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- import numpy as np
- from math import log, ceil
- from misc.bin2svg import bin2svg # https://pastebin.com/y8rY5Vj4
- from octahedral_permutations import * # https://pastebin.com/JBx0TSsC
- from store_svg import * # https://pastebin.com/FaBF6k7E
- def number_to_reverse_binary_list(n, length):
- bin_str = "{0:b}".format(n).zfill(length)[::-1]
- return [int(digit) for digit in bin_str]
- def perm_to_bin_mat(perm):
- long = len(perm)
- high = ceil(log(max(perm), 2))
- mat = np.zeros([high, long], dtype=bool)
- for i, e in enumerate(perm):
- mat[:, i] = number_to_reverse_binary_list(e, high)
- return mat
- def perm_to_svg_path(perm):
- mat = perm_to_bin_mat(perm)
- return bin2svg(mat)
- conjugacy_class_to_color = {
- 'A': 'white', 'B': 'white', 'C': 'white', 'D': 'green', 'E': 'orange',
- 'a': 'yellow', 'b': 'yellow', 'c': 'yellow', 'd': 'blue', 'e': 'red'
- }
- gray_cube_coordinates = [(0, 3), (0, 1), (1, 2), (1, 0), (2, 3), (2, 1), (3, 2), (3, 0)]
- arrow_cube_coordinates = [(0, 3), (0, 1), (.6, 2.2), (.6, .2), (2, 3), (2, 1), (2.6, 2.2), (2.6, .2)]
- for filenum in range(6):
- footer_perm_formulas = ''
- footer_perm_matrix = ''
- footer_invperm_formulas = ''
- footer_invperm_matrix = ''
- filename = 'test %s.svg' % filenum
- rectangles_svg = ''
- gray_matrix_text_svg = ''
- for rectnum in range(8):
- permdict = octahedral_permutations[(rectnum, filenum)]
- invpermdict = octahedral_permutations[permdict['inverse']]
- perm, invperm = permdict['perm'], invpermdict['perm']
- # background and cube colors
- rectbeige = 'f6e6d2' if permdict['parity'] else 'fcf9f0' # light if parity 0
- (bottomgray, topgray) = ('ddd', '888') if rectnum in [0, 3, 5, 6] else ('888', 'ddd')
- if rectnum == 0:
- (bottombeige, topbeige) = ('f6e6d2', 'fcf9f0') if permdict['parity'] else ('fcf9f0', 'f6e6d2')
- # conjugacy class colors
- conjug_letter = permdict['conjug']
- conjug_color_name = conjugacy_class_to_color[conjug_letter]
- conjug_color = {
- 'white': 'ffffff', 'green': '33d42a', 'orange': 'ffa200',
- 'yellow': 'ffff7f', 'blue': '3375ff', 'red': 'ef2500'
- }[conjug_color_name]
- # permutation IDs (0..23, 0'..23')
- int24 = permdict['int'] % 24
- apostrophe = permdict['int'] >= 24
- bold = int24 in [0, 7, 16, 23]
- perm_id = str(int24) + apostrophe*"'"
- perm_id_circle_svg = '<circle cx="0" cy="0" r="18" stroke="black" stroke-width="%s" fill="#%s" />' \
- '<g style="text-anchor: middle;" font-family="sans-serif" font-size="16px" font-weight="%s">' \
- '<text x="0" y="6">%s</text></g>' \
- % ('3' if bold else '1.5', conjug_color, 'bold' if bold else 'normal', perm_id)
- # arrows
- arrows_svg = ''
- for i, p in enumerate(perm):
- if i != p:
- c1 = arrow_cube_coordinates[i]
- c2 = arrow_cube_coordinates[p]
- diff = np.array(c2) - np.array(c1)
- diff_length = np.sqrt(diff[0] ** 2 + diff[1] ** 2)
- diff_short = diff * .32 / diff_length # .32 is the approximate length of the arrow end before scaling by 30
- if perm[p] == i: # if this is a transposition, make one double arrow
- if i < p:
- c1_short = c1 + diff_short
- c2_short = c2 - diff_short
- coordinates = (
- round(c1_short[0], 3), round(c1_short[1], 3), round(c2_short[0], 3), round(c2_short[1], 3)
- )
- arrows_svg += '<g opacity=".7">' \
- '<line x1="%s" y1="%s" x2="%s" y2="%s" ' \
- 'marker-start="url(#backward)" marker-end="url(#foreward)" />' \
- '</g>' % coordinates
- else: # if no transposition
- c2_short = c2 - diff_short
- coordinates = (c1[0], c1[1], round(c2_short[0], 3), round(c2_short[1], 3))
- arrows_svg += '<g opacity=".7">' \
- '<line x1="%s" y1="%s" x2="%s" y2="%s" marker-end="url(#foreward)" />' \
- '</g>' % coordinates
- # permuted numbers
- perm_vector = '<text x="0" y="0">%s</text><text x="15" y="0">%s</text>' \
- '<text x="30" y="0">%s</text><text x="45" y="0">%s</text>' \
- '<text x="67" y="0">%s</text><text x="82" y="0">%s</text>' \
- '<text x="97" y="0">%s</text><text x="112" y="0">%s</text>' % perm
- invperm_vector = '<text x="0" y="0">%s</text><text x="24" y="0">%s</text>' \
- '<text x="48" y="0">%s</text><text x="72" y="0">%s</text>' \
- '<text x="96" y="0">%s</text><text x="120" y="0">%s</text>' \
- '<text x="144" y="0">%s</text><text x="168" y="0">%s</text>' % invperm
- invperm_cube = '<text x="0" y="90">%s</text><text x="0" y="30">%s</text>' \
- '<text x="30" y="60">%s</text><text x="30" y="0">%s</text>' \
- '<text x="60" y="90">%s</text><text x="60" y="30">%s</text>' \
- '<text x="90" y="60">%s</text><text x="90" y="0">%s</text>' % invperm
- # letters
- perm_letters = '<use xlink:href="#%s" transform="translate(0)"/>' \
- '<use xlink:href="#%s" transform="translate(28)"/>' \
- '<use xlink:href="#%s" transform="translate(56)"/>' % permdict['letters']
- invperm_letters = '<use xlink:href="#%s" transform="translate(0)"/>' \
- '<use xlink:href="#%s" transform="translate(28)"/>' \
- '<use xlink:href="#%s" transform="translate(56)"/>' % invpermdict['letters']
- # negators
- perm_negators = ''
- for i, d in enumerate(permdict['negators']):
- if d:
- perm_negators += '<rect x="%s" y="31" width="16" height="2.5"/>' % (101 + i * 28)
- invperm_negators = ''
- for i, d in enumerate(invpermdict['negators']):
- if d:
- invperm_negators += '<rect x="%s" y="31" width="16" height="2.5"/>' % (101 + i * 28)
- # formulas (letters with negators)
- perm_formula = formula_svg_store.format(letters=perm_letters, negators=perm_negators)
- invperm_formula = formula_svg_store.format(letters=invperm_letters, negators=invperm_negators)
- # SVG matrices
- perm_mat = perm_to_svg_path(perm)
- invperm_mat = perm_to_svg_path(invperm)
- # where to move the rectangle
- (rectx, recty) = (gray_cube_coordinates[rectnum][0] * 200, gray_cube_coordinates[rectnum][1] * 200)
- # append to ``rectangles_svg``
- rectangles_svg += rectangle_svg_store.format(rectx=rectx, recty=recty,
- idcircle=perm_id_circle_svg,
- pmat=perm_mat, ipmat=invperm_mat,
- pform=perm_formula, ipform=invperm_formula,
- arrows=arrows_svg,
- cubenums=invperm_cube, pvect=perm_vector, ipvect=invperm_vector,
- bottomgray=bottomgray, topgray=topgray, beige=rectbeige)
- # append to footer variables
- footer_perm_formulas += '<g transform="translate(0, {y}) scale(.8, .8)">{f}</g>'.format(y=rectnum*24, f=perm_formula)
- footer_perm_matrix += '<g transform="translate(0, {y})">{v}</g>'.format(y=rectnum*24, v=perm_vector)
- footer_invperm_formulas += '<g transform="translate(0, {y}) scale(.8, .8)">{f}</g>'.format(y=rectnum*24, f=invperm_formula)
- footer_invperm_matrix += '<g transform="translate(0, {y})">{v}</g>'.format(y=rectnum*24, v=invperm_vector)
- # create SVG
- svg_string = svg_string_store.format(
- rectangles=rectangles_svg,
- pf=footer_perm_formulas,
- pm=footer_perm_matrix,
- ipf=footer_invperm_formulas,
- ipm=footer_invperm_matrix,
- bottombeige=bottombeige,
- topbeige=topbeige
- )
- svg_file = open(filename, 'w')
- svg_file.write(svg_string)
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