Built-in Mathematica Symbol

PolarPlot

,

_min,

_max}]
generates a polar plot of a curve with radius r as a function of angle

.

PolarPlot[{f₁, f₂, ...}, {

,

_min,

_max}]
makes a polar plot of curves with radius functions f₁, f₂, ....

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

PolarPlot has attribute HoldAll, and evaluates functions only after assigning specific numerical values to .

In some cases it may be more efficient to use Evaluate to evaluate functions symbolically before specific numerical values are assigned to .

PolarPlot has the same options as Graphics, with the following additions and changes:

Axes	True	whether to draw axes
AxesOrigin	{0,0}	the origin where axes cross
ColorFunction	Automatic	how to determine the coloring of curves
ColorFunctionScaling	True	whether to scale arguments to ColorFunction
EvaluationMonitor	None	expression to evaluate at every function evaluation
Exclusions	Automatic	points in to exclude
ExclusionsStyle	None	what to draw at excluded points
MaxRecursion	Automatic	the maximum number of recursive subdivisions allowed
Mesh	None	how many mesh points to draw on each curve
MeshFunctions	{#3&}	how to determine the placement of mesh points
MeshShading	None	how to shade regions between mesh points
MeshStyle	Automatic	the style for mesh points
Method	Automatic	the method to use for refining curves
PerformanceGoal	$PerformanceGoal	aspects of performance to try to optimize
PlotPoints	Automatic	initial number of sample points
PlotRange	Automatic	the range of values to include
PlotRangeClipping	True	whether to clip at the plot range
PlotStyle	Automatic	graphics directives to specify the style for each curve
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
RegionFunction	(True&)	how to determine whether a point should be included
WorkingPrecision	MachinePrecision	the precision used in internal computations

Interactive labeling can be specified for curves using Tooltip, StatusArea or Annotation.

PolarPlot[Tooltip[{f₁, f₂, ...}], {, _min, _max}] specifies that the f_i should be displayed as tooltip labels for the corresponding curves.

PolarPlot initially evaluates functions 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 at most MaxRecursion times.

You should realize that with the finite number of sample points used, it is possible for PolarPlot to miss features in your function. To check your results, you should try increasing the settings for PlotPoints and MaxRecursion.

On[PolarPlot::accbend] makes PolarPlot print a message if it is unable to reach a certain smoothness of curve.

With Mesh->All, PolarPlot will explicitly draw a point at every position on each curve where each function was sampled.

The arguments supplied to functions in MeshFunctions and RegionFunction are x, y, , r. Functions in ColorFunction are by default supplied with scaled versions of these arguments.

With the default settings Exclusions->Automatic and ExclusionsStyle->None, PolarPlot breaks curves at discontinuities it detects. Exclusions->None joins across discontinuities.