BUILT-IN MATHEMATICA SYMBOL

# SphericalPlot3D

SphericalPlot3D[r, , ]
generates a 3D plot with a spherical radius r as a function of spherical coordinates and .

SphericalPlot3D[r, {, min, max}, {, min, max}]
generates a 3D spherical plot over the specified ranges of spherical coordinates.

SphericalPlot3D[{r1, r2, ...}, {, min, max}, {, min, max}]
generates a 3D spherical plot with multiple surfaces.

## Details and OptionsDetails and Options

• The angles and are measured in radians.
• corresponds to "latitude"; is 0 at the "north pole", and at the "south pole".
• corresponds to "longitude", varying from 0 to counterclockwise looking from the north pole.
• SphericalPlot3D[r, , ] takes to have range 0 to , and to have range 0 to .
• The , , position corresponding to , , is , , . The variables and can have any values. The surfaces they define can overlap radially.
• Holes are left at positions where the etc. evaluate to None, or anything other than real numbers.
• SphericalPlot3D treats the variables and as local, effectively using Block.
• SphericalPlot3D has attribute HoldAll, and evaluates the only after assigning specific numerical values to variables.
• In some cases it may be more efficient to use Evaluate to evaluate the symbolically before specific numerical values are assigned to variables.
• SphericalPlot3D 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 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 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 curves or surfaces using Tooltip, StatusArea, or Annotation.
• SphericalPlot3D[Tooltip[{r1, r2, ...}], ...] specifies that the should be displayed as tooltip labels for the corresponding surfaces.
• Tooltip[r, label] specifies an explicit tooltip label for a surface.
• SphericalPlot3D 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 SphericalPlot3D to miss features in your functions. To check your results, you should try increasing the settings for PlotPoints and MaxRecursion.
• On[SphericalPlot3D::accbend] makes SphericalPlot3D print a message if it is unable to reach a certain smoothness of curve.
• The arguments supplied to functions in MeshFunctions and RegionFunction are , , , , , and . 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&).
• SphericalPlot3D returns Graphics3D[GraphicsComplex[data]].

## ExamplesExamplesopen allclose all

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

Plot a spherical surface:

 Out[1]=

Plot several spherical surfaces:

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Style the resulting surface:

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## TutorialsTutorials

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