The CrossSection command returns a plot or animation of the intersection between the surface f and the plane g. The intersection of multiple parallel planes can be shown by making the variable K a range or a list of real numbers.  If a range is used, a sequence of planes is generated within the range. The number of planes is determined by the optional argument planes. If a list is used, the planes are displayed in the order specified.

Curves of the form $f\left(x\,y\right)$ are assumed to be $z=f\left(x\,y\right)$.

To return level curves, specify a variable name for g(x,y,z), for example, z.

Planes that are not intersecting or tangent to the surface f are not displayed.

The CrossSectionTutor routine offers equivalent capabilities to CrossSection in a tutor interface. See the Student[MultivariateCalculus][CrossSectionTutor] help page.

The opts argument can contain any of the following equations that set output options.

functionoptions = list

Specifies the plot options for plotting the surface f. For more information on plotting options, see plot3d/options.

intersectionoptions = list

Specifies the plot options for plotting the curves formed by the intersections of the planes and the surface. For more information on plotting options, see plot3d/options.

output = plot or animation

This option controls the return value of the function.

* output = plot specifies that a plot displays, which shows the expression and all the planes.  The default is output = plot.

* output = animation specifies that an animation displays, which shows the expression and the chosen planes in succession.

planeoptions = list

Specifies the plot options for plotting the plane(s) g. For more information on plotting options, see plot3d/options.

planes = posint

Specifies the number of planes if the variable K is a range. The default is $10$.

showfunction = true or false

Determines whether the function f is plotted. The default is true.

caption = anything

A caption for the plot.

The default caption is constructed from the parameters and the command options. caption = "" disables the default caption. For more information about specifying a caption, see plot/typesetting.

For more information, see plot3d/options.

For information on how to change the default colors, see the Student[SetColors] help page.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{MultivariateCalculus}\right]\right)\:$

$\mathrm{CrossSection}\left(x^2+y^2+z^2=4\,x+y=\left[1.1\,0.1\right]\,x=-2..2\,y=-2..2\,z=-2..2\,\mathrm{showfunction}=\mathrm{false}\,\mathrm{title}=''Sphere''\right)$

$\mathrm{CrossSection}\left(x^2+y^2\,z=0..25\,x=-4..4\,y=-4..4\,\mathrm{planes}=10\right)$

$\mathrm{CrossSection}\left(x+y^2\,x+y-z=0\,x=2..4\,y=-1..2\right)$