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ParametricPlot[{fx, fy}, {u, umin, umax}]
generates a parametric plot of a curve with x and y coordinates fx and fy as a function of u.
ParametricPlot[{{fx, fy}, {gx, gy}, ...}, {u, umin, umax}]
plots several parametric curves.
ParametricPlot[{fx, fy}, {u, umin, umax}, {v, vmin, vmax}]
plots a parametric region.
ParametricPlot[{{fx, fy}, {gx, gy}, ...}, {u, umin, umax}, {v, vmin, vmax}]
plots several parametric regions.
  • ParametricPlot has attribute HoldAll, and evaluates the fi and gi only after assigning specific numerical values to variables.
  • In some cases it may be more efficient to use Evaluate to evaluate the fi and gi symbolically before specific numerical values are assigned to variables.
  • No curve is drawn in any regions where the corresponding fi or gi evaluate to None.
AspectRatioAutomaticratio of height to width
AxesTruewhether to draw axes
BoundaryStyleAutomatichow to draw boundaries of regions
ColorFunctionAutomatichow to apply coloring to curves or regions
ColorFunctionScalingTruewhether to scale arguments to ColorFunction
EvaluationMonitorNoneexpression to evaluate at every function evaluation
ExclusionsAutomaticu points or u, v curves to exclude
ExclusionsStyleNonewhat to draw at excluded points or curves
FrameAutomaticwhether to put a frame around the plot
MaxRecursionAutomaticthe maximum number of recursive subdivisions allowed
MeshAutomatichow many mesh divisions to draw
MeshFunctionsAutomatichow to determine the placement of mesh divisions
MeshShadingNonehow to shade regions between mesh points or lines
MeshStyleAutomaticthe style for mesh divisions
MethodAutomaticthe method to use for refining curves or regions
PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
PlotPointsAutomaticinitial number of sample points in each parameter
PlotRangeAutomaticrange of values to include
PlotRangeClippingTruewhether to clip at the plot range
PlotStyleAutomaticgraphics directives to specify the style for each object
RegionFunction(True&)how to determine whether a point should be included
WorkingPrecisionMachinePrecisionthe precision used in internal computations
  • ParametricPlot[Tooltip[{{fx, fy}, ...}, ...]] specifies that {fx, fy} should be displayed as tooltip labels for the corresponding curves or regions.
  • Tooltip[{fx, fy}, label] specifies an explicit tooltip label for a curve or region.
  • ParametricPlot 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 a given interval in each parameter at most MaxRecursion times.
  • You should realize that with the finite number of sample points used, it is possible for ParametricPlot to miss features in your functions. To check your results, you should try increasing the settings for PlotPoints and MaxRecursion.
  • On[ParametricPlot::accbend] makes ParametricPlot print a message if it is unable to reach a certain smoothness of curve.
  • The default setting Mesh->Automatic corresponds to None for curves, and 15 for regions.
  • With Mesh->All, ParametricPlot will explicitly draw a point at each sample point on each curve, or will draw a line to indicate each region subdivision.
  • The functions are evaluated all along each curve, or all over each region.
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