249 lines
6.9 KiB
Python
249 lines
6.9 KiB
Python
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from fontTools.pens.basePen import BasePen
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from functools import partial
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from itertools import count
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import sympy as sp
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import sys
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n = 3 # Max Bezier degree; 3 for cubic, 2 for quadratic
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t, x, y = sp.symbols("t x y", real=True)
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c = sp.symbols("c", real=False) # Complex representation instead of x/y
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X = tuple(sp.symbols("x:%d" % (n + 1), real=True))
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Y = tuple(sp.symbols("y:%d" % (n + 1), real=True))
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P = tuple(zip(*(sp.symbols("p:%d[%s]" % (n + 1, w), real=True) for w in "01")))
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C = tuple(sp.symbols("c:%d" % (n + 1), real=False))
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# Cubic Bernstein basis functions
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BinomialCoefficient = [(1, 0)]
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for i in range(1, n + 1):
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last = BinomialCoefficient[-1]
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this = tuple(last[j - 1] + last[j] for j in range(len(last))) + (0,)
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BinomialCoefficient.append(this)
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BinomialCoefficient = tuple(tuple(item[:-1]) for item in BinomialCoefficient)
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del last, this
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BernsteinPolynomial = tuple(
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tuple(c * t**i * (1 - t) ** (n - i) for i, c in enumerate(coeffs))
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for n, coeffs in enumerate(BinomialCoefficient)
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)
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BezierCurve = tuple(
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tuple(
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sum(P[i][j] * bernstein for i, bernstein in enumerate(bernsteins))
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for j in range(2)
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)
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for n, bernsteins in enumerate(BernsteinPolynomial)
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)
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BezierCurveC = tuple(
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sum(C[i] * bernstein for i, bernstein in enumerate(bernsteins))
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for n, bernsteins in enumerate(BernsteinPolynomial)
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)
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def green(f, curveXY):
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f = -sp.integrate(sp.sympify(f), y)
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f = f.subs({x: curveXY[0], y: curveXY[1]})
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f = sp.integrate(f * sp.diff(curveXY[0], t), (t, 0, 1))
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return f
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class _BezierFuncsLazy(dict):
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def __init__(self, symfunc):
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self._symfunc = symfunc
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self._bezfuncs = {}
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def __missing__(self, i):
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args = ["p%d" % d for d in range(i + 1)]
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f = green(self._symfunc, BezierCurve[i])
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f = sp.gcd_terms(f.collect(sum(P, ()))) # Optimize
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return sp.lambdify(args, f)
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class GreenPen(BasePen):
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_BezierFuncs = {}
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@classmethod
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def _getGreenBezierFuncs(celf, func):
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funcstr = str(func)
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if not funcstr in celf._BezierFuncs:
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celf._BezierFuncs[funcstr] = _BezierFuncsLazy(func)
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return celf._BezierFuncs[funcstr]
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def __init__(self, func, glyphset=None):
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BasePen.__init__(self, glyphset)
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self._funcs = self._getGreenBezierFuncs(func)
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self.value = 0
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def _moveTo(self, p0):
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self.__startPoint = p0
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def _closePath(self):
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p0 = self._getCurrentPoint()
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if p0 != self.__startPoint:
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self._lineTo(self.__startPoint)
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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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# Green theorem is not defined on open contours.
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raise NotImplementedError
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def _lineTo(self, p1):
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p0 = self._getCurrentPoint()
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self.value += self._funcs[1](p0, p1)
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def _qCurveToOne(self, p1, p2):
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p0 = self._getCurrentPoint()
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self.value += self._funcs[2](p0, p1, p2)
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def _curveToOne(self, p1, p2, p3):
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p0 = self._getCurrentPoint()
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self.value += self._funcs[3](p0, p1, p2, p3)
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# Sample pens.
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# Do not use this in real code.
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# Use fontTools.pens.momentsPen.MomentsPen instead.
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AreaPen = partial(GreenPen, func=1)
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MomentXPen = partial(GreenPen, func=x)
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MomentYPen = partial(GreenPen, func=y)
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MomentXXPen = partial(GreenPen, func=x * x)
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MomentYYPen = partial(GreenPen, func=y * y)
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MomentXYPen = partial(GreenPen, func=x * y)
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def printGreenPen(penName, funcs, file=sys.stdout, docstring=None):
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if docstring is not None:
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print('"""%s"""' % docstring)
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print(
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"""from fontTools.pens.basePen import BasePen, OpenContourError
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try:
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import cython
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COMPILED = cython.compiled
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except (AttributeError, ImportError):
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# if cython not installed, use mock module with no-op decorators and types
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from fontTools.misc import cython
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COMPILED = False
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__all__ = ["%s"]
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class %s(BasePen):
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def __init__(self, glyphset=None):
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BasePen.__init__(self, glyphset)
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"""
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% (penName, penName),
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file=file,
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)
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for name, f in funcs:
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print(" self.%s = 0" % name, file=file)
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print(
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"""
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def _moveTo(self, p0):
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self.__startPoint = p0
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def _closePath(self):
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p0 = self._getCurrentPoint()
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if p0 != self.__startPoint:
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self._lineTo(self.__startPoint)
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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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# Green theorem is not defined on open contours.
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raise OpenContourError(
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"Green theorem is not defined on open contours."
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)
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""",
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end="",
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file=file,
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)
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for n in (1, 2, 3):
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subs = {P[i][j]: [X, Y][j][i] for i in range(n + 1) for j in range(2)}
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greens = [green(f, BezierCurve[n]) for name, f in funcs]
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greens = [sp.gcd_terms(f.collect(sum(P, ()))) for f in greens] # Optimize
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greens = [f.subs(subs) for f in greens] # Convert to p to x/y
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defs, exprs = sp.cse(
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greens,
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optimizations="basic",
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symbols=(sp.Symbol("r%d" % i) for i in count()),
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)
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print()
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for name, value in defs:
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print(" @cython.locals(%s=cython.double)" % name, file=file)
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if n == 1:
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print(
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"""\
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@cython.locals(x0=cython.double, y0=cython.double)
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@cython.locals(x1=cython.double, y1=cython.double)
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def _lineTo(self, p1):
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x0,y0 = self._getCurrentPoint()
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x1,y1 = p1
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""",
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file=file,
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)
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elif n == 2:
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print(
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"""\
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@cython.locals(x0=cython.double, y0=cython.double)
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@cython.locals(x1=cython.double, y1=cython.double)
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@cython.locals(x2=cython.double, y2=cython.double)
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def _qCurveToOne(self, p1, p2):
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x0,y0 = self._getCurrentPoint()
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x1,y1 = p1
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x2,y2 = p2
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""",
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file=file,
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)
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elif n == 3:
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print(
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"""\
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@cython.locals(x0=cython.double, y0=cython.double)
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@cython.locals(x1=cython.double, y1=cython.double)
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@cython.locals(x2=cython.double, y2=cython.double)
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@cython.locals(x3=cython.double, y3=cython.double)
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def _curveToOne(self, p1, p2, p3):
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x0,y0 = self._getCurrentPoint()
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x1,y1 = p1
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x2,y2 = p2
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x3,y3 = p3
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""",
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file=file,
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)
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for name, value in defs:
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print(" %s = %s" % (name, value), file=file)
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print(file=file)
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for name, value in zip([f[0] for f in funcs], exprs):
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print(" self.%s += %s" % (name, value), file=file)
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print(
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"""
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if __name__ == '__main__':
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from fontTools.misc.symfont import x, y, printGreenPen
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printGreenPen('%s', ["""
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% penName,
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file=file,
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)
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for name, f in funcs:
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print(" ('%s', %s)," % (name, str(f)), file=file)
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print(" ])", file=file)
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if __name__ == "__main__":
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pen = AreaPen()
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pen.moveTo((100, 100))
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pen.lineTo((100, 200))
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pen.lineTo((200, 200))
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pen.curveTo((200, 250), (300, 300), (250, 350))
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pen.lineTo((200, 100))
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pen.closePath()
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print(pen.value)
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