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

.

ContourPlot3D[f

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

.

MORE INFORMATION

The contour surfaces plotted by ContourPlot3D can contain disconnected parts.

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

ContourPlot3D treats the variables , and as local, effectively using Block.

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 .

Nothing is plotted in any regions where evaluates to None.

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.

ContourPlot3D returns Graphics3D[GraphicsComplex[data]].

EXAMPLES

CLOSE ALL

Basic Examples (3)

Plot a 3D contour surface:

Plot several contour surfaces:

Use styling to emphasize features:

Plot a 3D contour surface:

In[1]:=

Out[1]=

Plot several contour surfaces:

In[1]:=

Out[1]=

Use styling to emphasize features:

In[1]:=

Out[1]=

Scope (11)

More points are sampled where the function changes quickly:

Areas where the function becomes nonreal are excluded:

Use PlotPoints and MaxRecursion to control adaptive sampling:

Use RegionFunction to show interior features:

Add labels:

Color the surface by height:

Apply styles to a contour:

Show multiple implicit surfaces with explicit styles:

Use transparency to show interior features:

Use an overlay mesh:

Fill with different colors between mesh lines:

Options (53)

Use a red boundary around the edges of the contours:

Use None to omit the boundary:

BoundaryStyle applies to holes cut by RegionFunction:

Use Automatic to show the natural scale of the surface:

Color the contours according to the

,

, or

values:

Use a named color gradient:

ColorFunction has higher priority than ContourStyle:

Use red when

:

ColorFunction has lower priority than MeshShading:

Use unscaled values to color the contours:

Use an overlay density based on the coordinate values:

Use 5 equally spaced contours:

Use automatic contour selection:

Use specific contours:

Use specific contours with specific styles:

Use transparent contours:

Use distinct colors for each contour:

Use FaceForm to get different colors on the inside and outside:

Alternate styles for contour surfaces:

Use the same style for all the equations:

Use different styles for different equations:

ColorFunction has higher priority than ContourStyle:

MeshShading has higher priority than ContourStyle:

Show where ContourPlot3D samples a function:

Count how many times

is evaluated:

Refine the contour where it changes quickly:

Show the initial and final sampling meshes:

Use None to not draw any mesh:

Use 5 mesh levels in each direction:

Use 5 mesh levels in the

direction and 10 in the

direction:

Use mesh lines at specific values:

Use different styles for different mesh lines:

Use a mesh evenly spaced in the

,

, and

directions:

Mesh with respect to radial distance:

Alternate red and blue sections in the

direction:

MeshShading has higher priority than ContourStyle for styling:

Use ContourStyle 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:

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

Use more initial points to get a smoother contour:

Show the contours over the Full

,

range:

Automatically compute the

,

range:

Select a region in

,

and

:

Remove a wedge to see hidden features:

Evaluate functions using machine-precision arithmetic:

Evaluate functions using arbitrary-precision arithmetic:

Applications (5)

Ellipsoidal surfaces [more info]:

Compute their volumes:

Conic surfaces [more info]:

Show a sphere and hyperboloids of one and two sheets:

Use Mesh to show that a hyperbolic paraboloid is a doubly ruled surface:

An implicitly defined torus [more info]:

An electrostatic potential built from a collection of point charges

at positions

:

Two charges

and

:

Two charges

and

:

Three charges

and

:

Properties & Relations (8)

ContourPlot3D samples more points where it needs to:

Plotting an implicit surface is the same as finding the zero contour of a related function:

The orientation of the contours depends on the form of the input:

Use ListContourPlot3D for plotting data:

Use RegionPlot3D for implicit regions in three dimensions:

Use Plot3D for surfaces:

Use ParametricPlot3D for parametric curves and regions in three dimensions:

Use ContourPlot and DensityPlot for contours and densities in two dimensions:

Possible Issues (3)

Use increased settings for PlotPoints or MaxRecursion to capture features of a surface:

Use more initial points to capture more components of the contour surface:

For functions that are always non-negative, it is not possible to find the 0 contour:

Neat Examples (1)

A transcendental periodic implicit surface: