Chapter 7. The Custom Ticks Window

The custom ticks window is for adding user specified ticks as interpretations aids to view windows. It can be brought up by selecting New Custom Ticks from the Graph menu. Figure 7.1 shows a blank custom ticks window:

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.

Hint: | The custom ticks window is very similar to the algebraic relation window. They have the following equivalent elements and properties: easy button support when editing constraint specifications, the title bar’s elements and functions, the parameter bar’s elements and functions, the constraint fields’ elements and functions, and the optional keystroke field below the current constraint field. This chapter still provides a complete explanation of these elements and properties so that the manual has a modular structure and can be used as a reference. The description for the equivalent elements and properties are mirrored in the Algebraic Relation Window chapter.

An easy button floating window is available for help in entering custom ticks specifications. Easy buttons are especially useful when entering symbols not readily available from standard keys on a keyboard, such as p, or any powers. For details, refer to the Easy Button Floating Window chapter.

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 specification. 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 custom 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 and unavailable if the custom ticks definition is not valid yet.

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

  Font Size pop-up menu
    The Font Size pop-up menu is for changing the font size used to display the tick’s specification in the custom ticks window. The control is useful for presentations via an overhead liquid crystal display (LCD) or large screen television. The font size can be changed by clicking on the Font Size pop-up menu to bring up the menu of available font sizes, and then selecting the desired size from it. 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 are for optimizing the readability of the custom ticks, and is useful in demonstrations and making print-outs. 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 affects 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 simplification;
    - bracketed, for simplified presentation of any parts within brackets; 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 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/2, 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 the constraint field, and the easy button floating window is available to offer support for the specification process;
  - a blinking cursor is present;
  - the Active checkbox of the custom ticks window is unselected, and greyed out unless all constraints are valid;
  - press the Tab key to move to the next constraint, or to create a new one if there is not a next constraint;
  - press the Tab key while holding down the Shift key to move to the previous constraint, or to create a new one if there is not a previous constraint.

  When functions are entered using multiple characters, the characters are unformatted, and presented in red, until GrafEq recognizes them as a function name: red signifies unrecognized entries. GrafEq can interpret “sin” as the sine function, instead of the product “s×i×n”, only after an argument, such as x, is entered. A good example is the square root function, when entered as “sqrt”: GrafEq will replace the letters with a graphical radical symbol after an argument is started.

  Hint: | If the cursor is positioned away from the end of the constraint string during editing, all characters to the right side of the cursor become unformatted. With the default preference settings, unformatted characters are shown in solid red on colour displays, while they are outlined in black (not filled in) on black-and-white displays.

  Tip: | The “Symbol” and “Times” TrueType fonts must be installed in order to produce attractive screen output, unless the font settings have been changed in the preferences.

  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 emanating 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 constraint, 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 have no obvious correspondence with the keys on a keyboard, such as p or any powers. 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 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 checkbox 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
To conclude this chapter of the manual, following are some examples of useful tick specifications:

- 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=10k.
- For “cross-hairs”, enter x=p for tick #1, and y=logp for tick #2.
- For circular ticks, in polar as well as cartesian views, enter r=k.
- For radial ticks, in polar as well as cartesian views, enter q=k(p/6).

  Tip: | Single tick lines or cross-hairs are desirable especially if memory is low or only specific regions are of interest. To the custom ticks x=10k, adding a constraint such as 0<k<4 allows GrafEq to concentrate on the region of interest. Further, the relation specification itself might also be modified to stand out specific regions of interest, in which case GrafEq need not bother with any custom ticks at all and can concentrate on graphing the relation. Mastering relation specification would take time and practise, but it can be done, and it is fun!

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