This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# RegionPlot3D

 RegionPlot3Dmakes a plot showing the three-dimensional region in which pred is True.
• 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.
 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 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 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.
Plot a 3D region:
Plot 3D regions defined by logical combinations of inequalities:
Use simple styling of region boundaries:
Plot a 3D region:
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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   (8)
Areas where the function is not True are excluded:
Use logical combinations of regions:
Regions do not have to be connected:
Provide an explicit PlotStyle for the region:
Use an overlay mesh:
Style the areas between mesh lines:
Color the region with an overlay density:
 Options   (46)
Use automatic labeling of axes:
Specify the axes labels:
Boundary lines are black by default:
Use None to not draw any boundary lines:
Use red boundary lines:
Regions are shown in a cube by default:
Use the natural scale of the region:
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:
Color regions according to a function of unscaled , , and values:
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:
Mesh lines in the , , and directions:
Mesh lines at fixed radii from the origin:
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:
Use a dashed mesh in the direction:
Use a dashed mesh in the direction and a blue mesh in the direction:
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:
Generate a higher-quality plot:
Emphasize performance, possibly at the cost of quality:
Use more initial points to get a smoother region:
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:
Textures use scaled and coordinates by default:
Use the and coordinates:
Use unscaled coordinates:
Use textures to highlight how parameters map onto a surface:
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:
Use RegionPlot for areas:
Use ContourPlot and ContourPlot3D for systems of equalities:
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:
The region between norm balls:
Plot a scalar field over a 3D region: