QMTools displays function plots on Graph tabs, labeled by the number and names of the independent variables used by those functions. A QMTools applet may have any number of Graph tabs (including none).

Graph tabs are managed automatically. When a plot request is made, the plot is added to an existing tab if one is found with matching variables; otherwise, a new tab is added. Also, a graph tab is removed when the last plot on that tab is deleted.

Plots are rendered differently, depending upon the number of independent variables. Functions of one and two variables are portrayed as line and surface plots, respectively. Functions of three variables are depicted as density plots, wherein [absolute] function values determine the intensity of color at the plotted points.

Graph Tab Layout

• All function plotting occurs on the [larger] left side of the graphics tab; the sidebar on the right – the legend – has an entry identifying each plot by its plot color and function name. The fraction of screen real estate devoted to the legend is easily altered by clicking on the divider and dragging it to the left or right.
• Every graphics operation can be accessed through popup menus. Right-click the mouse anywhere in the graphics background to bring up a menu of operations that affect all plots on the graph (global popup); to access plot-specific operations, right-click on the plot in question. Many operations have keyboard shortcuts, as noted at the far right of the corresponding menu entry.
  Menu entries having trailing ellipses (...) are gateways to other menus or dialogs. Notable among these are the GraphProperties Editor and the PlotProperties Editor. The latter can be accessed directly with the keyboard shortcut alt+ctrl+I. When activated from the keyboard, the PlotProperties Editor pertains to the top-most plot on the graph. The PlotProperties Editor also can be accessed by right-clicking on the desired plot entry in the graph legend.
• Unlike the Math tab, graph tabs may be 'torn off' from the applet and displayed in a separate window. The new window may be positioned and re-sized as desired. This is especially valuable in making side-by-side comparisons of different – but related – graphs; invoke this feature by selecting Display in Window... from the global popup menu. Click the Close button in the upper right of the detached window to restore the tab to the applet.

Back to Top

Managing Plot Appearance

The PlotProperties Editor is the repository for plotting styles and related information that affect plot appearance. The keyboard shortcut alt+ctrl+I is the quickest way to access the editor for the top-most plot. Editor fields are discussed below; available options vary depending on the number of function variables.

• Colors | Visibilities Here you can show or hide the plot, and edit the plot color. Color selection is done with the help of the ColorChooser, an interactive editor that affords complete control over plot color, including transparency.
  When a function is first plotted, the plot color is chosen randomly.
• A complex-valued function can be rendered as a single plot (instead of real and imaginary component plots) by checking the Color-4-phase box. In this display style, the phase of a complex number (the function value) is represented by color which – like phase angle – repeats with a definite period. The 'color wheel' follows the rainbow from red to green to violet, and then back to red again through magenta.
• A logarithmic scaling option is enabled if the function values are positive definite over the entire domain of the independent variable(s).
• Scale bias allows the ordinate scale to be adjusted independently of any others. The default setting is '0'; with each increment [decrement], the scale is enhanced [shrunk] by the factor √2.
  Scale bias is not available for density plots.
• Color saturation uses color saturation (purity) to provide visual clues about ordinate values; smaller [absolute] values are rendered with less purity. The default setting (50%) assigns 50% color saturation to mid-range data.
• Multiple plotting styles are available exclusively to functions of a single variable:
  • Normal (baseline fill) renders all points between the ordinate value and the axis in the plot color.
  • Envelope only renders only points at (and near) the ordinate value in the plot color.
  • Display in relief renders all points at and below the ordinate value in the plot color.

Back to Top

Manipulating the Graphics View

• To shift the viewpoint, click-drag the mouse in any direction; alternatively, press the left-right and up-down arrow keys to move the view point horizontally and vertically. For functions of two or more variables, the viewpoint also can be moved toward or away from the observer using the + and − keys.
  Holding down the shift key in combination with the action keys magnifies the movement tenfold.
• To rotate the line-of-sight about a horizontal or vertical axis, right-click and drag the mouse at a right angle to the desired rotation axis. Alternatively, hold down the ctrl key while pressing the left-right or up-down arrow keys.
• To zoom in or out, press and hold both mouse buttons while dragging the mouse toward you (zoom out) or away from you (zoom in). Zoom action also can be activated from the keyboard: press Z to zoom in; shift+Z to zoom out.
• To adjust the plot scale, hold down the alt key while pressing both mouse buttons and dragging the mouse. Equivalent keyboard shortcuts are S to scale up; shift+S to scale down.
  This action affects all plots equally. To adjust the scale of a single plot, use the Scale bias setting of the PlotProperties Editor.
  The ordinate scale used for each graph is set automatically from the range of function values when the first function is plotted. You can force re-scaling at any time by selecting Force Auto-scale from the global popup menu. With multiple plots, the new scale reflects the range of ordinate values for all visible plots. Plot visibility is toggled from the PlotProperties Editor.
• To change the plot order, click-drag the entries in the graph legend. Double-clicking on a plot also will bring it to the front, where its properties can be quickly accessed with the keyboard shortcut alt+ctrl+I.

Back to Top