WOLFRAM

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)Summary of the most common use cases

Plot a 3D region:

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Plot multiple regions:

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Plot 3D regions defined by logical combinations of inequalities:

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Use simple styling of region boundaries:

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Scope  (12)Survey of the scope of standard use cases

Sampling  (3)

Areas where the function is not True are excluded:

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Use logical combinations of regions:

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Regions do not have to be connected:

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Presentation  (9)

Provide an explicit PlotStyle for the region:

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Specify styles for each region:

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Add labels:

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Use an overlay mesh:

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Style the areas between mesh lines:

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Color the region with an overlay density:

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

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Use a monochrome theme:

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Apply a log scale to the z axis:

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Options  (54)Common values & functionality for each option

BoundaryStyle  (3)

Boundary lines are black by default:

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Use None to not draw any boundary lines:

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Use red boundary lines:

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BoxRatios  (2)

Regions are shown in a cube by default:

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Use the natural scale of the region:

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ColorFunction  (5)

Color regions by scaled , , and values:

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Named color functions use the scaled direction:

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

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ColorFunction has higher priority than PlotStyle:

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ColorFunction has lower priority than MeshShading:

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ColorFunctionScaling  (1)

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

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Mesh  (7)

Show the sampling mesh:

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Show no mesh:

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Use 5 mesh lines in each direction:

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

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Use mesh lines at specific values:

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Use different styles for different mesh lines:

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

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MeshFunctions  (2)

Mesh lines in the , , and directions:

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Mesh lines at fixed radii from the origin:

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MeshShading  (5)

Alternate red and blue sections:

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MeshShading has higher priority than ContourStyle for styling:

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

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MeshShading can be used with ColorFunction:

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Fill between regions defined by multiple mesh functions:

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MeshStyle  (2)

Use a dashed mesh in the direction:

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

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NormalsFunction  (4)

Normals are automatically calculated:

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Use None to get flat shading for all the polygons:

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Vary the effective normals used on the surface:

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The NormalsFunction does not get applied to clipped regions:

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PerformanceGoal  (2)

Generate a higher-quality plot:

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Emphasize performance, possibly at the cost of quality:

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PlotLegends  (3)

Identify regions with a legend:

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Use legends for color gradients:

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Use Placed to put legends above the plot:

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PlotPoints  (1)

Use more initial points to get a smoother region:

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PlotStyle  (5)

Regions are shown as solids:

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Use None to show a wireframe of the bounding surfaces:

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Use an orange surface:

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ColorFunction has higher priority than PlotStyle:

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MeshShading has higher priority than PlotStyle:

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PlotTheme  (2)

Use a highly stylized theme:

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Remove the mesh lines:

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ScalingFunctions  (5)

By default, plots have linear scales in all directions:

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Apply a log scale to the z axis:

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

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Use ScalingFunctions to reverse the coordinate direction in the direction:

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Use a scale defined by a function and its inverse:

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TextureCoordinateFunction  (4)

Textures use scaled and coordinates by default:

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Use the and coordinates:

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Use unscaled coordinates:

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Use textures to highlight how parameters map onto a surface:

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TextureCoordinateScaling  (1)

Use scaled or unscaled coordinates for textures:

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Applications  (3)Sample problems that can be solved with this function

Find the intersection of two half-spaces:

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Simple regions including a cube:

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Half of a cube shell:

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Ball:

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Half of a spherical shell:

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Ellipsoid:

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Half of an ellipsoidal shell:

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Spherical wedge:

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Combine PolyhedronData regions with other inequalities:

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Properties & Relations  (8)Properties of the function, and connections to other functions

Use RegionPlot for areas:

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Use ContourPlot and ContourPlot3D for systems of equalities:

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Use ComplexRegionPlot for regions in the complex plane:

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Use RegionFunction to constrain other plots:

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Use ParametricPlot3D for parametric curves and surfaces:

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Use Integrate or NIntegrate to integrate over regions:

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The integration region:

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

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Use Reduce to get a cylindrical representation of the region:

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Use FindInstance to find specific samples in regions:

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Neat Examples  (2)Surprising or curious use cases

The region between norm balls:

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Plot a scalar field over a 3D region:

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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).

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 ]}

@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 ]}

@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 ]}