BUILT-IN MATHEMATICA SYMBOL

# RevolutionPlot3D

RevolutionPlot3D[fz, {t, tmin, tmax}]
generates a plot of the surface of revolution with height at radius t.

RevolutionPlot3D[fz, {t, tmin, tmax}, {, min, max}]
takes the azimuthal angle to vary between and .

RevolutionPlot3D[{fx, fz}, {t, tmin, tmax}]
generates a plot of the surface obtained by rotating the parametric curve with x, z coordinates around the z axis.

RevolutionPlot3D[{fx, fz}, {t, tmin, tmax}, {, min, max}]
takes the azimuthal angle to vary from to .

RevolutionPlot3D[{fx, fy, fz}, {t, tmin, tmax}, ...]
plots the surface obtained by rotating the parametric curve with x, y, z coordinates .

## Details and OptionsDetails and Options

• RevolutionPlot3D[fz, {t, ...}] is equivalent to RevolutionPlot3D[{t, 0, fz}, {t, ...}].
• RevolutionPlot3D[fz, {t, tmin, tmax}, {, min, max}] corresponds to plotting the 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 PlotLegends None legends for surfaces 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 TextureCoordinateFunction Automatic how to determine texture coordinates TextureCoordinateScaling True whether to scale arguments to TextureCoordinateFunction 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 , 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 and TextureCoordinateFunction 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]].

## ExamplesExamplesopen allclose all

### Basic Examples (3)Basic Examples (3)

Revolve a function curve around the axis:

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Revolve a parametric curve around the axis:

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Revolve a parametric curve halfway around the axis:

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