RegionPlot3D

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  (54)

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)

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

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)

Alternate red and blue sections:

MeshShading has higher priority than ContourStyle for styling:

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

MeshShading can be used with ColorFunction:

Fill between regions defined by multiple mesh functions:

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)

Regions are shown as solids:

Use None to show a wireframe of the bounding surfaces:

Use an orange surface:

ColorFunction has higher priority than PlotStyle:

MeshShading has higher priority than PlotStyle:

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:

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)

Use RegionPlot for areas:

Use ContourPlot and ContourPlot3D for systems of equalities:

Use ComplexRegionPlot for regions in the complex plane:

Use RegionFunction to constrain other plots:

Use ParametricPlot3D for parametric curves and surfaces:

Use Integrate or NIntegrate to integrate over regions:

The integration region:

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

Use Reduce to get a cylindrical representation of the region:

Use FindInstance to find specific samples in regions:

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_2023_regionplot3d, author="Wolfram Research", title="{RegionPlot3D}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/RegionPlot3D.html}", note=[Accessed: 05-December-2023 ]}

BibLaTeX

@online{reference.wolfram_2023_regionplot3d, organization={Wolfram Research}, title={RegionPlot3D}, year={2022}, url={https://reference.wolfram.com/language/ref/RegionPlot3D.html}, note=[Accessed: 05-December-2023 ]}