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RegionPlot3D

RegionPlot3D[pred, {x, x_min, x_max}, {y, y_min, y_max}, {z, z_min, z_max}]
makes a plot showing the three-dimensional region in which pred is True.

MORE INFORMATION

The predicate pred can be any logical combination of inequalities.

The region plotted by RegionPlot3D can contain disconnected parts.

By default, RegionPlot3D shows the boundary of each region as a surface with opacity 0.8, and with surface normals pointing outward.

RegionPlot3D has the same options as Graphics3D, with the following additions and changes:

	Axes	True	whether to draw axes
	BoundaryStyle	Automatic	how to draw boundaries of regions
	BoxRatios	{1,1,1}	bounding 3D box ratios
	ColorFunction	Automatic	how to color surfaces
	ColorFunctionScaling	True	whether to scale arguments to ColorFunction
	EvaluationMonitor	None	expression to evaluate at every function evaluation
	MaxRecursion	Automatic	the maximum number of recursive subdivisions allowed
	Mesh	Automatic	how many mesh lines in each direction to draw
	MeshFunctions	{#1&,#2&,#3&}	how to determine the placement of mesh lines
	MeshShading	None	how to shade regions between mesh lines
	MeshStyle	Automatic	the style for mesh lines
	Method	Automatic	the method to use for refining surfaces
	NormalsFunction	Automatic	how to determine effective surface normals
	PerformanceGoal	$PerformanceGoal	aspects of performance to try to optimize
	PlotPoints	Automatic	the initial number of sample points in each direction
	PlotRange	Full	the range of values to include in the plot
	PlotStyle	Automatic	graphics directives for the style of the surface of each region
	WorkingPrecision	MachinePrecision	the precision used in internal computations

RegionPlot3D initially evaluates pred at a 3D 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 RegionPlot3D 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, RegionPlot3D will explicitly include the full ranges x_min to x_max, etc.

With Mesh->All, RegionPlot3D will explicitly draw mesh lines to indicate the subdivisions it used to find each region.

RegionPlot3D 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 and z. Functions in ColorFunction are by default supplied with scaled versions of these arguments.

RegionPlot3D returns Graphics3D[GraphicsComplex[data]].

Basic Examples (3)

Plot a 3D region:

Plot 3D regions defined by logical combinations of inequalities:

Use simple styling of region boundaries:

Applications (3)

Properties & Relations (7)

Neat Examples (2)

ContourPlot3D RegionPlot ParametricPlot3D ListSurfacePlot3D RegionFunction Reduce FindInstance Boole

Function Visualization

New in 6.0: Function Visualization

New in 6.0: Mathematics & Algorithms

New in 6.0: Visualization & Graphics

Demonstrations with RegionPlot3D (Wolfram Demonstrations Project)

New in 6

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