PolarPlot

PolarPlot[r,{θ,θmin,θmax}]

generates a polar plot of a curve with radius r as a function of angle θ.

PolarPlot[{r1,r2,},{θ,θmin,θmax}]

makes a polar plot of curves with radius functions r1, r2, .

Details and Options

Examples

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Basic Examples  (3)

Make a polar plot:

Make several polar plots:

Style the curves:

Scope  (23)

Sampling  (6)

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:

Labeling and Legending  (7)

Use Callout to add the expressions as a label:

Use any text as a label:

Place the label along the curve:

Place the label at a scaled position:

Place the labels relative to the inside of the curve:

Place the labels relative to the outside of the curve:

Label the curve with PlotLabels:

Label multiple curves:

Use a scaled position:

Specify the text position relative to the point:

Specify the label at {x,y} position:

Presentation  (10)

Multiple curves are automatically colored to be distinct:

Provide explicit styling to different curves and regions:

Add labels:

Provide an interactive Tooltip for each curve:

Create an overlay mesh:

Style the areas between mesh levels:

Color by parameter values:

Legend multiple curves:

Use a theme with dark background and high-contrast colors:

Use a theme with minimal styling:

Use a log scale on the radial components of a polar plot:

Scale only the x direction:

Options  (123)

AspectRatio  (3)

By default, the ratio of the height to width for the plot is determined automatically:

Make the height the same as the width with AspectRatio1:

AspectRatioFull adjusts the height and width to tightly fit inside other constructs:

Axes  (4)

By default, axes are drawn:

Use AxesFalse to turn off axes:

Use AxesOrigin to specify where the axes intersect:

Turn each axis on individually:

AxesLabel  (3)

No axes labels are drawn by default:

Place a label on the axis:

Specify axes labels:

AxesOrigin  (2)

The position of the axes is determined automatically:

Specify an explicit origin for the axes:

AxesStyle  (4)

Change the style for the axes:

Specify the style of each axis:

Use different styles for the ticks and the axes:

Use different styles for the labels and the axes:

ColorFunction  (4)

Color the curve by scaled , , , or value:

Use a named color gradient:

ColorFunction has higher priority than PlotStyle:

Use red for the parameter :

ColorFunctionScaling  (1)

Color the curve by angle:

EvaluationMonitor  (3)

Find the list of parameter values evaluated:

Find the coordinate values:

Count how many times the function is evaluated:

Exclusions  (3)

Automatically determine exclusions:

Provide an explicit list of points for exclusions:

Specify exclusions using equations:

ExclusionsStyle  (2)

Specify explicit styling for lines joining exclusion points:

Provide styling for both exclusion points and the lines joining them:

Frame  (4)

PolarPlot does not use a frame by default:

Use FrameTrue to turn on the frame:

Draw a frame on the left and right edges:

Draw a frame on the left and bottom edges:

FrameLabel  (3)

Place a label along the bottom frame of a plot:

Place labels on the bottom and left frame edges:

Place labels on each of the edges in the frame:

FrameStyle  (2)

Specify the style of the frame:

Specify style for each frame edge:

FrameTicks  (8)

Frame ticks are placed automatically by default:

Use a frame with no ticks:

Use frame ticks on the bottom edge:

By default, the top and right edges have tick marks but no tick labels:

Use All to include tick labels on all edges:

Place tick marks at specific positions:

Draw frame tick marks at the specified positions with specific labels:

Specify the lengths for tick marks as a fraction of the graphics size:

Use different sizes in the positive and negative directions for each tick mark:

Specify a style for each frame tick:

FrameTicksStyle  (3)

By default, the frame ticks and frame tick labels use the same styles as the frame:

Specify an overall style for the ticks, including the labels:

Use different styles for the different frame edges:

ImageSize  (7)

Use named sizes such as Tiny, Small, Medium and Large:

Specify the width of the plot:

Specify the height of the plot:

Allow the width and height to be up to a certain size:

Specify the width and height for a graphic, padding with space if necessary:

Setting AspectRatioFull will fill the available space:

Use maximum sizes for the width and height:

Use ImageSizeFull to fill the available space in an object:

Specify the image size as a fraction of the available space:

LabelingSize  (2)

Textual labels are shown at their actual sizes:

Specify the size of the text:

Image labels are resized to fit in the plot:

Specify the labeling size:

MaxRecursion  (1)

Each level of MaxRecursion will adaptively subdivide the initial mesh into a finer mesh:

Mesh  (4)

Show the initial and final sampling meshes:

Use 10 mesh points evenly spaced in the direction:

Use an explicit list of values for the mesh in the direction:

Use explicit value and style for the mesh:

MeshFunctions  (2)

Use a mesh evenly spaced in the , , , and directions:

Show five mesh levels in the direction (red) and 10 in the direction (blue):

MeshShading  (6)

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:

MeshStyle  (4)

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:

PerformanceGoal  (2)

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

PlotLabels  (6)

PlotLabels->"Expressions" uses functions as curve labels:

Specify the text to label the curves:

Place the labels above the curves:

Place the labels differently for each curve:

Use callouts to identify the curves:

Put labels relative to the outside of the curves:

Use None to not add a label:

PlotLegends  (7)

Use the automatic legend:

No legends are used by default:

Use legends:

Show no legends:

PlotLegends automatically picks up PlotStyle option values:

Show expressions as legends in TraditionalForm:

Specify a list of labels for legends:

Place legends outside:

Place legends inside:

Legend layout changes automatically along with position:

Use LineLegend to adjust the appearance of the legend:

Specify LegendMarkers:

PlotPoints  (1)

Use more initial points to get a smoother plot:

PlotRange  (2)

Show the curve 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:

PlotStyle  (5)

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:

PlotStyle can be combined with MeshShading:

PlotTheme  (1)

Use a theme with polar grid lines and bright colors:

Add another theme with legends:

Change plot styles:

RegionFunction  (1)

Show the plot where :

ScalingFunctions  (8)

By default, PolarPlot uses natural scale in both axes:

Log-scaled plots will only plot intervals over which Log is defined:

Use a shifted log scale to show a function with negative values:

Use ScalingFunctions to reverse the coordinate direction in the direction:

Use a reciprocal scale in the direction:

Use a scale defined by a function and its inverse:

Use a scale for r:

Use a scale for θ; it affects how the plot is sampled, but not the overall appearance of the plot:

Ticks  (9)

Ticks are placed automatically in each plot:

Use TicksNone to draw axes without any tick marks:

Use ticks on the axis, but not the axis:

Place tick marks at specific positions:

Draw tick marks at the specified positions with specific labels:

Use specific ticks on one axis and automatic ticks on the other:

Specify the lengths for ticks as a fraction on graphics size:

Use different sizes in the positive and negative directions for each tick:

Specify a style for each tick:

Construct a function that places ticks at the midpoint and extremes of the axis:

TicksStyle  (4)

By default, the ticks and tick labels use the same styles as the axis:

Specify an overall ticks style, including the tick labels:

Specify ticks style for each of the axes:

Use a different style for the tick labels and tick marks:

WorkingPrecision  (2)

Evaluate functions using machine-precision arithmetic:

Evaluate functions using arbitrary-precision arithmetic:

Applications  (4)

Plot a circle:

A spiral:

An oscillation around a circle:

Archimedean spirals of the form :

Archimedean spirals of the form :

Logarithmic spirals have the form :

Create a Guilloché pattern [more info]:

Properties & Relations  (5)

PolarPlot is a special case of ParametricPlot for curves:

Use ListPolarPlot for data:

Use Plot3D and ParametricPlot3D for function and parametric surfaces:

Use RevolutionPlot3D and SphericalPlot3D for cylindrical and spherical coordinates:

Use ContourPlot and RegionPlot for implicit curves and regions:

Neat Examples  (2)

Wolfram Research (2007), PolarPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/PolarPlot.html (updated 2022).

Text

Wolfram Research (2007), PolarPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/PolarPlot.html (updated 2022).

CMS

Wolfram Language. 2007. "PolarPlot." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/PolarPlot.html.

APA

Wolfram Language. (2007). PolarPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PolarPlot.html

BibTeX

@misc{reference.wolfram_2023_polarplot, author="Wolfram Research", title="{PolarPlot}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/PolarPlot.html}", note=[Accessed: 21-February-2024 ]}

BibLaTeX

@online{reference.wolfram_2023_polarplot, organization={Wolfram Research}, title={PolarPlot}, year={2022}, url={https://reference.wolfram.com/language/ref/PolarPlot.html}, note=[Accessed: 21-February-2024 ]}