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RegionPlot3D—Wolfram Documentation

RegionPlot3D[pred,{x,xmin,xmax},{y,ymin,ymax},{z,zmin,zmax}]

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

RegionPlot3D[{pred1,pred2,…},…]

plots several regions corresponding to the predi.

Details and Options

Examples

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Basic Examples  (4)

Plot a 3D region:

Plot multiple regions:

Plot 3D regions defined by logical combinations of inequalities:

Use simple styling of region boundaries:

Scope  (12)

Sampling  (3)

Areas where the function is not True are excluded:

Use logical combinations of regions:

Regions do not have to be connected:

Presentation  (9)

Provide an explicit PlotStyle for the region:

Specify styles for each region:

Add labels:

Use an overlay mesh:

Style the areas between mesh lines:

Color the region with an overlay density:

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

Use a monochrome theme:

Apply a log scale to the z axis:

Options  (82)

Axes  (3)

By default, Axes are drawn:

Use AxesFalse to turn off axes:

Turn each axis on individually:

AxesLabel  (4)

No axes labels are drawn by default:

Place a label on the axis:

Specify axes labels:

Use labels based on variables specified in RegionPlot3D:

AxesOrigin  (2)

The position of the axes is determined automatically:

Specify an explicit origin for the axes:

AxesStyle  (3)

Change the style for the axes:

Specify the style of each axis:

Use different styles for the ticks and the axes:

BoundaryStyle  (3)

Boundary lines are black by default:

Use None to not draw any boundary lines:

Use red boundary lines:

BoxRatios  (2)

Regions are shown in a cube by default:

Use the natural scale of the region:

ColorFunction  (5)

Color regions by scaled , , and values:

Named color functions use the scaled direction:

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

ColorFunction has higher priority than PlotStyle:

ColorFunction has lower priority than MeshShading:

ColorFunctionScaling  (1)

ImageSize  (7)

Use named sizes, such as Tiny, Small, Medium and Large:

Specify the width of the plot:

Specify the height of the plot:

Allow the width and height to be up to a certain size:

Specify the width and height for a graphic, padding with space if necessary:

Setting AspectRatioFull will fill the available space:

Use maximum sizes for the width and height:

Use ImageSizeFull to fill the available space in an object:

Specify the image size as a fraction of the available space:

Mesh  (7)

Show the sampling mesh:

Show no mesh:

Use 5 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 to each component:

MeshFunctions  (2)

Mesh lines in the , , and directions:

Mesh lines at fixed radii from the origin:

MeshShading  (5)

MeshStyle  (2)

Use a dashed mesh in the direction:

Use a dashed mesh in the direction and a blue mesh in the direction:

NormalsFunction  (4)

Normals are automatically calculated:

Use None to get flat shading for all the polygons:

Vary the effective normals used on the surface:

The NormalsFunction does not get applied to clipped regions:

PerformanceGoal  (2)

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

PlotLegends  (3)

Identify regions with a legend:

Use legends for color gradients:

Use Placed to put legends above the plot:

PlotPoints  (1)

Use more initial points to get a smoother region:

PlotStyle  (5)

PlotTheme  (2)

Use a highly stylized theme:

Remove the mesh lines:

ScalingFunctions  (5)

By default, plots have linear scales in all directions:

Apply a log scale to the z axis:

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

Use ScalingFunctions to reverse the coordinate direction in the direction:

Use a scale defined by a function and its inverse:

TextureCoordinateFunction  (4)

Textures use scaled and coordinates by default:

Use the and coordinates:

Use unscaled coordinates:

Use textures to highlight how parameters map onto a surface:

TextureCoordinateScaling  (1)

Use scaled or unscaled coordinates for textures:

Ticks  (6)

Ticks are placed automatically in each plot:

Use TicksNone to not draw any tick marks:

Place tick marks at specific positions:

Draw tick marks at the specified positions with the specified labels:

Specify tick marks with scaled lengths:

Customize each tick with position, length, labeling and styling:

TicksStyle  (3)

By default, the ticks and tick labels use the same styles as the axis:

Specify overall tick style, including the tick labels:

Specify tick style for each of the axes:

Applications  (3)

Find the intersection of two half-spaces:

Simple regions including a cube:

Half of a cube shell:

Ball:

Half of a spherical shell:

Ellipsoid:

Half of an ellipsoidal shell:

Spherical wedge:

Combine PolyhedronData regions with other inequalities:

Properties & Relations  (8)

Neat Examples  (2)

The region between norm balls:

Plot a scalar field over a 3D region:

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).

CMS

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

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: 03-March-2026]}

BibLaTeX

@online{reference.wolfram_2025_regionplot3d, organization={Wolfram Research}, title={RegionPlot3D}, year={2022}, url={https://reference.wolfram.com/language/ref/RegionPlot3D.html}, note=[Accessed: 03-March-2026]}