CrossSection - Maple Help

Student[MultivariateCalculus]

 CrossSection
 show the intersection between a plane and a surface

 Calling Sequence CrossSection(f(x,y), g(x,y,z)=K, x=a..b, y=c..d, opts) CrossSection(f(x,y,z), g(x,y,z)=K, x=a..b, y=c..d, z=e..f, opts)

Parameters

 f(x, y) - algebraic expression f(x, y, z) - algebraic equation or expression g(x, y, z) - linear algebraic expression K - constant, list, or range of constants x, y, z - name; specify the independent variables a, b, c, d, e, f - real constants; range of the function opts - (optional) equation(s) of the form option=value where option is one of functionoptions, intersectionoptions, output, planeoptions, planes or showfunction; specify output options

Description

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

Examples

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

Return z=constant level curves.

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

The command to create the plot from the Plotting Guide is

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