This is documentation for Mathematica 3, which was
based on an earlier version of the Wolfram Language.
 Graphics`ContourPlot3D` 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]:= <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]}, {RGBColor[1,0,0]}}]