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BUILT-IN MATHEMATICA SYMBOL
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.
Details and Options
- 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.
- RegionPlot3D has the same options as Graphics3D, with the following additions and changes:
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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 the default setting PlotRange->Full, RegionPlot3D will explicitly include the full ranges
to 
, 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 and RegionFunction 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]].
New in 6 | Last modified in 8
