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. This produces a three-dimensional plot of the zero values of the function.
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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  .
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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. Here is a plot of the contours  and  specified by green and red contour surfaces, respectively.
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