BUILT-IN MATHEMATICA SYMBOL

RegionPlot

makes a plot showing the region in which pred is True.

MORE INFORMATION

The predicate pred can be any logical combination of inequalities.

The region plotted by RegionPlot can contain disconnected parts.

By default, the interior of each part is shown in gray, with a black line as its boundary.

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

AspectRatio	1	ratio of height to width
BoundaryStyle	Automatic	the style for the boundary of each region
ColorFunction	Automatic	how to color the interior of each region
ColorFunctionScaling	True	whether to scale the argument to ColorFunction
EvaluationMonitor	None	expression to evaluate at every function evaluation
Frame	True	whether to draw a frame around the plot
MaxRecursion	Automatic	the maximum number of recursive subdivisions allowed
Mesh	None	how many mesh lines to draw
MeshFunctions	{#1&,#2&}	what mesh lines to draw
MeshShading	None	how to shade regions between mesh lines
MeshStyle	Automatic	the style for mesh lines
Method	Automatic	the method to use for refining regions
PerformanceGoal	$PerformanceGoal	aspects of performance to try to optimize
PlotPoints	Automatic	initial number of sample points
PlotRange	Full	the range of values to include in the plot
PlotRangeClipping	True	whether to clip at the plot range
PlotRangePadding	Automatic	how much to pad the range of values
PlotStyle	Automatic	graphics directives to specify the style for regions
TextureCoordinateFunction	Automatic	how to determine texture coordinates
TextureCoordinateScaling	True	whether to scale arguments to TextureCoordinateFunction
WorkingPrecision	MachinePrecision	the precision used in internal computations

RegionPlot initially evaluates pred at a grid of equally spaced sample points specified by PlotPoints. Then it uses an adaptive algorithm to subdivide at most MaxRecursion times, attempting to find the boundaries of all regions in which pred is True.

You should realize that since it uses only a finite number of sample points, it is possible for RegionPlot to miss regions in which pred is True. To check your results, you should try increasing the settings for PlotPoints and MaxRecursion.

With the default setting PlotRange->Full, RegionPlot will explicitly include the full ranges to and to for x and y.

With Mesh->All, RegionPlot will explicitly draw mesh lines to indicate the subdivisions it used to find each region.

RegionPlot can in general only find regions of positive measure; it cannot find regions that are just lines or points.

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

RegionPlot returns Graphics[GraphicsComplex[data]].

EXAMPLES

CLOSE ALL

Basic Examples (4)

Plot a region defined by an inequality:

Plot a region defined by logical combinations of inequalities:

Plot disconnected regions:

Style the region:

Plot a region defined by an inequality:

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Plot a region defined by logical combinations of inequalities:

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Plot disconnected regions:

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Style the region:

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Scope (10)

More points are sampled where the function changes quickly:

Areas where the function is not True are excluded:

Use PlotPoints and MaxRecursion to control adaptive sampling:

Use logical combinations of regions:

Provide an explicit PlotStyle for the region:

Provide an explicit BoundaryStyle for the region boundary:

Add labels:

Use an overlay mesh:

Style the areas between mesh lines:

Color the region with an overlay density:

Options (41)

Regions are shown with AspectRatio set to 1:

Use the natural scale to show regions:

Regions have a gray boundary:

Use None to show regions without any boundary:

Use a blue boundary:

Use a thicker dashed boundary:

Color regions by scaled

and

values:

Named color functions use the scaled

direction:

Color regions according to a function of

and

:

ColorFunction has higher priority than PlotStyle:

ColorFunction has lower priority than MeshShading:

Use unscaled

and

coordinates for coloring the regions:

Refine the region where it changes quickly:

Use no mesh:

Show the initial and final sampling meshes:

Use 10 mesh lines in each direction:

Use 3 mesh lines in the

direction and 6 mesh lines in the

direction:

Use mesh lines at specific values:

Use different styles for different mesh lines:

Mesh lines apply to the whole region, not each component:

Mesh lines in the

and

directions:

Mesh lines at fixed radii from the origin:

Use None to remove regions:

Lay a checkerboard pattern over a region:

MeshShading has a higher priority than PlotStyle:

MeshShading has a higher priority than ColorFunction:

Use red mesh lines:

Use red mesh lines in the

direction and dashed mesh lines in the

direction:

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

Use more initial points to get smoother regions:

Show the region over the full

,

range:

Automatically compute the

,

range:

Regions are shown in light blue:

Use None to just show the boundary of the region:

Use light orange:

Distinct colors are used for different regions:

Use transparent colors for different regions:

Textures use scaled

and

coordinates by default:

Use unscaled coordinates:

Use scaled or unscaled coordinates for textures:

Applications (8)

Find the intersection of two half-spaces:

Simple regions including a disk:

Disk annulus:

Ellipse:

Ellipse annulus:

Disk segment:

Disk segment annulus:

Illustrate set operations:

Visualize regions in the complex plane:

Identify where a function is real-valued:

Integrate over a region that contains parameters:

Visualize the regions for the three different cases:

Absolute stability regions for Euler forward:

Stability regions for Euler backward and Tustin or midpoint rules:

Stability regions for explicit Runge-Kutta rules of order 2, 3, 4, and 5:

Relative stability or order-stars regions for

Pade approximants:

Order-star regions for

Pade approximants:

Properties & Relations (8)

RegionPlot samples more points where it needs to:

Use RegionPlot3D for volumes:

Use ContourPlot and ContourPlot3D for systems of equalities:

Use RegionFunction to constrain other plots:

Use ParametricPlot for plane parametric curves and regions:

Use Integrate or NIntegrate to integrate over regions:

The integration region:

Use Maximize, NMaximize, or FindMaximum to optimize over regions:

Use Reduce to get a cylindrical representation of the region:

Use FindInstance to find specific samples in regions:

Possible Issues (2)

RegionPlot will only visualize two-dimensional regions:

Use ContourPlot to visualize one-dimensional regions:

Piecewise constant functions can have two-dimensional level sets:

Neat Examples (2)

Overlay colors on a transcendental region:

Exclusive OR of five disks: