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RevolutionPlot3D

RevolutionPlot3D[fz, {t, tmin, tmax}]
generates a plot of the surface of revolution with height fz at radius t.
RevolutionPlot3D[fz, {t, tmin, tmax}, {, min, max}]
takes the azimuthal angle to vary between min and max.
RevolutionPlot3D[{fx, fz}, {t, tmin, tmax}]
generates a plot of the surface obtained by rotating the parametric curve with x, z coordinates {fx, fz} around the z axis.
RevolutionPlot3D[{fx, fz}, {t, tmin, tmax}, {, min, max}]
takes the azimuthal angle to vary from min to max.
RevolutionPlot3D[{fx, fy, fz}, {t, tmin, tmax}, ...]
plots the surface obtained by rotating the parametric curve with x, y, z coordinates {fx, fy, fz}.
  • RevolutionPlot3D[fz, {t, tmin, tmax}, {, min, max}] corresponds to plotting the fz 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 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.
AxesTruewhether to draw axes
BoundaryStyleAutomatichow to draw boundary lines for surfaces
BoxRatiosAutomaticside ratios for the bounding 3D box
ColorFunctionAutomatichow to determine the color of curves and surfaces
ColorFunctionScalingTruewhether to scale arguments to ColorFunction
EvaluationMonitorNoneexpression to evaluate at every function evaluation
ExclusionsAutomatictheta, phi curves to exclude
ExclusionsStyleNonewhat to draw at excluded points or curves
MaxRecursionAutomaticthe maximum number of recursive subdivisions allowed
MeshAutomatichow many mesh divisions in each direction to draw
MeshFunctions{#4&,#5&}how to determine the placement of mesh divisions
MeshShadingNonehow to shade regions between mesh divisions
MeshStyleAutomaticthe style for mesh divisions
MethodAutomaticthe method to use for refining surfaces
NormalsFunctionAutomatichow to determine effective surface normals
PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
PlotPointsAutomaticthe initial number of sample points in each parameter
PlotStyleAutomaticgraphics directives for the style for each object
RegionFunction(True&)how to determine whether a point should be included
WorkingPrecisionMachinePrecisionthe precision used in internal computations
  • 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 functions are evaluated all over each surface.
  • By default, surfaces are treated as uniform white diffuse reflectors, corresponding to ColorFunction->(White&).
Revolve a function curve around the z axis:
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Revolve a parametric curve around the z axis:
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Revolve a parametric curve halfway around the z axis:
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