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C.3.1 X Axis Tic Marks

The first function should print the X axis tic marks. We must specify the tic marks themselves and their spacing:

     (defvar X-axis-label-spacing
       (if (boundp 'graph-blank)
           (* 5 (length graph-blank)) 5)
       "Number of units from one X axis label to next.")

(Note that the value of graph-blank is set by another defvar. The boundp predicate checks whether it has already been set; boundp returns nil if it has not. If graph-blank were unbound and we did not use this conditional construction, in a recent GNU Emacs, we would enter the debugger and see an error message saying ‘Debugger entered--Lisp error: (void-variable graph-blank)’.)

Here is the defvar for X-axis-tic-symbol:

     (defvar X-axis-tic-symbol "|"
       "String to insert to point to a column in X axis.")

The goal is to make a line that looks like this:

            |   |    |    |

The first tic is indented so that it is under the first column, which is indented to provide space for the Y axis labels.

A tic element consists of the blank spaces that stretch from one tic to the next plus a tic symbol. The number of blanks is determined by the width of the tic symbol and the X-axis-label-spacing.

The code looks like this:

     ;;; X-axis-tic-element
     ...
     (concat
      (make-string
       ;; Make a string of blanks.
       (-  (* symbol-width X-axis-label-spacing)
           (length X-axis-tic-symbol))
       ? )
      ;; Concatenate blanks with tic symbol.
      X-axis-tic-symbol)
     ...

Next, we determine how many blanks are needed to indent the first tic mark to the first column of the graph. This uses the value of full-Y-label-width passed it by the print-graph function.

The code to make X-axis-leading-spaces looks like this:

     ;; X-axis-leading-spaces
     ...
     (make-string full-Y-label-width ? )
     ...

We also need to determine the length of the horizontal axis, which is the length of the numbers list, and the number of ticks in the horizontal axis:

     ;; X-length
     ...
     (length numbers-list)
     
     ;; tic-width
     ...
     (* symbol-width X-axis-label-spacing)
     
     ;; number-of-X-ticks
     (if (zerop (% (X-length tic-width)))
         (/ (X-length tic-width))
       (1+ (/ (X-length tic-width))))

All this leads us directly to the function for printing the X axis tic line:

     (defun print-X-axis-tic-line
       (number-of-X-tics X-axis-leading-spaces X-axis-tic-element)
       "Print ticks for X axis."
         (insert X-axis-leading-spaces)
         (insert X-axis-tic-symbol)  ; Under first column.
         ;; Insert second tic in the right spot.
         (insert (concat
                  (make-string
                   (-  (* symbol-width X-axis-label-spacing)
                       ;; Insert white space up to second tic symbol.
                       (* 2 (length X-axis-tic-symbol)))
                   ? )
                  X-axis-tic-symbol))
         ;; Insert remaining ticks.
         (while (> number-of-X-tics 1)
           (insert X-axis-tic-element)
           (setq number-of-X-tics (1- number-of-X-tics))))

The line of numbers is equally straightforward:

First, we create a numbered element with blank spaces before each number:

     (defun X-axis-element (number)
       "Construct a numbered X axis element."
       (let ((leading-spaces
              (-  (* symbol-width X-axis-label-spacing)
                  (length (number-to-string number)))))
         (concat (make-string leading-spaces ? )
                 (number-to-string number))))

Next, we create the function to print the numbered line, starting with the number “1” under the first column:

     (defun print-X-axis-numbered-line
       (number-of-X-tics X-axis-leading-spaces)
       "Print line of X-axis numbers"
       (let ((number X-axis-label-spacing))
         (insert X-axis-leading-spaces)
         (insert "1")
         (insert (concat
                  (make-string
                   ;; Insert white space up to next number.
                   (-  (* symbol-width X-axis-label-spacing) 2)
                   ? )
                  (number-to-string number)))
         ;; Insert remaining numbers.
         (setq number (+ number X-axis-label-spacing))
         (while (> number-of-X-tics 1)
           (insert (X-axis-element number))
           (setq number (+ number X-axis-label-spacing))
           (setq number-of-X-tics (1- number-of-X-tics)))))

Finally, we need to write the print-X-axis that uses print-X-axis-tic-line and print-X-axis-numbered-line.

The function must determine the local values of the variables used by both print-X-axis-tic-line and print-X-axis-numbered-line, and then it must call them. Also, it must print the carriage return that separates the two lines.

The function consists of a varlist that specifies five local variables, and calls to each of the two line printing functions:

     (defun print-X-axis (numbers-list)
       "Print X axis labels to length of NUMBERS-LIST."
       (let* ((leading-spaces
               (make-string full-Y-label-width ? ))
            ;; symbol-width is provided by graph-body-print
            (tic-width (* symbol-width X-axis-label-spacing))
            (X-length (length numbers-list))
            (X-tic
             (concat
              (make-string
               ;; Make a string of blanks.
               (-  (* symbol-width X-axis-label-spacing)
                   (length X-axis-tic-symbol))
               ? )
              ;; Concatenate blanks with tic symbol.
              X-axis-tic-symbol))
            (tic-number
             (if (zerop (% X-length tic-width))
                 (/ X-length tic-width)
               (1+ (/ X-length tic-width)))))
         (print-X-axis-tic-line tic-number leading-spaces X-tic)
         (insert "\n")
         (print-X-axis-numbered-line tic-number leading-spaces)))

You can test print-X-axis:

  1. Install X-axis-tic-symbol, X-axis-label-spacing, print-X-axis-tic-line, as well as X-axis-element, print-X-axis-numbered-line, and print-X-axis.
  2. Copy the following expression:
              (progn
               (let ((full-Y-label-width 5)
                     (symbol-width 1))
                 (print-X-axis
                  '(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16))))
    
  3. Switch to the *scratch* buffer and place the cursor where you want the axis labels to start.
  4. Type M-: (eval-expression).
  5. Yank the test expression into the minibuffer with C-y (yank).
  6. Press <RET> to evaluate the expression.

Emacs will print the horizontal axis like this:


          |   |    |    |    |
          1   5   10   15   20