# Source code for fontTools.misc.symfont

    from fontTools.pens.basePen import BasePen
    from functools import partial
    from itertools import count
    import sympy as sp
    import sys

    n = 3  # Max Bezier degree; 3 for cubic, 2 for quadratic

    t, x, y = sp.symbols("t x y", real=True)
    c = sp.symbols("c", real=False)  # Complex representation instead of x/y

    X = tuple(sp.symbols("x:%d" % (n + 1), real=True))
    Y = tuple(sp.symbols("y:%d" % (n + 1), real=True))
    P = tuple(zip(*(sp.symbols("p:%d[%s]" % (n + 1, w), real=True) for w in "01")))
    C = tuple(sp.symbols("c:%d" % (n + 1), real=False))

    # Cubic Bernstein basis functions
    BinomialCoefficient = [(1, 0)]
    for i in range(1, n + 1):
        last = BinomialCoefficient[-1]
        this = tuple(last[j - 1] + last[j] for j in range(len(last))) + (0,)
        BinomialCoefficient.append(this)
    BinomialCoefficient = tuple(tuple(item[:-1]) for item in BinomialCoefficient)
    del last, this

    BernsteinPolynomial = tuple(
        tuple(c * t**i * (1 - t) ** (n - i) for i, c in enumerate(coeffs))
        for n, coeffs in enumerate(BinomialCoefficient)
    )

    BezierCurve = tuple(
        tuple(
            sum(P[i][j] * bernstein for i, bernstein in enumerate(bernsteins))
            for j in range(2)
        )
        for n, bernsteins in enumerate(BernsteinPolynomial)
    )
    BezierCurveC = tuple(
        sum(C[i] * bernstein for i, bernstein in enumerate(bernsteins))
        for n, bernsteins in enumerate(BernsteinPolynomial)
    )

    def green(f, curveXY):
        f = -sp.integrate(sp.sympify(f), y)
        f = f.subs({x: curveXY[0], y: curveXY[1]})
        f = sp.integrate(f * sp.diff(curveXY[0], t), (t, 0, 1))
        return f

    class _BezierFuncsLazy(dict):
        def __init__(self, symfunc):
            self._symfunc = symfunc
            self._bezfuncs = {}

        def __missing__(self, i):
            args = ["p%d" % d for d in range(i + 1)]
            f = green(self._symfunc, BezierCurve[i])
            f = sp.gcd_terms(f.collect(sum(P, ())))  # Optimize
            return sp.lambdify(args, f)

    class GreenPen(BasePen):
        _BezierFuncs = {}

        @classmethod
        def _getGreenBezierFuncs(celf, func):
            funcstr = str(func)
            if not funcstr in celf._BezierFuncs:
                celf._BezierFuncs[funcstr] = _BezierFuncsLazy(func)
            return celf._BezierFuncs[funcstr]

        def __init__(self, func, glyphset=None):
            BasePen.__init__(self, glyphset)
            self._funcs = self._getGreenBezierFuncs(func)
            self.value = 0

        def _moveTo(self, p0):
            self._startPoint = p0

        def _closePath(self):
            p0 = self._getCurrentPoint()
            if p0 != self._startPoint:
                self._lineTo(self._startPoint)

        def _endPath(self):
            p0 = self._getCurrentPoint()
            if p0 != self._startPoint:
                # Green theorem is not defined on open contours.
                raise NotImplementedError

        def _lineTo(self, p1):
            p0 = self._getCurrentPoint()
            self.value += self._funcs[1](p0, p1)

        def _qCurveToOne(self, p1, p2):
            p0 = self._getCurrentPoint()
            self.value += self._funcs[2](p0, p1, p2)

        def _curveToOne(self, p1, p2, p3):
            p0 = self._getCurrentPoint()
            self.value += self._funcs[3](p0, p1, p2, p3)

    # Sample pens.
    # Do not use this in real code.
    # Use fontTools.pens.momentsPen.MomentsPen instead.
    AreaPen = partial(GreenPen, func=1)
    MomentXPen = partial(GreenPen, func=x)
    MomentYPen = partial(GreenPen, func=y)
    MomentXXPen = partial(GreenPen, func=x * x)
    MomentYYPen = partial(GreenPen, func=y * y)
    MomentXYPen = partial(GreenPen, func=x * y)

    def printGreenPen(penName, funcs, file=sys.stdout, docstring=None):
        if docstring is not None:
            print('"""%s"""' % docstring)

        print(
            """from fontTools.pens.basePen import BasePen, OpenContourError
    try:
    	import cython
    except (AttributeError, ImportError):
    	# if cython not installed, use mock module with no-op decorators and types
    	from fontTools.misc import cython
    COMPILED = cython.compiled

    __all__ = ["%s"]

    class %s(BasePen):

    	def __init__(self, glyphset=None):
    		BasePen.__init__(self, glyphset)
    """
            % (penName, penName),
            file=file,
        )
        for name, f in funcs:
            print("		self.%s = 0" % name, file=file)
        print(
            """
    	def _moveTo(self, p0):
    		self._startPoint = p0

    	def _closePath(self):
    		p0 = self._getCurrentPoint()
    		if p0 != self._startPoint:
    			self._lineTo(self._startPoint)

    	def _endPath(self):
    		p0 = self._getCurrentPoint()
    		if p0 != self._startPoint:
    			raise OpenContourError(
    							"Glyph statistics is not defined on open contours."
    			)
    """,
            end="",
            file=file,
        )

        for n in (1, 2, 3):
            subs = {P[i][j]: [X, Y][j][i] for i in range(n + 1) for j in range(2)}
            greens = [green(f, BezierCurve[n]) for name, f in funcs]
            greens = [sp.gcd_terms(f.collect(sum(P, ()))) for f in greens]  # Optimize
            greens = [f.subs(subs) for f in greens]  # Convert to p to x/y
            defs, exprs = sp.cse(
                greens,
                optimizations="basic",
                symbols=(sp.Symbol("r%d" % i) for i in count()),
            )

            print()
            for name, value in defs:
                print("	@cython.locals(%s=cython.double)" % name, file=file)
            if n == 1:
                print(
                    """\
    	@cython.locals(x0=cython.double, y0=cython.double)
    	@cython.locals(x1=cython.double, y1=cython.double)
    	def _lineTo(self, p1):
    		x0,y0 = self._getCurrentPoint()
    		x1,y1 = p1
    """,
                    file=file,
                )
            elif n == 2:
                print(
                    """\
    	@cython.locals(x0=cython.double, y0=cython.double)
    	@cython.locals(x1=cython.double, y1=cython.double)
    	@cython.locals(x2=cython.double, y2=cython.double)
    	def _qCurveToOne(self, p1, p2):
    		x0,y0 = self._getCurrentPoint()
    		x1,y1 = p1
    		x2,y2 = p2
    """,
                    file=file,
                )
            elif n == 3:
                print(
                    """\
    	@cython.locals(x0=cython.double, y0=cython.double)
    	@cython.locals(x1=cython.double, y1=cython.double)
    	@cython.locals(x2=cython.double, y2=cython.double)
    	@cython.locals(x3=cython.double, y3=cython.double)
    	def _curveToOne(self, p1, p2, p3):
    		x0,y0 = self._getCurrentPoint()
    		x1,y1 = p1
    		x2,y2 = p2
    		x3,y3 = p3
    """,
                    file=file,
                )
            for name, value in defs:
                print("		%s = %s" % (name, value), file=file)

            print(file=file)
            for name, value in zip([f[0] for f in funcs], exprs):
                print("		self.%s += %s" % (name, value), file=file)

        print(
            """
    if __name__ == '__main__':
    	from fontTools.misc.symfont import x, y, printGreenPen
    	printGreenPen('%s', ["""
            % penName,
            file=file,
        )
        for name, f in funcs:
            print("		      ('%s', %s)," % (name, str(f)), file=file)
        print("		     ])", file=file)

    if __name__ == "__main__":
        pen = AreaPen()
        pen.moveTo((100, 100))
        pen.lineTo((100, 200))
        pen.lineTo((200, 200))
        pen.curveTo((200, 250), (300, 300), (250, 350))
        pen.lineTo((200, 100))
        pen.closePath()
        print(pen.value)