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, 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