This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)


Updated In 8 Graphic
generates a parametric plot of a curve with x and y coordinates and as a function of u.
plots several parametric curves.
plots a parametric region.
plots several parametric regions.
  • ParametricPlot has attribute HoldAll, and evaluates the and only after assigning specific numerical values to variables.
  • In some cases it may be more efficient to use Evaluate to evaluate the and symbolically before specific numerical values are assigned to variables.
  • No curve is drawn in any regions where the corresponding or 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
TextureCoordinateFunctionAutomatichow to determine texture coordinates
TextureCoordinateScalingTruewhether to scale arguments to TextureCoordinateFunction
WorkingPrecisionMachinePrecisionthe precision used in internal computations
  • ParametricPlot[Tooltip[{{fx, fy}, ...}, ...]] specifies that should be displayed as tooltip labels for the corresponding curves or regions.
  • Tooltip 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 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 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.
Plot a parametric curve:
Plot a parametric region:
Plot several parametric curves:
Plot overlapping regions:
Plot a parametric curve:
Click for copyable input
Plot a parametric region:
Click for copyable input
Plot several parametric curves:
Click for copyable input
Plot overlapping regions:
Click for copyable input
More points are sampled when the function changes quickly:
The plot range is selected automatically:
Ranges where the function becomes nonreal are excluded:
The curve 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 curve:
Multiple curves and regions are automatically colored to be distinct:
Provide explicit styling to different curves and regions:
Add labels:
Provide an interactive Tooltip for each curve or region:
Create an overlay mesh:
Style the areas between mesh levels:
Color by parameter values:
By default, AspectRatio comes from PlotRange:
Set a different AspectRatio:
Draw no axes:
Specify labels for the and axes:
Determine where the axes cross automatically:
Specify the axes origin at the point :
Use a red boundary around the edges of the surface:
BoundaryStyle applies to regions cut by RegionFunction:
BoundaryStyle does not apply to holes cut by Exclusions:
Color the curve by scaled , , or values:
Color by scaled and parameter values:
Use a named color gradient:
ColorFunction has higher priority than PlotStyle:
Use red for the parameter :
Color the curve by angle:
Color the region by angle and vary opacity across the region:
Find the list of parameter values evaluated:
Find the parametric coordinate values:
Count how many times the function is evaluated:
Automatically determine exclusions:
Specify exclusions using equations:
Exclude a fixed set of points:
Use no exclusions:
Exclude an equation and the automatically chosen points:
Specify explicit styling for lines joining exclusion points:
Provide styling for both exclusion points and the lines joining them:
Draw red lines where the region is cut by excluded curves:
Each level of MaxRecursion will adaptively subdivide the initial mesh into a finer mesh:
Subdivision for parametric regions:
Show the initial and final sampling meshes:
Use 10 mesh levels evenly spaced in the parameter directions:
Use a different number of mesh lines in 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:
Use a mesh evenly spaced in the , , , and directions:
Show five mesh levels in the direction (red) and 10 in the direction (blue):
Alternate red and blue arcs in the direction:
Use None to remove segments:
MeshShading can be used with PlotStyle:
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:
Automatically choose the mesh style:
Use a red mesh in the direction:
Use a red mesh in the direction and a blue mesh in the direction:
Use big red mesh levels in the direction:
Generate a higher-quality plot:
Emphasize performance, possibly at the cost of quality:
Use more initial points to get a smoother plot:
Use fewer plot points in directions that do not change much:
Show the plot where and :
With the natural range of values, the fine detail around the origin is not visible:
Use PlotRange to focus in on areas of interest:
Use different style directives:
By default different styles are chosen for multiple curves and regions:
Explicitly specify the style for different curves and regions:
PlotStyle can be combined with ColorFunction:
Show the plot where :
Textures use scaled and parameters by default:
Use the and coordinates:
Use unscaled coordinates:
Use textures to highlight how parameters map onto a surface:
Use scaled or unscaled coordinates for textures:
Evaluate functions using machine-precision arithmetic:
Evaluate functions using arbitrary-precision arithmetic:
Simple parametric curves including a line:
Circle segment:
Ellipse segment:
Simple parametric regions including a rectangle:
Disk segment:
Disk annulus:
Disk segment annulus:
Rotated ellipses:
Plot a whole family of rotated ellipses:
Different parametrizations of circles:
This rational parametrization is for :
Plot Lissajous curves:
Plot a Nyquist curve:
Make a phase space plot of a solution to the Lotka-Volterra predator-prey equations:
Plot complex mappings:
A Joukowski map:
Model a 2-link planar robot:
Plot the range of motion of the end effector for and :
Plot is a special case of ParametricPlot for curves:
PolarPlot is a special case of ParametricPlot for curves:
Use ListPlot and ListLinePlot for data:
Use ContourPlot and RegionPlot for implicit curves and regions:
Use LogPlot, LogLinearPlot, and LogLogPlot for logarithmic plots:
Use Plot3D and ParametricPlot3D for function and parametric surfaces:
Use RevolutionPlot3D and SphericalPlot3D for cylindrical and spherical coordinates:
By default, the argument is not evaluated, and is styled as one composite function:
Use Evaluate to get an explicit list of curves:
Forced undersampling:
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