123 lines
3.6 KiB
Python
123 lines
3.6 KiB
Python
"""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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import math
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from fontTools.pens.momentsPen import MomentsPen
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__all__ = ["StatisticsPen"]
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class StatisticsPen(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 all the calculated values are 'signed'. Ie. if the
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glyph shape is self-intersecting, the values are not correct
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(but well-defined). As such, area will be negative if contour
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directions are clockwise. Moreover, variance might be negative
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if the shapes are self-intersecting in certain ways."""
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def __init__(self, glyphset=None):
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MomentsPen.__init__(self, glyphset=glyphset)
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self.__zero()
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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 __zero(self):
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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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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 = varianceX = self.momentXX / area - meanX**2
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self.varianceY = varianceY = self.momentYY / area - meanY**2
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self.stddevX = stddevX = math.copysign(abs(varianceX) ** 0.5, varianceX)
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self.stddevY = stddevY = math.copysign(abs(varianceY) ** 0.5, varianceY)
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# Covariance(X,Y) = ( E[X.Y] - E[X]E[Y] )
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self.covariance = covariance = self.momentXY / area - meanX * meanY
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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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correlation = covariance / (stddevX * stddevY)
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self.correlation = correlation if abs(correlation) > 1e-3 else 0
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slant = covariance / varianceY if varianceY != 0 else float("NaN")
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self.slant = slant if abs(slant) > 1e-3 else 0
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def _test(glyphset, upem, glyphs):
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from fontTools.pens.transformPen import TransformPen
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from fontTools.misc.transform import Scale
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print("upem", upem)
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for glyph_name in glyphs:
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print()
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print("glyph:", glyph_name)
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glyph = glyphset[glyph_name]
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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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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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def main(args):
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if not args:
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return
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filename, glyphs = args[0], args[1:]
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from fontTools.ttLib import TTFont
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font = TTFont(filename)
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if not glyphs:
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glyphs = font.getGlyphOrder()
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_test(font.getGlyphSet(), font["head"].unitsPerEm, glyphs)
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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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