Built-in Mathematica Symbol

ContourPlot3D

ContourPlot3D[f, {x, x_min, x_max}, {y, y_min, y_max}, {z, z_min, z_max}]
produces a three-dimensional contour plot of

as a function of

,

and

.

g, {x, x_min, x_max}, {y, y_min, y_max}, {z, z_min, z_max}]
plots the contour surface for which

.

By default, ContourPlot3D shows each contour level as an opaque white surface, with normals pointing outward.

ContourPlot3D has attribute HoldAll, and evaluates and only after assigning specific numerical values to , and .

In some cases it may be more efficient to use Evaluate to evaluate and symbolically before specific numerical values are assigned to , and .

ContourPlot3D has the same options as Graphics3D, with the following additions and changes:

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 contour surfaces
ColorFunctionScaling	True	whether to scale arguments to ColorFunction
Contours	Automatic	how many or what contour surfaces to show
ContourStyle	White	the style for contour surfaces
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 divisions
MeshShading	None	how to shade regions between mesh divisions
MeshStyle	Automatic	the style for mesh lines
Method	Automatic	the method to use for refining contour 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,Full,Full,Automatic}	the range of values to include
RegionFunction	(True&)	how to determine whether a point should be included
WorkingPrecision	MachinePrecision	the precision used in internal computations

ContourPlot3D initially evaluates at a 3D grid of equally spaced sample points specified by PlotPoints. Then it uses an adaptive algorithm to subdivide at most MaxRecursion times to generate smooth contours.

You should realize that since it uses only a finite number of sample points, it is possible for ContourPlot3D to miss features of your functions. To check your results, you should try increasing the settings for PlotPoints and MaxRecursion.

The arguments supplied to functions in MeshFunctions and RegionFunction are , , , . Functions in ColorFunction are by default supplied with scaled versions of these arguments.