plot3d

The ``plot3d'' command plots the graph of a function of two variables over a domain in the plane. The graph of f on a domain is the surface in space that consists of points of the form (x,y,f(x,y)) , where (x,y) is a point in the domain. Maple will accept domains that are rectangles or region between the graphs of two functions. Let us plot the graph of f(x,y) = x² - y² on the rectangle $[-1,1] \times [-2,2]$.

    plot3d(f(x,y),x=-1..1,y=-2..2);

The default plot displays the graph as a colored grid without axes. As with the other plot commands, clicking on the plot causes a menubar and toolbar with plot options to be displayed across the top of the Maple window. You should experiment with the different options that are available using the pull-down menus or the graphics icons. After you highlight an option or an icon with the left mouse button, the plot will be replaced by a box that bounds the image--a bounding box. To replot the image, use the right mouse button (on a two-button mouse) or the middle mouse button (on a three-button mouse.) It is possible to rotate the image in space by using the left-hand mouse button to click and drag the bounding box before replotting the image. It is important to note that when Maple initially plots an image, the default option is to render the plot so that it fills the screen. This may result in a plot that is not displayed with true proportions. To plot the image so that the units on all the axes have the same length, use the ``Constrained'' option from the ``Projection'' pull-down menu or the ``1:1'' button from the graphics tool bar.

The ``plot3d'' command has several options which can be found in the ``plot3d'' entry in the Help utility. One option that will prove useful is the ``grid'' option. A Maple ``plot3d'' image is made up of a number of small quadrilaterals called cells. The default option is that there are 24 x 24 cells which are determined by 25 equally spaced points along each axis. At times it is helpful to use more points and thus more and smaller cells, which make the plot appear smoother. This is accomplished by using the ``grid'' option. For example, try the following command.

    plot3d(f(x,y),x=-1..1,y=-2..2,grid=[5,40]);

(For more information, click on plot3d.)