blob: d09efac43e0d706447b94a4febc34cdcb70a816e [file] [log] [blame]
 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)