Cistercian Numerals

# The paths to create the digits 1–9 in the "units" position.
d_paths = {
(0, 1): ((1, 0), (2, 0)),
(0, 2): ((1, 1), (2, 1)),
(0, 3): ((1, 0), (2, 1)),
(0, 4): ((1, 1), (2, 0)),
(0, 5): ((1, 1), (2, 0), (1, 0)),
(0, 6): ((2, 0), (2, 1)),
(0, 7): ((1, 0), (2, 0), (2, 1)),
(0, 8): ((1, 1), (2, 1), (2, 0)),
(0, 9): ((1, 1), (2, 1), (2, 0), (1, 0)),
}
# Generate the paths for the digits in the 10s, 100s and 1000s position by
# reflection.
for i in range(1, 10):
    d_paths[(1, i)] = [(2-x, y) for x, y in d_paths[(0, i)]]
    d_paths[(2, i)] = [(x, 3-y) for x, y in d_paths[(0, i)]]
    d_paths[(3, i)] = [(2-x, 3-y) for x, y in d_paths[(0, i)]]

def transform(x, y, dx, dy, sc):
    """Transform the coordinates (x, y) into the scaled, displaced system."""
    return x*sc + dx, y*sc + dy

def get_path(i, d):
    """Return the SVG path to render the digit d in decimal position i."""
    if d == 0:
        return
    path = d_paths[(i, d)]
    return 'M{},{} '.format(*transform(*path[0], *tprms)) + ' '.join(
                ['L{},{}'.format(*transform(*xy, *tprms)) for xy in path[1:]])

def make_digit(i, d):
    """Output the SVG path element for digit d in decimal position i."""
    print('<path d="{}"/>'.format(get_path(i, d)), file=fo)

def make_stave():
    """Output the SVG line element for the vertical stave."""
    x1, y1 = transform(1, 0, *tprms)
    x2, y2 = transform(1, 3, *tprms)
    print('<line x1="{}" y1="{}" x2="{}" y2="{}"/>'.format(x1, y1, x2, y2),
          file=fo)


def svg_preamble(fo):
    """Write the SVG preamble, including the styles."""

    # Set the path stroke-width appropriate to the scale.
    stroke_width = max(1.5, tprms[2] / 5)
    print("""<?xml version="1.0" encoding="utf-8"?>
<svg xmlns="http://www.w3.org/2000/svg"
     xmlns:xlink="http://www.w3.org/1999/xlink" width="2000" height="2005" >
<defs>
<style type="text/css"><![CDATA[
line, path {
  stroke: black;
  stroke-width: %d;
  stroke-linecap: square;
}
path {
  fill: none;
}
]]>
</style>
</defs>
""" % stroke_width, file=fo)

def make_numeral(n, fo):
    """Output the SVG for the number n using the current transform."""
    make_stave()
    for i, s_d in enumerate(str(n)[::-1]):
        make_digit(i, int(s_d))

# Transform parameters: dx, dy, scale.
tprms = [5, 5, 5]

with open('all_cistercian_numerals.svg', 'w') as fo:
    svg_preamble(fo)
    for i in range(10000):
        # Locate this number at the position dx, dy = tprms[:2].
        tprms[0] = 15 * (i % 125) + 5
        tprms[1] = 25 * (i // 125) + 5
        make_numeral(i, fo)
    print("""</svg>""", file=fo)