RegionPlot3D
✖
RegionPlot3D
makes a plot showing the three-dimensional region in which pred is True.
Details and Options




- The predicate pred can be any logical combination of inequalities.
- The region plotted by RegionPlot3D can contain disconnected parts.
- RegionPlot3D treats the variables x, y and z as local, effectively using Block.
- RegionPlot3D has attribute HoldAll and evaluates pred after assigning numerical values to x, y and z. In some cases, it may be more efficient to use Evaluate to evaluate pred symbolically first.
- RegionPlot3D has the same options as Graphics3D, with the following additions and changes: [List of all options]
-
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 PlotLegends None legends for surfaces 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 PlotTheme $PlotTheme overall theme for the plot ScalingFunctions None how to scale individual coordinates TextureCoordinateFunction Automatic how to determine texture coordinates TextureCoordinateScaling True whether to scale arguments to TextureCoordinateFunction 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 xmin to xmax, 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 are x, y, and z. Functions in ColorFunction and TextureCoordinateFunction are by default supplied with scaled versions of these arguments.
- RegionPlot3D returns Graphics3D[GraphicsComplex[data]].
- Possible settings for ScalingFunctions include:
-
{sx,sy,sz} scale x, y and z axes - Common built-in scaling functions s include:
-
"Log" log scale with automatic tick labeling "Log10" base-10 log scale with powers of 10 for ticks "SignedLog" log-like scale that includes 0 and negative numbers "Reverse" reverse the coordinate direction -
AlignmentPoint Center the default point in the graphic to align with AspectRatio Automatic ratio of height to width Axes True whether to draw axes AxesEdge Automatic on which edges to put axes AxesLabel None axes labels AxesOrigin Automatic where axes should cross AxesStyle {} graphics directives to specify the style for axes Background None background color for the plot BaselinePosition Automatic how to align with a surrounding text baseline BaseStyle {} base style specifications for the graphic BoundaryStyle Automatic how to draw boundaries of regions Boxed True whether to draw the bounding box BoxRatios {1,1,1} bounding 3D box ratios BoxStyle {} style specifications for the box ClipPlanes None clipping planes ClipPlanesStyle Automatic style specifications for clipping planes ColorFunction Automatic how to color surfaces ColorFunctionScaling True whether to scale arguments to ColorFunction ContentSelectable Automatic whether to allow contents to be selected ControllerLinking False when to link to external rotation controllers ControllerPath Automatic what external controllers to try to use Epilog {} 2D graphics primitives to be rendered after the main plot EvaluationMonitor None expression to evaluate at every function evaluation FaceGrids None grid lines to draw on the bounding box FaceGridsStyle {} style specifications for face grids FormatType TraditionalForm default format type for text ImageMargins 0. the margins to leave around the graphic ImagePadding All what extra padding to allow for labels, etc. ImageSize Automatic absolute size at which to render the graphic LabelStyle {} style specifications for labels Lighting Automatic simulated light sources to use 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 PlotLabel None a label for the plot PlotLegends None legends for surfaces PlotPoints Automatic the initial number of sample points in each direction PlotRange Full the range of values to include in the plot PlotRangePadding Automatic how much to pad the range of values PlotRegion Automatic final display region to be filled PlotStyle Automatic graphics directives for the style of the surface of each region PlotTheme $PlotTheme overall theme for the plot PreserveImageOptions Automatic whether to preserve image options when displaying new versions of the same graphic Prolog {} 2D graphics primitives to be rendered before the main plot RotationAction "Fit" how to render after interactive rotation ScalingFunctions None how to scale individual coordinates SphericalRegion Automatic whether to make the circumscribing sphere fit in the final display area TextureCoordinateFunction Automatic how to determine texture coordinates TextureCoordinateScaling True whether to scale arguments to TextureCoordinateFunction Ticks Automatic specification for ticks TicksStyle {} style specification for ticks TouchscreenAutoZoom False whether to zoom to fullscreen when activated on a touchscreen ViewAngle Automatic angle of the field of view ViewCenter Automatic point to display at the center ViewMatrix Automatic explicit transformation matrix ViewPoint {1.3,-2.4,2.} viewing position ViewProjection Automatic projection method for rendering objects distant from the viewer ViewRange All range of viewing distances to include ViewVector Automatic position and direction of a simulated camera ViewVertical {0,0,1} direction to make vertical WorkingPrecision MachinePrecision the precision used in internal computations

List of all options




Examples
open allclose allBasic Examples (4)Summary of the most common use cases

https://wolfram.com/xid/0d6g6quw2w-k2y


https://wolfram.com/xid/0d6g6quw2w-79v8l1

Plot 3D regions defined by logical combinations of inequalities:

https://wolfram.com/xid/0d6g6quw2w-dwx3gb

Use simple styling of region boundaries:

https://wolfram.com/xid/0d6g6quw2w-ch6vth

Scope (12)Survey of the scope of standard use cases
Sampling (3)
Areas where the function is not True are excluded:

https://wolfram.com/xid/0d6g6quw2w-q5mv44

Use logical combinations of regions:

https://wolfram.com/xid/0d6g6quw2w-5v9ny3

Regions do not have to be connected:

https://wolfram.com/xid/0d6g6quw2w-zaqpk2

Presentation (9)
Provide an explicit PlotStyle for the region:

https://wolfram.com/xid/0d6g6quw2w-ehykaq

Specify styles for each region:

https://wolfram.com/xid/0d6g6quw2w-t6vje


https://wolfram.com/xid/0d6g6quw2w-wr40d


https://wolfram.com/xid/0d6g6quw2w-2zm69g

Style the areas between mesh lines:

https://wolfram.com/xid/0d6g6quw2w-ywz6e8

Color the region with an overlay density:

https://wolfram.com/xid/0d6g6quw2w-xcb0to

Use a theme with simple ticks in a bright color scheme:

https://wolfram.com/xid/0d6g6quw2w-vjk74x


https://wolfram.com/xid/0d6g6quw2w-ot7p7r

Apply a log scale to the z axis:

https://wolfram.com/xid/0d6g6quw2w-3tjrjt

Options (54)Common values & functionality for each option
BoundaryStyle (3)
Boundary lines are black by default:

https://wolfram.com/xid/0d6g6quw2w-zahwy7

Use None to not draw any boundary lines:

https://wolfram.com/xid/0d6g6quw2w-nff8cs


https://wolfram.com/xid/0d6g6quw2w-z7s3qd

BoxRatios (2)
ColorFunction (5)
Color regions by scaled ,
, and
values:

https://wolfram.com/xid/0d6g6quw2w-rqr8hk

Named color functions use the scaled direction:

https://wolfram.com/xid/0d6g6quw2w-ga262v

Color regions according to a function of unscaled ,
, and
values:

https://wolfram.com/xid/0d6g6quw2w-wdqsr

ColorFunction has higher priority than PlotStyle:

https://wolfram.com/xid/0d6g6quw2w-pio7he

ColorFunction has lower priority than MeshShading:

https://wolfram.com/xid/0d6g6quw2w-8d059i

ColorFunctionScaling (1)
Mesh (7)

https://wolfram.com/xid/0d6g6quw2w-fbjz4w


https://wolfram.com/xid/0d6g6quw2w-090wq

Use 5 mesh lines in each direction:

https://wolfram.com/xid/0d6g6quw2w-g2u

Use 3 mesh lines in the direction and 6 mesh lines in the
direction:

https://wolfram.com/xid/0d6g6quw2w-2as1z2

Use mesh lines at specific values:

https://wolfram.com/xid/0d6g6quw2w-pkl2jw

Use different styles for different mesh lines:

https://wolfram.com/xid/0d6g6quw2w-9kwnuy

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

https://wolfram.com/xid/0d6g6quw2w-dgunp5

MeshFunctions (2)
MeshShading (5)
Alternate red and blue sections:

https://wolfram.com/xid/0d6g6quw2w-0cxb3n

MeshShading has higher priority than ContourStyle for styling:

https://wolfram.com/xid/0d6g6quw2w-7l5k1g

Use the PlotStyle for some segments by setting MeshShading to Automatic:

https://wolfram.com/xid/0d6g6quw2w-st3m0g

MeshShading can be used with ColorFunction:

https://wolfram.com/xid/0d6g6quw2w-kvyovy

Fill between regions defined by multiple mesh functions:

https://wolfram.com/xid/0d6g6quw2w-fmrvn8

MeshStyle (2)
NormalsFunction (4)
Normals are automatically calculated:

https://wolfram.com/xid/0d6g6quw2w-uxompn

Use None to get flat shading for all the polygons:

https://wolfram.com/xid/0d6g6quw2w-w76mq3

Vary the effective normals used on the surface:

https://wolfram.com/xid/0d6g6quw2w-bf0msq

The NormalsFunction does not get applied to clipped regions:

https://wolfram.com/xid/0d6g6quw2w-h64exc

PerformanceGoal (2)
PlotLegends (3)
Identify regions with a legend:

https://wolfram.com/xid/0d6g6quw2w-7wvkcm

Use legends for color gradients:

https://wolfram.com/xid/0d6g6quw2w-9dywm6

Use Placed to put legends above the plot:

https://wolfram.com/xid/0d6g6quw2w-l0fx9a

PlotPoints (1)
PlotStyle (5)

https://wolfram.com/xid/0d6g6quw2w-hwk5hl

Use None to show a wireframe of the bounding surfaces:

https://wolfram.com/xid/0d6g6quw2w-1x0v84


https://wolfram.com/xid/0d6g6quw2w-1oij6u

ColorFunction has higher priority than PlotStyle:

https://wolfram.com/xid/0d6g6quw2w-15l4a7

MeshShading has higher priority than PlotStyle:

https://wolfram.com/xid/0d6g6quw2w-xe1lxb

PlotTheme (2)
ScalingFunctions (5)
By default, plots have linear scales in all directions:

https://wolfram.com/xid/0d6g6quw2w-gtf8tb

Apply a log scale to the z axis:

https://wolfram.com/xid/0d6g6quw2w-hswwl

Use a shifted log scale to show a function with negative values:

https://wolfram.com/xid/0d6g6quw2w-z3l30

Use ScalingFunctions to reverse the coordinate direction in the direction:

https://wolfram.com/xid/0d6g6quw2w-cjjav5

Use a scale defined by a function and its inverse:

https://wolfram.com/xid/0d6g6quw2w-kl8tm2

TextureCoordinateFunction (4)
Textures use scaled and
coordinates by default:

https://wolfram.com/xid/0d6g6quw2w-r5pmzv


https://wolfram.com/xid/0d6g6quw2w-88ic21


https://wolfram.com/xid/0d6g6quw2w-8ybp0p

Use textures to highlight how parameters map onto a surface:

https://wolfram.com/xid/0d6g6quw2w-9r5psj


https://wolfram.com/xid/0d6g6quw2w-tl4b7v

Applications (3)Sample problems that can be solved with this function
Find the intersection of two half-spaces:

https://wolfram.com/xid/0d6g6quw2w-eoipfk

Simple regions including a cube:

https://wolfram.com/xid/0d6g6quw2w-ryb9u


https://wolfram.com/xid/0d6g6quw2w-bb3ltr


https://wolfram.com/xid/0d6g6quw2w-e1tsh2


https://wolfram.com/xid/0d6g6quw2w-1kzj3


https://wolfram.com/xid/0d6g6quw2w-bb0e4v


https://wolfram.com/xid/0d6g6quw2w-czrknf


https://wolfram.com/xid/0d6g6quw2w-jd7le2

Combine PolyhedronData regions with other inequalities:

https://wolfram.com/xid/0d6g6quw2w-t9i0


https://wolfram.com/xid/0d6g6quw2w-fobho

Properties & Relations (8)Properties of the function, and connections to other functions
Use RegionPlot for areas:

https://wolfram.com/xid/0d6g6quw2w-dqgfqo

Use ContourPlot and ContourPlot3D for systems of equalities:

https://wolfram.com/xid/0d6g6quw2w-8qtxio


https://wolfram.com/xid/0d6g6quw2w-vslw0h

Use ComplexRegionPlot for regions in the complex plane:

https://wolfram.com/xid/0d6g6quw2w-ile2og

Use RegionFunction to constrain other plots:

https://wolfram.com/xid/0d6g6quw2w-8d5lk0


https://wolfram.com/xid/0d6g6quw2w-xpj5um

Use ParametricPlot3D for parametric curves and surfaces:

https://wolfram.com/xid/0d6g6quw2w-fuibr

Use Integrate or NIntegrate to integrate over regions:

https://wolfram.com/xid/0d6g6quw2w-4mgq2h


https://wolfram.com/xid/0d6g6quw2w-nqujmb


https://wolfram.com/xid/0d6g6quw2w-lsw18p

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

https://wolfram.com/xid/0d6g6quw2w-ymla3


https://wolfram.com/xid/0d6g6quw2w-eqz18m


https://wolfram.com/xid/0d6g6quw2w-q7yhq

Use Reduce to get a cylindrical representation of the region:

https://wolfram.com/xid/0d6g6quw2w-bwkfer

Use FindInstance to find specific samples in regions:

https://wolfram.com/xid/0d6g6quw2w-bk9h9l

Wolfram Research (2007), RegionPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionPlot3D.html (updated 2022).
Text
Wolfram Research (2007), RegionPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionPlot3D.html (updated 2022).
Wolfram Research (2007), RegionPlot3D, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionPlot3D.html (updated 2022).
CMS
Wolfram Language. 2007. "RegionPlot3D." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/RegionPlot3D.html.
Wolfram Language. 2007. "RegionPlot3D." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/RegionPlot3D.html.
APA
Wolfram Language. (2007). RegionPlot3D. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RegionPlot3D.html
Wolfram Language. (2007). RegionPlot3D. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RegionPlot3D.html
BibTeX
@misc{reference.wolfram_2025_regionplot3d, author="Wolfram Research", title="{RegionPlot3D}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/RegionPlot3D.html}", note=[Accessed: 20-June-2025
]}
BibLaTeX
@online{reference.wolfram_2025_regionplot3d, organization={Wolfram Research}, title={RegionPlot3D}, year={2022}, url={https://reference.wolfram.com/language/ref/RegionPlot3D.html}, note=[Accessed: 20-June-2025
]}