---
title: "Hex Movement Library"
type: "article"
slug: "hex-movement-library"
url: "http://localhost/article/hex-movement-library/"
markdown_url: "http://localhost/article/hex-movement-library.md"
published_at: "2025-11-30T07:51:06+00:00"
modified_at: "2026-06-21T23:21:47+00:00"
featured_image:
  url: "http://localhost/wp-content/uploads/2022/04/20230809-041332.jpg"
excerpt: "Recently I've been distracted by one of my other hobby, wargaming. There has been a discussion on USENET about freeware space combat games. Having designed one a few years back, I quickly did an ASCII version and posted it. This then lead to further distractions in that hobby. Feeling guilty about \"abandoning\" the QL, I…"
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  - name: "Sinclair QL"
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  - name: "Tim Swenson"
    slug: "tim-swenson"
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publication_r:
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  title: "QL Hacker’s Journal"
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issue: "15"
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  - id: 61551
    title: "QL Hacker’s Journal 15"
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pubdate: "October 1993"
archive_link: true
---

# Hex Movement Library

Recently I’ve been distracted by one of my other hobby, wargaming. There has been a discussion on USENET about freeware space combat games. Having designed one a few years back, I quickly did an ASCII version and posted it. This then lead to further distractions in that hobby. Feeling guilty about “abandoning” the QL, I wanted to come up with some program that would tie the two hobbies together.

Most wargames are based on hex maps. One of the difficulties in putting wargames on a computer is the hex map system. A square map system is nothing more than a 2D array. But a hex map system, with each cell having 6 neighbors is takes some work. It’s workable with a square map, by extending the rules for what squares are “next” to the current square.

After pondering over this, and pursuing how I would represent a hex map in an array, I discovered that I really don’t need to store the hex map, just a way of determining what hex was next to the current hex. Anything relating to what is in a hex can be stored in an array, looked up by the hex number.

These routines will determine two things, what hex is next to the current hex (given any direction), and the distance (in hexes) between two hexes. Determining what hex is next to another hex was fairly easy. Finding the proper distance was a more challenging task. I first tried the distance formula used in square coordinate system. This had some flaws.

I then tried a different approach based on simple common sense about hexes. This worked until I got back to the program the next day and THEN saw that it did not work. Back to the distance formula. After much plugging and chugging, plus some tinking with the distance formula, I found an algorithm that worked (at least in the cases that I tested). I found the general case that failed in the plain distance formula and found a fix for these cases. I’m pretty sure that it all works fine, but I have not tested all cases.

The hex number system that I used came from my favorite wargame, [OGRE](https://www.sjgames.com/ogre/). I have not played with other numbering systems. Each hex number is two numbers combined, a column number and a row number. 0102 is column 01 and row 02. Below is a quick drawing of the numbering system.

```
             __
            /  \
         __/ Y  \__
        /  \    /  \     /|\     Hex X = 0102
       / X  \__/ Z  \     |      Hex Y = 0201
       \    /  \    /            Hex Z = 0302
        \__/ A  \__/      N      Hex A = 0202
           \    /
            \__/
```

```
100 DEFine FuNction even(num)
110  true = 1 : false = 0
120  IF (num MOD 2) = 0 THEN
130    RETurn true
140  ELSE
150    RETurn false
160  END IF
170 END DEFine
190 DEFine FuNction odd(num)
200  true = 1 : false = 0
210  IF (num MOD 2) > 0 THEN
220    RETurn true
230  ELSE
240    RETurn false
250  END IF
260 END DEFine
270 DEFine FuNction hex_north$(hex_num$)
280 LOCal column$, row, temp$
290  column$ = hex_num$(1 TO 2)
300  row = hex_num$(3 TO 4)
310  row = row - 1
320  temp$ = row
330  IF LEN(temp$) = 1 THEN temp$="0"&temp$
340  RETurn column$&temp$
350 END DEFine
360 DEFine FuNction hex_south$(hex_num$)
370 LOCal column$, row, temp$
380  column$ = hex_num$(1 TO 2)
390  row = hex_num$(3 TO 4)
400  row = row + 1
410  temp$ = row
420  IF LEN(temp$) = 1 THEN temp$="0"&temp$
430  RETurn column$&temp$
440 END DEFine
450 DEFine FuNction hex_ne$(hex_num$)
460 LOCal temp1$,temp2$,column,row
470  column = hex_num$(1 TO 2)
480  row = hex_num$(3 TO 4)
490  IF odd(column) THEN row=row-1
500  column=column+1
510  temp1$ = row
520  IF LEN(temp1$) = 1 THEN temp1$ = "0"&temp1$
530  temp2$ = column
540  IF LEN(temp2$) = 1 THEN temp2$ = "0"&temp2$
550  RETurn temp2$&temp1$
560 END DEFine
570 DEFine FuNction hex_se$(hex_num$)
580 LOCal temp1$,temp2$,column,row
590  column = hex_num$(1 TO 2)
600  row = hex_num$(3 TO 4)
610  IF even(column) THEN row=row+1
620  column=column+1
630  temp1$ = row
640  IF LEN(temp1$) = 1 THEN temp1$ = "0"&temp1$
650  temp2$ = column
660  IF LEN(temp2$) = 1 THEN temp2$ = "0"&temp2$
670  RETurn temp2$&temp1$
680 END DEFine
690 DEFine FuNction hex_nw$(hex_num$)
700 LOCal temp1$,temp2$,column,row
710  column = hex_num$(1 TO 2)
720  row = hex_num$(3 TO 4)
730  IF odd(column) THEN row=row-1
740  column=column-1
750  temp1$ = row
760  IF LEN(temp1$) = 1 THEN temp1$ = "0"&temp1$
770  temp2$ = column
780  IF LEN(temp2$) = 1 THEN temp2$ = "0"&temp2$
790  RETurn temp2$&temp1$
800 END DEFine
810 DEFine FuNction hex_sw$(hex_num$)
820  LOCal temp1$,temp2$,column,row
830  column = hex_num$(1 TO 2)
840  row = hex_num$(3 TO 4)
850  IF even(column) THEN row=row+1
860  column=column-1
870  temp1$ = row
880  IF LEN(temp1$) = 1 THEN temp1$ = "0"&temp1$
890  temp2$ = column
900  IF LEN(temp2$) = 1 THEN temp2$ = "0"&temp2$
910  RETurn temp2$&temp1$
920 END DEFine
930 DEFine FuNction hex_dist(hex1$,hex2$)
940 LOCal temp1, temp2, col1, col2, row1, row2, dist
950  col1 = hex1$(1 TO 2)
960  row1 = hex1$(3 TO 4)
970  col2 = hex2$(1 TO 2)
980  row2 = hex2$(3 TO 4)
990  temp1 = col2 - col1
1000  temp2 = row2 - row1
1010  dist = temp1^2 + temp2^2
1020  dist = SQRT(dist)
1030  IF INT(dist) < dist THEN
1040     IF row2 = row1-1 THEN
1050         dist = INT(dist)
1060     ELSE
1070        dist = INT(dist)+1
1080     END IF
1090  END IF
1100  RETurn dist
1110 END DEFine
```

As a side note, if there are any QLer’s out there that are interested in Wargaming, I’ve got a few Freeware wargames that I have designed and a few that I have picked up off the Internet. I’ve designed one tactical space combat and one tank combat game. I have all of these as Quill documents. If any are interested, please contact me.