis:

In[1]:=

Out[1]=

Scope (15)

More points are sampled when the function changes quickly:

The plot range is selected automatically:

Ranges where the function becomes nonreal are excluded:

The surface is split when there are discontinuities in the function:

Use PlotPoints and MaxRecursion to control adaptive sampling:

Use PlotRange to focus in on areas of interest:

Use Exclusions to remove points or split the resulting surface:

Plot multiple surfaces:

Provide explicit styling to different surfaces:

Add labels:

Provide an interactive Tooltip for a surface:

Create an overlay mesh:

Style the areas between mesh levels:

Color by parameter values:

Use named color schemes:

Remove portions of a curve or surface:

Options (52)

BoundaryStyle automatically matches MeshStyle:

Use a thick red boundary:

Boundaries are drawn where the surface is clipped by RegionFunction:

Boundaries are not drawn where the surface is clipped by Exclusions:

The default BoxRatios preserve the AspectRatio used by Plot:

The default BoxRatios preserve the revolved circles:

Use specific BoxRatios:

Color a surface by

,

and

parameters:

Use ColorData for predefined color gradients:

Named color gradients color in the

direction:

ColorFunction has higher priority than PlotStyle:

ColorFunction has lower priority than MeshShading:

Use scaled coordinates in the

direction and unscaled coordinates in the

direction:

Show where RevolutionPlot3D samples a function in

coordinates:

Count how many times

is evaluated:

Use automatic methods to compute exclusions, in this case from branch cuts:

Indicate that no exclusions should be computed:

Give a set of exclusions as an equation:

Give two sets of exclusions:

Use both automatically computed and explicit exclusions:

Style the boundary with a thick blue line:

Style the boundary with a thick blue line and the surface in between with yellow:

Refine the surface where it changes quickly:

Show the initial and final sampling meshes:

Use 10 mesh levels evenly spaced in the parameter directions:

Use a different number of mesh lines for different directions:

Use an explicit list of values for the mesh in the

parameter and no mesh in the

parameter:

Use explicit value and style for the

mesh:

Use a mesh evenly spaced in the

,

and

directions:

Show five mesh levels in the

direction (red) and ten in the

direction (blue):

Alternate red and blue arcs in the

direction:

Use None to remove segments:

MeshShading has higher priority than PlotStyle for styling:

Use PlotStyle for some segments by setting MeshShading to Automatic:

MeshShading can be used with ColorFunction:

Fill between regions defined by multiple mesh functions:

Use FaceForm to use different styles for different sides of a surface:

Use a red mesh in the

direction:

Use a red mesh in the

direction and a blue mesh in the

direction:

Normals are automatically calculated:

Use None to get flat shading for all the polygons:

Vary the effective normals used on the surface:

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

Use more initial points to get a smoother plot:

Use different style directives:

Explicitly specify the style for different surfaces:

Use a different style inside the surface:

Select a region in

,

and

:

Select a region in parameter space:

Evaluate functions using machine-precision arithmetic:

Evaluate functions using arbitrary-precision arithmetic:

Applications (3)

Produce well-known shapes such as the surfaces of revolution, including the cylinder:

Cone:

Sphere:

Torus:

Find the volume of a cone:

Model a drum beating:

Properties & Relations (8)

RevolutionPlot3D is a special case of ParametricPlot3D:

The default BoxRatios preserve the AspectRatio used by Plot:

The default BoxRatios preserve the revolved circles:

Use SphericalPlot3D for spherical coordinates:

Use ParametricPlot3D for arbitrary curves and surfaces in three dimensions:

Use PolarPlot for curves in polar coordinates:

Use ParametricPlot for curves and regions in two dimensions:

Use ContourPlot3D and RegionPlot3D for implicitly defined surfaces and regions:

Use ListPlot3D and ListSurfacePlot3D for data:

Possible Issues (2)

Surfaces that have multiple coverings may exhibit unusual behavior:

RevolutionPlot3D always revolves around the

axis:

Neat Examples (1)

Revolving a self-intersecting curve: