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

Here's a Python solution which is basically equivalent to the C# solution posted by @jgosar, except that it corrects a deviation from the thonky.com table for version 32 (that other solution reports 110 for the second last position, whereas the linked table says 112):

def get_alignment_positions(version):
    positions = []
    if version > 1:
        n_patterns = version // 7 + 2
        first_pos = 6
        positions.append(first_pos)
        matrix_width = 17 + 4 * version
        last_pos = matrix_width - 1 - first_pos
        second_last_pos = (
            (first_pos + last_pos * (n_patterns - 2)  # Interpolate end points to get point
            + (n_patterns - 1) // 2)                  # Round to nearest int by adding half
                                                      # of divisor before division
            // (n_patterns - 1)                       # Floor-divide by number of intervals
                                                      # to complete interpolation
            ) & -2                                    # Round down to even integer
        pos_step = last_pos - second_last_pos
        second_pos = last_pos - (n_patterns - 2) * pos_step
        positions.extend(range(second_pos, last_pos + 1, pos_step))
    return positions

The correction consists of first rounding the second last position (up or down) to the nearest integer and then rounding down to the nearest even integer (instead of directly rounding down to the nearest even integer).

Disclaimer: Like @jgosar, I don't know whether the thonky.com table is correct (I'm not going to buy the spec to find out). I've simply verified (by pasting the table into a suitable wrapper around the above function) that my solution matches that table in its current version.