Calculating the position of QR Code alignment patterns

Question

I need to know how to calculate the positions of the QR Code alignment patterns as defined in the table of ISO/IEC 18004:2000 Annex E.

I don\'t understand how it\'s

Answer 1

While the specification does provide a table of the alignment, this is a reasonable question (and one I found myself with :-)) - the possibility of generating the positions procedurally has its merits (less typo-prone code, smaller code footprint, knowing pattern/properties of the positions).

I'm happy to report that, yes, a procedure exists (and it is even fairly simple). The specification itself says most of it:

[The alignment patterns] are spaced as evenly as possible between the Timing Pattern and the opposite side of the symbol, any uneven spacing being accommodated between the timing pattern and the first alignment pattern in the symbol interior.

That is, only the interval between the first and second coordinate may differ from the rest of the intervals. The rest must be equal. Another important bit is of course that, for the APs to agree with the timing patterns, the intervals must be even. The remaining tricky bit is just getting the rounding right.

Anyway - here's code printing the alignment position table:

def size_for_version(version):
    return 17 + 4 * version

def alignment_coord_list(version):
    if version == 1:
        return []
    divs = 2 + version // 7
    size = size_for_version(version)
    total_dist = size - 7 - 6
    divisor = 2 * (divs - 1)
    # Step must be even, for alignment patterns to agree with timing patterns
    step = (total_dist + divisor // 2 + 1) // divisor * 2 # Get the rounding right
    coords = [6]
    for i in range(divs - 2, -1, -1): # divs-2 down to 0, inclusive
        coords.append(size - 7 - i * step)
    return coords

for version in range(1, 40 + 1): # 1 to 40 inclusive
    print("V%d: %s" % (version, alignment_coord_list(version)))