Built-in Mathematica Symbol

ListPolarPlot

ListPolarPlot[{r₁, r₂, ...}]
plots points equally spaced in angle at radii r_i.

ListPolarPlot[{{

₁, r₁}, {

₂, r₂}, ...}]
plots points at polar coordinates

_i, r_i.

ListPolarPlot[{list₁, list₂, ...}]
plots several lists of values.

MORE INFORMATION

ListPolarPlot[list] by default plots each element of list as a separate point.

ListPolarPlot[list, Joined->True] draws a line through the list of points.

The angle is measured in radians, counterclockwise from the positive axis.

The , position corresponding to , is , . The value of need not be between 0 and .

In ListPolarPlot[{r₁, ..., r_n}], r₁ is taken to be associated with , and r_n with ).

ListPolarPlot has the same options as ListPlot, with the following changes:

AspectRatio	Automatic	ratio of height to width
AxesOrigin	{0,0}	where axes should cross
MeshFunctions	{#3&}	how to determine placement of mesh points
PolarAxes	False	whether to draw polar axes
PolarAxesOrigin	Automatic	where to draw polar axes
PolarGridLines	None	polar gridlines to draw
PolarTicks	Automatic	polar axes ticks

EXAMPLES

CLOSE ALL

Basic Examples (3)

Plot a list of radii

equally spaced in angle:

Join the points with a line:

Use

,

coordinates for the data:

Show multiple sets of data:

Plot a list of radii

equally spaced in angle:

In[1]:=

Out[1]=

Join the points with a line:

In[2]:=

Out[2]=

Use

,

coordinates for the data:

In[1]:=

Out[1]=

Show multiple sets of data:

In[1]:=

Out[1]=

Scope (15)

For regular data consisting of

values, the

data range is uniformly spaced:

Provide an explicit

data range by using DataRange:

Plot multiple sets of regular data:

For irregular data consisting of

value pairs the

data range is inferred from data:

Plot multiple sets of irregular data:

Ranges where the data is nonreal are excluded:

Use MaxPlotPoints to limit the number of points used:

PlotRange is selected automatically:

Use PlotRange to focus on areas of interest:

Use Joined to connect datasets with lines:

Multiple datasets are automatically colored to be distinct:

Provide explicit styling to different sets:

Add labels:

Provide an interactive Tooltip for the data:

Use shapes to distinguish different datasets:

Use InterpolationOrder to smooth joined data:

Options (62)

The axes normally intersect at

:

Specify where the axes cross:

ColorFunction only applies to Joined datasets:

Color by scaled

,

and

coordinates:

Color with a named color scheme:

ColorFunction has higher priority than PlotStyle for coloring the curve:

Use Automatic in MeshShading to use ColorFunction:

ColorFunctionScaling only applies to Joined datasets:

Color the line based on the scaled

value:

Manually scale the

value:

Lists of radii are equally spaced in angle around the origin:

Give the starting and ending angles:

Each dataset is scaled to the same domain:

Pairs are interpreted as

coordinates:

Specifying DataRange in this case has no effect, since

values are part of the data:

Joined lines can be interpolated:

By default, linear interpolation is used:

Use zero-order or piecewise-constant interpolation:

Use third-order spline interpolation:

Interpolation order zero to 5:

Join the dataset with a line:

Join the first dataset with a line, but use points for the second dataset:

Join the dataset with a line, and show the original points:

All points are included by default:

Uniformly spaced data is downsampled:

In this case, downsample from

to

points:

Mesh only applies to Joined datasets:

The initial and final sampling meshes are typically the same:

Interpolated data may introduce points:

Use 20 mesh levels evenly spaced in the

direction:

Use an explicit list of values for the mesh in the

direction:

Use explicit styles at specific points:

MeshFunctions only applies to Joined datasets:

Use a mesh evenly spaced in the

,

and

directions:

Show five mesh levels in the

direction (red) and ten in the

direction (blue):

MeshShading only applies to Joined datasets:

Alternate red and blue segments of equal angles in the

direction:

Use None to remove segments:

MeshShading can be used with PlotStyle:

MeshShading has higher priority than PlotStyle for styling the curve:

Use PlotStyle for some segments by setting MeshShading to Automatic:

MeshShading can be used with ColorFunction and has higher priority:

MeshStyle only applies to Joined datasets:

Color the mesh the same color as the plot:

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 points in the

direction:

ListPolarPlot normally uses distinct colors to distinguish different sets of data:

Automatically use colors and shapes to distinguish sets of data:

Use shapes only:

Change the size of the default plot markers:

Use arbitrary text for plot markers:

Use explicit graphics for plot markers:

Use the same symbol for all the sets of data:

Explicitly use a symbol and size:

PlotRange is automatically calculated:

Show the whole dataset:

Use different style directives:

By default, different styles are chosen for multiple datasets:

Explicitly specify the style for different datasets:

PlotStyle applies to both lines and points:

PlotStyle can be combined with ColorFunction:

PlotStyle can be combined with MeshShading and has lower priority:

MeshStyle by default uses the same style as PlotStyle:

Properties & Relations (12)

ListPolarPlot is a special case of ListPlot:

Use PolarPlot for functions:

Use ListPlot and ListLinePlot for Cartesian plots:

Use ListLogPlot, ListLogLogPlot and ListLogLinearPlot for logarithmic plots:

Use DateListPlot to show data over time:

Use ListPointPlot3D to show three-dimensional points:

Use ListPlot3D to create surfaces from data:

Use ListContourPlot to create contours from continuous data:

Use ListDensityPlot to create densities from continuous data:

Use ArrayPlot and MatrixPlot for arrays of discrete values:

Use RevolutionPlot3D and SphericalPlot3D for cylindrical and spherical coordinates:

Use ParametricPlot for parametric curves:

Neat Examples (1)

Parametrized butterflies: