Framing 3D Plots

Imagine that the surface of an expression being plotted is enclosed in a transparent box just spanning the maximum and minimum computed values of x, y, and z. Your monitor screen is between the box and an eye fixed somewhere in front of the screen. Each point on the wire frame projects onto the screen along the line joining that point to the eye.

For maximum resolution it is usually desirable to magnify the surface as much as possible while keeping it entirely within the 3D-plot window. Therefore, Derive automatically magnifies the image horizontally so the surface just fits the full width of the 3D-plot window. Also, if using the optional automatic vertical centering and scaling, Derive automatically tries to magnify and shift the image vertically so the surface just fits the height of the 3D-plot window. Naturally this is impossible if the surface projects as a horizontal line, in which case Derive generates an error beep.

To impose a specific scaling in all three directions, turn off the automatic centering and scaling of new plots using the Options > Autoscale New Plots command10DHZF7. For example, you may want to impose equal scaling in all three directions. Alternatively, you may want to magnify certain details at the expense of having portions clipped at the top or bottom edge of the plot window.

The framing challenge for three dimensions is more difficult than for two dimensions because of the lower effective resolution and the extra dimension to search. If a few experiments do not reveal appropriate ranges for the two variables in your expression or equation, then use a 2D-plot window to plot cross-sections obtained by substituting various numeric values for one or the other of the two variables. The ten-fold greater resolution of 2D plots often more quickly reveals appropriate ranges for viewing the two variables in a 3D-plot window. If you zoom in on a 2D plot until the features of interest are at least 1/nth of the window width, they have a chance of being resolved in a 3D-plot window of that size using n grid lines for that coordinate.