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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.
  • 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.
AxesTruewhether to draw axes
BoundaryStyleAutomatichow to draw boundaries of regions
BoxRatios{1,1,1}bounding 3D box ratios
ColorFunctionAutomatichow to color surfaces
ColorFunctionScalingTruewhether to scale arguments to ColorFunction
EvaluationMonitorNoneexpression to evaluate at every function evaluation
MaxRecursionAutomaticthe maximum number of recursive subdivisions allowed
MeshAutomatichow many mesh lines in each direction to draw
MeshFunctions{#1&,#2&,#3&}how to determine the placement of mesh lines
MeshShadingNonehow to shade regions between mesh lines
MeshStyleAutomaticthe style for mesh lines
MethodAutomaticthe method to use for refining surfaces
NormalsFunctionAutomatichow to determine effective surface normals
PerformanceGoal$PerformanceGoalaspects of performance to try to optimize
PlotPointsAutomaticthe initial number of sample points in each direction
PlotRangeFullthe range of values to include in the plot
PlotStyleAutomaticgraphics directives for the style of the surface of each region
WorkingPrecisionMachinePrecisionthe 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.
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