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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:]) | |