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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, quiet=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] | |
| pen = StatisticsPen(glyphset=glyphset) | |
| transformer = TransformPen(pen, Scale(1.0 / upem)) | |
| glyph.draw(transformer) | |
| wght_sum += abs(pen.area) | |
| wght_sum_perceptual += abs(pen.area) * glyph.width | |
| wdth_sum += glyph.width | |
| slnt_sum += pen.slant | |
| slnt_sum_perceptual += pen.slant * glyph.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" % -math.degrees(math.atan(slant))) | |
| slant_perceptual = slnt_sum_perceptual / wdth_sum | |
| print("slant (perceptual): %g" % slant_perceptual) | |
| print("slant (perceptual) angle: %g" % -math.degrees(math.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( | |
| "-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, | |
| ) | |
| if __name__ == "__main__": | |
| import sys | |
| main(sys.argv[1:]) | |