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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 fx,y are assumed to be z=fx,y.

• 

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.

Examples

withStudent[MultivariateCalculus]:

CrossSectionx2+y2+z2=4,x+y=1.1,0.1,x=2..2,y=2..2,z=2..2,showfunction=false,title=Sphere

Return z=constant level curves.

CrossSectionx2+y2,z=0..25,x=4..4,y=4..4,planes=10

The command to create the plot from the Plotting Guide is

CrossSectionx+y2,x+yz=0,x=2..4,y=1..2

See Also

plot3d/options, Student, Student[MultivariateCalculus], Student[MultivariateCalculus][CrossSectionTutor]


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