Testing in Python whether one glyph is a reflectio

Question

Inspired by List of all unicode's open/close brackets? I'm trying to find a list of all unicode glyphs in a given font that are reflections of each other. First I just need to be able to test whether one glyph is a reflection of another. Below I have two different attempts (two different implementations of my render_char function) but I'm not able to identify '(' and ')' as mirror images using either one. How can I do this?

from PIL import Image,ImageDraw,ImageFont
import freetype
import numpy as np

def render_char0(c):
    # Based on https://github.com/rougier/freetype-py/blob/master/examples/hello-world.py
    # Needs numpy (blech) and the image comes out the inverse of the way I expect
    face = freetype.Face("/Library/Fonts/Verdana.ttf")
    face.set_char_size( 48*64 )
    face.load_char(c)
    bitmap = face.glyph.bitmap
    w,h = bitmap.width, bitmap.rows
    Z = np.array(bitmap.buffer, dtype=np.ubyte).reshape(h,w)
    return Image.fromarray(Z, mode='L').convert('1')

def render_char1(c):
    # Based on https://stackoverflow.com/a/14446201/2829764
    verdana_font = ImageFont.truetype("/Library/Fonts/Verdana.ttf", 20, encoding="unic")
    text_width, text_height = verdana_font.getsize(c)
    canvas = Image.new('RGB', (text_width+10, text_height+10), (255, 255, 255))
    draw = ImageDraw.Draw(canvas)
    draw.text((5,5), c, font = verdana_font, fill = "#000000")
    return canvas

for render_char in [render_char0, render_char1]:
    lparen = render_char('(')
    rparen = render_char(')')
    mirror = lparen.transpose(Image.FLIP_LEFT_RIGHT)

    mirror.show()
    rparen.show()
    print mirror.tobytes() == rparen.tobytes() # False

Answer 1

There is a text file called BidiMirroring.txt in the Unicode plain-text database with a list of all mirrored characters. That file is easy to parse by programs.

Current url is http://www.unicode.org/Public/UNIDATA/BidiMirroring.txt

I don't think using the rendered glyphs can work reliably. There's a lot of reasons why eg. ( and ) are no exact mirror images, like spacing around the character, hinting and anti-aliasing, maybe the font is slightly slanted, or maybe the font designer has just make the two brackets a bit different etc. Other characters are rotated, rather than mirrored, like “ and ” in some fonts, and the Chinese quotation marks 「 and 」.

Answer 2

I think rendering is the wrong aproach. It depends on the font and wether the font knows how to render this. I heard that unicode characters have a specification for this symmetry. Maybe it is encoded in their name. "LEFT" and "RIGHT" "SUBSCRIPT". Have a look at http://xahlee.info/comp/unicode_matching_brackets.html