DOCUMENTATION CENTER SEARCH

Mathematica > Visualization and Graphics > Function Visualization >

Built-in Mathematica Symbol

See Also »|More About »

RegionPlot

RegionPlot[pred, {x, x_min, x_max}, {y, y_min, y_max}]
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
	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 x_min to x_max and y_min to y_max 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, RegionFunction, and ColorFunction are x, y.

RegionPlot returns Graphics[GraphicsComplex[data]].

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:

Applications (8)

Properties & Relations (8)

Possible Issues (2)

Neat Examples (2)

ContourPlot DensityPlot RegionPlot3D RegionFunction ParametricPlot Reduce FindInstance Boole

Function Visualization

Precollege Education

New in 6.0: Function Visualization

New in 6.0: Mathematics & Algorithms

New in 6.0: Visualization & Graphics

Demonstrations with RegionPlot (Wolfram Demonstrations Project)

New in 6

Ask a question about this page | Suggest an improvement | Leave a message for the team