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You can create standard two-dimensional contour plots using the built-in functions ContourPlot and ListContourPlot. ContourPlot3D is the three-dimensional analog of ContourPlot. ContourPlot[f, x, xmin, xmax, y, ymin, ymax] will plot lines showing particular values of as a function of and . Similarly, ContourPlot3D[f, x, xmin, xmax, y, ymin, ymax, z, zmin, zmax] will plot surfaces showing particular values of as a function of , , and . ContourPlot3D works by dividing the three-dimensional space into cubes and deciding if the surface intersects each cube. If the surface does intersect a cube, ContourPlot3D will subdivide this cube further, and so on.

Making three-dimensional contour plots.

This loads the package.

In[1]:= <<Graphics`ContourPlot3D`

This produces a three-dimensional plot of the zero values of the function.

In[2]:= ContourPlot3D[Cos[Sqrt[ x^2 + y^2 + z^2 ]],
{x,-2,2}, {y,0,2}, {z,-2,2}]


Options for ContourPlot3D.

Each value specified in Contours generates a different surface. ContourStyle colors each surface. To use this option, you must set Lighting -> False. MaxRecursion sets the number of times you subdivide each cube. However, if the surface does not intersect the cube, the cube is not subdivided. With MaxRecursion -> 0 the plot points are chosen from PlotPoints ->x or PlotPoints ->x, y, z. If MaxRecursion is greater than , recursion takes place. You can give a different number of plot points for the first and subsequent divisions of a cube. PlotPoints ->, means that plot points are used first, and then if you subdivide, plot points are used. PlotPoints ->, , , , , is also valid. ContourPlot3D and ListContourPlot3D return a Graphics3D object. This means the functions will accept any option that can be specified for a Graphics3D object.

Here is another plot showing a contour value of .

In[3]:= ContourPlot3D[x y z,
{x,-1,1}, {y,-1,1}, {z,-1,1},
Contours -> {.1}]


Options for ListContourPlot3D.

ListContourPlot3D takes a three-dimensional data set interpreted as a representation of a function , where the ranges of x, y, and z are set by the MeshRange option. With the default value of Automatic for MeshRange, the ranges of x, y, and z are specified by the dimensions of the data set.

This defines a three-dimensional array of data.

In[4]:= data = Table[x^2 + 2*y^2 + 3*z^2,
{z, -1, 1, .25},
{y, -1, 1, .25},
{x, -1, 1, .25}];

Here is a plot of the contours and specified by green and red contour surfaces, respectively.

In[5]:= ListContourPlot3D[data,
MeshRange -> {{-1,1}, {-1,1}, {-1,1}},
Contours -> {1.5, 3.},
Lighting -> False, Axes -> True,
ContourStyle -> {{RGBColor[0,1,0]},