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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
COMPILED = cython.compiled
except (AttributeError, ImportError):
# if cython not installed, use mock module with no-op decorators and types
from fontTools.misc import cython
COMPILED = False
__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:
# Green theorem is not defined on open contours.
raise OpenContourError(
"Green theorem 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)
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