This applet is designed to show how the
graph of a function in two variables can be constructed from the cross
sections, which are each graphs of one variable.
The applet has a control window and 4 graphics windows.
The first graphical window is the domain window. It
contains shows a grid of points, along with the cross section lines in
the x-y plane. The coordinates of the key point are (x0,y0) and
they can be controlled a number of ways in the control panel. The
single arrows move the value by a single step. The double arrows
move the value through an animation to the end of the range. A
value can also be typed in.
There are windows for an x-slice and a y-slice, the two cross
sections of the 3-D graph obtained by holding y and x, respectively,
constant at the hot spot.
The fourth window gives a graph of the surface. It is
worthwhile to step through the range for (x0,y0) while the style of the
graph window is open surface. This lets you see the wire from
constructed from cross sections. There are check boxes on
the control panel that lets you look at either the surface, or the
intersection of the surface running parallel with the x or y axis, or
wireframe grid of the surface. This lets you see that the
wireframe is constructed from the cross section curves.
Things to notice:
It is worth looking at the graph window from the view "up the
z-axis" and to compare that view with the domain window.