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[symfont] Minor

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This commit is contained in:
Behdad Esfahbod 2017-02-19 13:55:46 -06:00
parent 5f82438206
commit 8869a5b343
1 changed files with 14 additions and 7 deletions
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21
Snippets/symfont.py
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@ -23,8 +23,10 @@ from itertools import count
n = 3 # Max Bezier degree; 3 for cubic, 2 for quadratic n = 3 # Max Bezier degree; 3 for cubic, 2 for quadratic
t, x, y = sp.symbols('t x y', real=True) t, x, y = sp.symbols('t x y', real=True)
c = sp.symbols('c', real=False) # Complex representation instead of x/y
P = tuple(zip(*(sp.symbols('%s:%d'%(w,n+1), real=True) for w in 'xy'))) P = tuple(zip(*(sp.symbols('%s:%d'%(w,n+1), real=True) for w in 'xy')))
C = tuple(sp.symbols('c:%d'%(n+1), real=False))
# Cubic Bernstein basis functions # Cubic Bernstein basis functions
BinomialCoefficient = [(1, 0)] BinomialCoefficient = [(1, 0)]
@ -33,6 +35,7 @@ for i in range(1, n+1):
this = tuple(last[j-1]+last[j] for j in range(len(last)))+(0,) this = tuple(last[j-1]+last[j] for j in range(len(last)))+(0,)
BinomialCoefficient.append(this) BinomialCoefficient.append(this)
BinomialCoefficient = tuple(tuple(item[:-1]) for item in BinomialCoefficient) BinomialCoefficient = tuple(tuple(item[:-1]) for item in BinomialCoefficient)
del last, this
BernsteinPolynomial = tuple( BernsteinPolynomial = tuple(
tuple(c * t**i * (1-t)**(n-i) for i,c in enumerate(coeffs)) tuple(c * t**i * (1-t)**(n-i) for i,c in enumerate(coeffs))
@ -42,12 +45,16 @@ BezierCurve = tuple(
tuple(sum(P[i][j]*bernstein for i,bernstein in enumerate(bernsteins)) tuple(sum(P[i][j]*bernstein for i,bernstein in enumerate(bernsteins))
for j in range(2)) for j in range(2))
for n,bernsteins in enumerate(BernsteinPolynomial)) 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, Bezier=BezierCurve[n]): def green(f, curveXY, optimize=True):
f = -sp.integrate(sp.sympify(f), y) f = -sp.integrate(sp.sympify(f), y)
f = f.subs({x:Bezier[0], y:Bezier[1]}) f = f.subs({x:curveXY[0], y:curveXY[1]})
f = sp.integrate(f * sp.diff(Bezier[0], t), (t, 0, 1)) f = sp.integrate(f * sp.diff(curveXY[0], t), (t, 0, 1))
f = sp.gcd_terms(f.collect(sum(P,()))) # Optimize a bit if optimize:
f = sp.gcd_terms(f.collect(sum(P,())))
return f return f
class BezierFuncs(object): class BezierFuncs(object):
@ -62,7 +69,7 @@ class BezierFuncs(object):
for d in range(i+1): for d in range(i+1):
args.append('x%d' % d) args.append('x%d' % d)
args.append('y%d' % d) args.append('y%d' % d)
self._bezfuncs[i] = sp.lambdify(args, green(self._symfunc, Bezier=BezierCurve[i])) self._bezfuncs[i] = sp.lambdify(args, green(self._symfunc, BezierCurve[i]))
return self._bezfuncs[i] return self._bezfuncs[i]
_BezierFuncs = {} _BezierFuncs = {}
@ -78,7 +85,7 @@ def printCache(func):
funcstr = str(func) funcstr = str(func)
print("_BezierFuncs['%s'] = [" % funcstr) print("_BezierFuncs['%s'] = [" % funcstr)
for i in range(n+1): for i in range(n+1):
print(' lambda P:', green(func, Bezier=BezierCurve[i]), ',') print(' lambda P:', green(func, BezierCurve[i]), ',')
print(']') print(']')
def printPen(name, funcs): def printPen(name, funcs):
@ -128,7 +135,7 @@ class {name}(BasePen):
x2,y2 = p2 x2,y2 = p2
x3,y3 = p3 x3,y3 = p3
''') ''')
defs, exprs = sp.cse([green(f,Bezier=BezierCurve[n]) for name,f in funcs], defs, exprs = sp.cse([green(f, BezierCurve[n]) for name,f in funcs],
optimizations='basic', optimizations='basic',
symbols=(sp.Symbol('r%d'%i) for i in count())) symbols=(sp.Symbol('r%d'%i) for i in count()))
for name,value in defs: for name,value in defs: