Figure 7.1: A blank custom ticks window

The custom ticks window consists of the following elements:

• a title bar,
• a parameter bar,
• a ticks control bar, and
• some tick specification fields.

The elements of the custom ticks window are explained as follows:

Title bar

The title bar displays the graph title and the custom ticks title. The default title, “Custom Ticks #1”, can be changed using the parameter bar’s title edit box. Figure 7.2 shows the title bar:

Figure 7.2: The title bar of the custom ticks window

Parameter bar

The parameter bar is for changing the title, showing and hiding the custom ticks, modifying the tick’s colour, and changing the font size used to display the tick’s defining relation. Figure 7.3 shows the parameter bar:

Figure 7.3: The parameter bar of the custom ticks window

The elements, from left to right on the custom ticks window parameter bar, are explained as follows:

Title edit box

The title edit box is for changing the title of the current ticks specification. Title editing is useful in demonstrations and for print-outs. The default title, “Custom Ticks #1”, can be changed by clicking on the title edit box to access the edit mode. The new title will be reflected in all GrafEq menus, windows, and buttons that show the custom tick’s title.

Active checkbox

The Active checkbox is for showing and hiding the custom ticks in all opened graph view windows. Clicking on the checkbox, or the checkbox name, toggles between the selected and unselected states. Deselecting the box hides the custom ticks from all graph views.

Hint: The Active checkbox is greyed out if the custom ticks definition is not valid yet.

Colour pop-up menu

The colour pop-up menu is for changing the colour of the custom ticks. The control is useful for optimizing the clarity of graph views. The default colour can be changed by clicking on the colour box to access the pop-up colour table, and then selecting the desired colour from the table.

Font Size pop-up menu

The Font Size pop-up menu is for changing the font size used for the tick’s definition in the custom ticks window. The control is useful for presentations via an overhead liquid crystal display (LCD) or large screen television. The default font size can be changed by clicking on the Font Size box to show the list of available font sizes, and then selecting from the list. All constraints used for the tick specification will be displayed in the selected font size.

Hint: Some options in the custom ticks window’s parameter bar do not change behaviour or appearance within the custom ticks window itself: The Active checkbox affects the appearance (custom ticks display) in graph view windows. The Colour pop-up menu affects the appearance (custom ticks colour) in graph view windows.

Ticks control bar

The ticks control bar is for changing the appearance of custom ticks in all view window(s) of the associated graph. The controls, useful in demonstrations and print-outs, are for optimizing the readability of the custom ticks. Figure 7.4 shows the ticks control bar.

Figure 7.4: The tick control bar of the custom ticks window

The elements, from left to right on the custom ticks window tick control bar, are explained as follows:

Labels pop-up menu

The labels pop-up menu is for changing which ends of the custom tick lines are labelled. This control does not affect polar views. Available options include:

• no labels,
• labels on the top (or left),
• labels on the bottom (or right),
• labels alternating between the top and the bottom (or left and right),
• labels alternating between the bottom and the top (or right and left), and
• labels on both the top and bottom (or left and right).

Figure 7.5 shows example views with various label options:

No labels


Labels on the top


Labels on the bottom


Labels alternating between the top and the bottom


Tick labels alternating between the bottom and the top


Labels on both the bottom and the top

Figure 7.5: Example views with various label options

Line pop-up menu

The line pop-up menu is for changing the style used to display the custom tick lines. This control affect both polar and cartesian views. Available options include:

• no lines,
• dotted lines,
• dashed lines, and
• solid lines.

Figure 7.6 shows views with various line options:

No lines


Dotted lines


Dashed lines


Solid lines

Figure 7.6: Views with various line options

Symbolic simplification pop-up menu

The symbolic simplification pop-up menu is for changing how much simplification is to be applied to the custom tick labels. This control does not affect polar views. Available options include:

• none, for no simplication;
• bracketed, for simplified presentation of any parts with brckets; and
• complete, for a simplified presentation.

Figure 7.7 shows views with various symbolic simplification options:

No symbolic simplification


Bracketed symbolic simplification


Complete symbolic simplification

Figure 7.7: Views with various symbolic simplification options

Label font size pop-up menu

The label font size pop-up menu is for changing the font size of the tick line labels. This control does not affect polar views. Eight sizes are available, ranging from very small fonts to very large fonts.

Outline pop-up menu

The outline pop-up menu is for changing the thickness of any outlining around displayed custom tick lines and labels. Outlining is useful when parts of the custom ticks are obscured by graph regions. This control does not affect polar views. Available options include:

• no outline,
• minimal outline,
• moderate outline, and
• maximal outline.

Figure 7.8 shows views with various outline options:

No outline


Minimal outline


Moderate outline


Maximal outline

Figure 7.8: Views with various outline options

Display variable pop-up menu

The display variable pop-up menu is for selecting whether or not the variable is displayed within tick labels. This control does not affect polar views. figure 7.9 shows views with, and without, the variable being displayed:

Variable displayed in labels


Variable not displayed in labels

Figure 7.9: Views with, and without, the variable being displayed

Hint: All options in the custom ticks control bar only affect the appearance of custom ticks in graph view windows. They do not affect the behaviour or appearance within the custom ticks window itself.

Custom tick constraint fields

Custom tick constraint fields are for specifying the custom ticks. They also display the entered specification in standard mathematics notations. Prompts appear at the bottom of the field, while a constraint is being entered, to offer basic tips during the specification process. Figure 7.10 shows examples simple and complex custom tick specifications:

Simple tick specification	Complex tick specification

Figure 7.10: Custom ticks windows displaying simple and complex specifications

Custom ticks constraints should be specified in terms of the domain or range variable. The simple tick specification in figure 7.10 creates vertical ticks in multiples of p, which is especially useful for graphing trigonometric relations. Additional samples of useful tick specifications are provided at the end of this manual chapter.

While a constraint is being entered or changed,

• prompts appear at the bottom of its field,
• a blinking cursor is available,
• the Active checkbox of the custom ticks window is unselected, and
• the easy button floating window is available.

Custom ticks constraints are presented in standard mathematics format. When functions are entered using multiple characters, the characters are presented in red until the GrafEq recognizes them as a function name. Red signifies unrecognized entries, and is used here because GrafEq can interpret “sin” as the sine function instead of the product “s×i×n” only after an argument, such as x, is entered. The function “sqrt” is a good example that demonstrates GrafEq formatting functions as they are recognized.

Standard mathematics format is desirable for inclusion in handouts or documents (by copying from GrafEq and pasting into a word processor). The presentation also gives some visual feedback that constraints are interpreted as intended.

Additional constraint fields can be brought up by pressing the tab key.

Hint: If the cursor is positioned away from the end of the relation string during editing, all characters to the right side of the cursor are unformatted.

Hint: With default preference settings, unformatted characters are red in colour displays, and outlined in black-and-white displays.

Tip: The Symbol and Times TrueType fonts must be installed in order to produce attractive screen output, unless default preferences are changed.

Tip: More information on the format and structure of constraints and the parser is available in the How GrafEq Works chapter.

Following are some additional hints and tips about custom ticks and the custom ticks window:

• Custom ticks are usually either domain or range interpretation aids: For cartesian views, they would be vertical or horizontal lines. For polar views, they would be radial lines eminating from the origin, or concentric circles about the origin. Custom ticks are usually specified in terms of the domain variable or the range variable. For both cartesian and polar views, custom ticks can be specified using r or q.
• Each custom ticks window describes one set of custom ticks; the custom ticks can be defined using a single constraints, or by using multiple constraints. Additional constraint fields can be brought up by pressing the tab key from within the custom ticks window.
• Each graph can have one or more sets of custom ticks. Each set is described in its own custom ticks window. Additional custom ticks windows can be opened by selecting New Custom Ticks... from the Graph menu.
• The keystrokes field is a strip beneath the current constraint field. It shows the keystrokes used to produce the formatted relation in the constraint field. Keystrokes information is especially useful when the intuitive mathematics symbols and notation do not correspond to general keyboard entries. Figure 7.11 shows a sample keystrokes field with its corresponding constraint field:
  
  Figure 7.11: A custom ticks window with its keystroke field
  
  Prior to version 2.04, GrafEq always provided this information via the keystroke field. But as of GrafEq 2.04, keystroke information can be revealed within the constraint entry fields by positioning the cursor to the left of the entries. The keystroke field is hidden using the default preferences, but remains useful for printing purposes. To display the keystroke field, change the default preference setting.
• A custom tick entry can be completed by selecting the Active box of its custom ticks window or by pressing return. When custom tick entries are completed, the custom tick window will collapse to display just the title bar, parameter bar, ticks control bar, and constraint fields - prompts, the blinking cursor, the keystroke field, and the easy button floating window will disappear. The Active checkbox will be selected, but it can be freely deselected and selected without editing any constraints.
• Clicking within any constraint field of a completed custom ticks window will return you to the edit mode and remove the corresponding set of custom ticks from any opened graph views.

Conclusion

• For a single vertical tick line through (p,3), enter x=p.
• For horizontal tick lines through multiples of 1/2p, enter y=k(p/2).
• For “log-paper”, enter x=10^k.
• For “cross-hairs”, enter x=p for tick #1, and y=logp for tick #2.
• For circular ticks, in cartesian views, enter r=k.
• For radial ticks, in polar views, enter q=k(p/6).

  Hint: Single tick lines or cross-hairs are desirable, especially if memory is low or only specific regions are of interest. Instead of using custom ticks, adding constraints such as x=10k; 0<k<4 allows GrafEq to concentrate on the region of interest and not bother with custom ticks.