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Refactored splitting logic; added splitQuadraticAtT() and splitCubicAtT()

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git-svn-id: svn://svn.code.sf.net/p/fonttools/code/trunk@492 4cde692c-a291-49d1-8350-778aa11640f8
This commit is contained in:
jvr 2005-02-25 12:28:45 +00:00
parent 0ec07f2dbc
commit 10de259aec
1 changed files with 57 additions and 24 deletions
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79
Lib/fontTools/misc/bezierTools.py
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@ -1,9 +1,12 @@
"""fontTools.misc.bezierTools.py -- tools for working with bezier path segments.""" """fontTools.misc.bezierTools.py -- tools for working with bezier path segments."""
__all__ = ["calcQuadraticBounds", "calcCubicBounds", "splitLine", "splitQuadratic", __all__ = [
"splitCubic", "solveQuadratic", "solveCubic"] "calcQuadraticBounds", "calcCubicBounds",
"splitLine", "splitQuadratic", "splitCubic",
"splitQuadraticAtT", "splitCubicAtT",
"solveQuadratic", "solveCubic",
]
from fontTools.misc.arrayTools import calcBounds from fontTools.misc.arrayTools import calcBounds
import Numeric import Numeric
@ -109,21 +112,7 @@ def splitQuadratic(pt1, pt2, pt3, where, isHorizontal):
solutions.sort() solutions.sort()
if not solutions: if not solutions:
return [(pt1, pt2, pt3)] return [(pt1, pt2, pt3)]
return _splitQuadraticAtT(a, b, c, *solutions)
segments = []
solutions.insert(0, 0.0)
solutions.append(1.0)
for i in range(len(solutions) - 1):
t1 = solutions[i]
t2 = solutions[i+1]
delta = (t2 - t1)
# calc new a, b and c
a1 = a * delta**2
b1 = (2*a*t1 + b) * delta
c1 = a*t1**2 + b*t1 + c
pt1, pt2, pt3 = calcQuadraticPoints(a1, b1, c1)
segments.append((pt1, pt2, pt3))
return segments
def splitCubic(pt1, pt2, pt3, pt4, where, isHorizontal): def splitCubic(pt1, pt2, pt3, pt4, where, isHorizontal):
@ -145,13 +134,57 @@ def splitCubic(pt1, pt2, pt3, pt4, where, isHorizontal):
solutions.sort() solutions.sort()
if not solutions: if not solutions:
return [(pt1, pt2, pt3, pt4)] return [(pt1, pt2, pt3, pt4)]
return _splitCubicAtT(a, b, c, d, *solutions)
def splitQuadraticAtT(pt1, pt2, pt3, *ts):
"""
>>> _testrepr(splitQuadraticAtT((0, 0), (50, 100), (100, 0), 0.5))
'(((0.0, 0.0), (25.0, 50.0), (50.0, 50.0)), ((50.0, 50.0), (75.0, 50.0), (100.0, 0.0)))'
>>> _testrepr(splitQuadraticAtT((0, 0), (50, 100), (100, 0), 0.5, 0.75))
'(((0.0, 0.0), (25.0, 50.0), (50.0, 50.0)), ((50.0, 50.0), (62.5, 50.0), (75.0, 37.5)), ((75.0, 37.5), (87.5, 25.0), (100.0, 0.0)))'
"""
a, b, c = calcQuadraticParameters(pt1, pt2, pt3)
return _splitQuadraticAtT(a, b, c, *ts)
def splitCubicAtT(pt1, pt2, pt3, pt4, *ts):
"""
>>> _testrepr(splitCubicAtT((0, 0), (25, 100), (75, 100), (100, 0), 0.5))
'(((0.0, 0.0), (12.5, 50.0), (31.25, 75.0), (50.0, 75.0)), ((50.0, 75.0), (68.75, 75.0), (87.5, 50.0), (100.0, 0.0)))'
>>> _testrepr(splitCubicAtT((0, 0), (25, 100), (75, 100), (100, 0), 0.5, 0.75))
'(((0.0, 0.0), (12.5, 50.0), (31.25, 75.0), (50.0, 75.0)), ((50.0, 75.0), (59.375, 75.0), (68.75, 68.75), (77.34375, 56.25)), ((77.34375, 56.25), (85.9375, 43.75), (93.75, 25.0), (100.0, 0.0)))'
"""
a, b, c, d = calcCubicParameters(pt1, pt2, pt3, pt4)
return _splitCubicAtT(a, b, c, d, *ts)
def _splitQuadraticAtT(a, b, c, *ts):
ts = list(ts)
segments = [] segments = []
solutions.insert(0, 0.0) ts.insert(0, 0.0)
solutions.append(1.0) ts.append(1.0)
for i in range(len(solutions) - 1): for i in range(len(ts) - 1):
t1 = solutions[i] t1 = ts[i]
t2 = solutions[i+1] t2 = ts[i+1]
delta = (t2 - t1)
# calc new a, b and c
a1 = a * delta**2
b1 = (2*a*t1 + b) * delta
c1 = a*t1**2 + b*t1 + c
pt1, pt2, pt3 = calcQuadraticPoints(a1, b1, c1)
segments.append((pt1, pt2, pt3))
return segments
def _splitCubicAtT(a, b, c, d, *ts):
ts = list(ts)
ts.insert(0, 0.0)
ts.append(1.0)
segments = []
for i in range(len(ts) - 1):
t1 = ts[i]
t2 = ts[i+1]
delta = (t2 - t1) delta = (t2 - t1)
# calc new a, b, c and d # calc new a, b, c and d
a1 = a * delta**3 a1 = a * delta**3