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