/usr/lib/python3/dist-packages/fontTools/misc/symfont.py is in python3-fonttools 3.21.2-1.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 | from __future__ import print_function, division, absolute_import
from fontTools.misc.py23 import *
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):
print(
'''from __future__ import print_function, division, absolute_import
from fontTools.misc.py23 import *
from fontTools.pens.basePen import BasePen
class %s(BasePen):
def __init__(self, glyphset=None):
BasePen.__init__(self, glyphset)
'''%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 NotImplementedError
''', end='', file=file)
for n in (1, 2, 3):
if n == 1:
print('''
def _lineTo(self, p1):
x0,y0 = self._getCurrentPoint()
x1,y1 = p1
''', file=file)
elif n == 2:
print('''
def _qCurveToOne(self, p1, p2):
x0,y0 = self._getCurrentPoint()
x1,y1 = p1
x2,y2 = p2
''', file=file)
elif n == 3:
print('''
def _curveToOne(self, p1, p2, p3):
x0,y0 = self._getCurrentPoint()
x1,y1 = p1
x2,y2 = p2
x3,y3 = p3
''', file=file)
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()))
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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