"""Pen calculating area, center of mass, variance and standard-deviation,
covariance and correlation, and slant, of glyph shapes."""
from math import sqrt, degrees, atan
from fontTools.pens.basePen import BasePen, OpenContourError
from fontTools.pens.momentsPen import MomentsPen
__all__ = ["StatisticsPen", "StatisticsControlPen"]
class StatisticsBase:
def __init__(self):
self._zero()
def _zero(self):
self.area = 0
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):
# XXX The variance formulas should never produce a negative value,
# but due to reasons I don't understand, both of our pens do.
# So we take the absolute value here.
self.varianceX = abs(self.varianceX)
self.varianceY = abs(self.varianceY)
self.stddevX = stddevX = sqrt(self.varianceX)
self.stddevY = stddevY = sqrt(self.varianceY)
# 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:
# XXX The above formula should never produce a value outside
# the range [-1, 1], but due to reasons I don't understand,
# (probably the same issue as above), it does. So we clamp.
correlation = self.covariance / (stddevX * stddevY)
correlation = max(-1, min(1, correlation))
self.correlation = correlation if abs(correlation) > 1e-3 else 0
slant = (
self.covariance / self.varianceY if self.varianceY != 0 else float("NaN")
)
self.slant = slant if abs(slant) > 1e-3 else 0
[docs]
class StatisticsPen(StatisticsBase, MomentsPen):
"""Pen calculating area, center of mass, variance and
standard-deviation, covariance and correlation, and slant,
of glyph shapes.
Note that if the glyph shape is self-intersecting, the values
are not correct (but well-defined). Moreover, area will be
negative if contour directions are clockwise."""
def __init__(self, glyphset=None):
MomentsPen.__init__(self, glyphset=glyphset)
StatisticsBase.__init__(self)
def _closePath(self):
MomentsPen._closePath(self)
self._update()
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 = self.momentXX / area - meanX * meanX
self.varianceY = self.momentYY / area - meanY * meanY
# Covariance(X,Y) = (E[X.Y] - E[X]E[Y])
self.covariance = self.momentXY / area - meanX * meanY
StatisticsBase._update(self)
[docs]
class StatisticsControlPen(StatisticsBase, BasePen):
"""Pen calculating area, center of mass, variance and
standard-deviation, covariance and correlation, and slant,
of glyph shapes, using the control polygon only.
Note that if the glyph shape is self-intersecting, the values
are not correct (but well-defined). Moreover, area will be
negative if contour directions are clockwise."""
def __init__(self, glyphset=None):
BasePen.__init__(self, glyphset)
StatisticsBase.__init__(self)
self._nodes = []
def _moveTo(self, pt):
self._nodes.append(complex(*pt))
def _lineTo(self, pt):
self._nodes.append(complex(*pt))
def _qCurveToOne(self, pt1, pt2):
for pt in (pt1, pt2):
self._nodes.append(complex(*pt))
def _curveToOne(self, pt1, pt2, pt3):
for pt in (pt1, pt2, pt3):
self._nodes.append(complex(*pt))
def _closePath(self):
self._update()
def _endPath(self):
p0 = self._getCurrentPoint()
if p0 != self._startPoint:
raise OpenContourError("Glyph statistics not defined on open contours.")
def _update(self):
nodes = self._nodes
n = len(nodes)
# Triangle formula
self.area = (
sum(
(p0.real * p1.imag - p1.real * p0.imag)
for p0, p1 in zip(nodes, nodes[1:] + nodes[:1])
)
/ 2
)
# Center of mass
# https://en.wikipedia.org/wiki/Center_of_mass#A_system_of_particles
sumNodes = sum(nodes)
self.meanX = meanX = sumNodes.real / n
self.meanY = meanY = sumNodes.imag / n
if n > 1:
# Var(X) = (sum[X^2] - sum[X]^2 / n) / (n - 1)
# https://www.statisticshowto.com/probability-and-statistics/descriptive-statistics/sample-variance/
self.varianceX = varianceX = (
sum(p.real * p.real for p in nodes)
- (sumNodes.real * sumNodes.real) / n
) / (n - 1)
self.varianceY = varianceY = (
sum(p.imag * p.imag for p in nodes)
- (sumNodes.imag * sumNodes.imag) / n
) / (n - 1)
# Covariance(X,Y) = (sum[X.Y] - sum[X].sum[Y] / n) / (n - 1)
self.covariance = covariance = (
sum(p.real * p.imag for p in nodes)
- (sumNodes.real * sumNodes.imag) / n
) / (n - 1)
else:
self.varianceX = varianceX = 0
self.varianceY = varianceY = 0
self.covariance = covariance = 0
StatisticsBase._update(self)
def _test(glyphset, upem, glyphs, quiet=False, *, control=False):
from fontTools.pens.transformPen import TransformPen
from fontTools.misc.transform import Scale
wght_sum = 0
wght_sum_perceptual = 0
wdth_sum = 0
slnt_sum = 0
slnt_sum_perceptual = 0
for glyph_name in glyphs:
glyph = glyphset[glyph_name]
if control:
pen = StatisticsControlPen(glyphset=glyphset)
else:
pen = StatisticsPen(glyphset=glyphset)
transformer = TransformPen(pen, Scale(1.0 / upem))
glyph.draw(transformer)
area = abs(pen.area)
width = glyph.width
wght_sum += area
wght_sum_perceptual += pen.area * width
wdth_sum += width
slnt_sum += pen.slant
slnt_sum_perceptual += pen.slant * width
if quiet:
continue
print()
print("glyph:", glyph_name)
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)))
if not quiet:
print()
print("font:")
print("weight: %g" % (wght_sum * upem / wdth_sum))
print("weight (perceptual): %g" % (wght_sum_perceptual / wdth_sum))
print("width: %g" % (wdth_sum / upem / len(glyphs)))
slant = slnt_sum / len(glyphs)
print("slant: %g" % slant)
print("slant angle: %g" % -degrees(atan(slant)))
slant_perceptual = slnt_sum_perceptual / wdth_sum
print("slant (perceptual): %g" % slant_perceptual)
print("slant (perceptual) angle: %g" % -degrees(atan(slant_perceptual)))
def main(args):
"""Report font glyph shape geometricsl statistics"""
if args is None:
import sys
args = sys.argv[1:]
import argparse
parser = argparse.ArgumentParser(
"fonttools pens.statisticsPen",
description="Report font glyph shape geometricsl statistics",
)
parser.add_argument("font", metavar="font.ttf", help="Font file.")
parser.add_argument("glyphs", metavar="glyph-name", help="Glyph names.", nargs="*")
parser.add_argument(
"-y",
metavar="<number>",
help="Face index into a collection to open. Zero based.",
)
parser.add_argument(
"-c",
"--control",
action="store_true",
help="Use the control-box pen instead of the Green therem.",
)
parser.add_argument(
"-q", "--quiet", action="store_true", help="Only report font-wide statistics."
)
parser.add_argument(
"--variations",
metavar="AXIS=LOC",
default="",
help="List of space separated locations. A location consist in "
"the name of a variation axis, followed by '=' and a number. E.g.: "
"wght=700 wdth=80. The default is the location of the base master.",
)
options = parser.parse_args(args)
glyphs = options.glyphs
fontNumber = int(options.y) if options.y is not None else 0
location = {}
for tag_v in options.variations.split():
fields = tag_v.split("=")
tag = fields[0].strip()
v = int(fields[1])
location[tag] = v
from fontTools.ttLib import TTFont
font = TTFont(options.font, fontNumber=fontNumber)
if not glyphs:
glyphs = font.getGlyphOrder()
_test(
font.getGlyphSet(location=location),
font["head"].unitsPerEm,
glyphs,
quiet=options.quiet,
control=options.control,
)
if __name__ == "__main__":
import sys
main(sys.argv[1:])