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"""Pen calculating area, center of mass, variance and standard-deviation,
covariance and correlation, and slant, of glyph shapes."""
import math
from fontTools.pens.momentsPen import MomentsPen
__all__ = ["StatisticsPen"]
class StatisticsPen(MomentsPen):
"""Pen calculating area, center of mass, variance and
standard-deviation, covariance and correlation, and slant,
of glyph shapes.
Note that all the calculated values are 'signed'. Ie. if the
glyph shape is self-intersecting, the values are not correct
(but well-defined). As such, area will be negative if contour
directions are clockwise. Moreover, variance might be negative
if the shapes are self-intersecting in certain ways."""
def __init__(self, glyphset=None):
MomentsPen.__init__(self, glyphset=glyphset)
self.__zero()
def _closePath(self):
MomentsPen._closePath(self)
self.__update()
def __zero(self):
self.meanX = 0
self.meanY = 0
self.varianceX = 0
self.varianceY = 0
self.stddevX = 0
self.stddevY = 0
self.covariance = 0
self.correlation = 0
self.slant = 0
def __update(self):
area = self.area
if not area:
self.__zero()
return
# Center of mass
# https://en.wikipedia.org/wiki/Center_of_mass#A_continuous_volume
self.meanX = meanX = self.momentX / area
self.meanY = meanY = self.momentY / area
# Var(X) = E[X^2] - E[X]^2
self.varianceX = varianceX = self.momentXX / area - meanX**2
self.varianceY = varianceY = self.momentYY / area - meanY**2
self.stddevX = stddevX = math.copysign(abs(varianceX) ** 0.5, varianceX)
self.stddevY = stddevY = math.copysign(abs(varianceY) ** 0.5, varianceY)
# Covariance(X,Y) = ( E[X.Y] - E[X]E[Y] )
self.covariance = covariance = self.momentXY / area - meanX * meanY
# Correlation(X,Y) = Covariance(X,Y) / ( stddev(X) * stddev(Y) )
# https://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient
if stddevX * stddevY == 0:
correlation = float("NaN")
else:
correlation = covariance / (stddevX * stddevY)
self.correlation = correlation if abs(correlation) > 1e-3 else 0
slant = covariance / varianceY if varianceY != 0 else float("NaN")
self.slant = slant if abs(slant) > 1e-3 else 0
def _test(glyphset, upem, glyphs):
from fontTools.pens.transformPen import TransformPen
from fontTools.misc.transform import Scale
print("upem", upem)
for glyph_name in glyphs:
print()
print("glyph:", glyph_name)
glyph = glyphset[glyph_name]
pen = StatisticsPen(glyphset=glyphset)
transformer = TransformPen(pen, Scale(1.0 / upem))
glyph.draw(transformer)
for item in [
"area",
"momentX",
"momentY",
"momentXX",
"momentYY",
"momentXY",
"meanX",
"meanY",
"varianceX",
"varianceY",
"stddevX",
"stddevY",
"covariance",
"correlation",
"slant",
]:
print("%s: %g" % (item, getattr(pen, item)))
def main(args):
if not args:
return
filename, glyphs = args[0], args[1:]
from fontTools.ttLib import TTFont
font = TTFont(filename)
if not glyphs:
glyphs = font.getGlyphOrder()
_test(font.getGlyphSet(), font["head"].unitsPerEm, glyphs)
if __name__ == "__main__":
import sys
main(sys.argv[1:])
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