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[bezier] Add a few more complex versions of functions

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This commit is contained in:
Behdad Esfahbod 2023-02-14 00:54:54 -07:00
parent 83398db061
commit c4e3322b20
1 changed files with 98 additions and 0 deletions
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98
Lib/fontTools/misc/bezierTools.py
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@ -33,6 +33,7 @@ __all__ = [
"splitCubic",
"splitQuadraticAtT",
"splitCubicAtT",
"splitCubicAtTC",
"splitCubicIntoTwoAtTC",
"solveQuadratic",
"solveCubic",
@ -636,6 +637,30 @@ def splitCubicAtT(pt1, pt2, pt3, pt4, *ts):
return _splitCubicAtT(a, b, c, d, *ts)
@cython.locals(
pt1=cython.complex,
pt2=cython.complex,
pt3=cython.complex,
pt4=cython.complex,
a=cython.complex,
b=cython.complex,
c=cython.complex,
d=cython.complex,
)
def splitCubicAtTC(pt1, pt2, pt3, pt4, *ts):
"""Split a cubic Bezier curve at one or more values of t.
Args:
pt1,pt2,pt3,pt4: Control points of the Bezier as complex numbers..
*ts: Positions at which to split the curve.
Returns:
A list of curve segments (each curve segment being four complex numbers).
"""
a, b, c, d = calcCubicParametersC(pt1, pt2, pt3, pt4)
return _splitCubicAtTC(a, b, c, d, *ts)
@cython.returns(cython.complex)
@cython.locals(
t=cython.double,
@ -738,6 +763,46 @@ def _splitCubicAtT(a, b, c, d, *ts):
return segments
@cython.locals(
a=cython.complex,
b=cython.complex,
c=cython.complex,
d=cython.complex,
t1=cython.double,
t2=cython.double,
delta=cython.double,
delta_2=cython.double,
delta_3=cython.double,
a1=cython.complex,
b1=cython.complex,
c1=cython.complex,
d1=cython.complex,
)
def _splitCubicAtTC(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_2 = delta * delta
delta_3 = delta * delta_2
t1_2 = t1 * t1
t1_3 = t1 * t1_2
# calc new a, b, c and d
a1 = a * delta_3
b1 = (3 * a * t1 + b) * delta_2
c1 = (2 * b * t1 + c + 3 * a * t1_2) * delta
d1 = a * t1_3 + b * t1_2 + c * t1 + d
pt1, pt2, pt3, pt4 = calcCubicPointsC(a1, b1, c1, d1)
segments.append((pt1, pt2, pt3, pt4))
return segments
#
# Equation solvers.
#
@ -900,6 +965,22 @@ def calcCubicParameters(pt1, pt2, pt3, pt4):
return (ax, ay), (bx, by), (cx, cy), (dx, dy)
@cython.locals(
pt1=cython.complex,
pt2=cython.complex,
pt3=cython.complex,
pt4=cython.complex,
a=cython.complex,
b=cython.complex,
c=cython.complex,
)
def calcCubicParametersC(pt1, pt2, pt3, pt4):
c = (pt2 - pt1) * 3.0
b = (pt3 - pt2) * 3.0 - c
a = pt4 - pt1 - c - b
return (a, b, c, pt1)
def calcQuadraticPoints(a, b, c):
ax, ay = a
bx, by = b
@ -929,6 +1010,23 @@ def calcCubicPoints(a, b, c, d):
return (x1, y1), (x2, y2), (x3, y3), (x4, y4)
@cython.locals(
a=cython.complex,
b=cython.complex,
c=cython.complex,
d=cython.complex,
p2=cython.complex,
p3=cython.complex,
p4=cython.complex,
_1_3=cython.double,
)
def calcCubicPointsC(a, b, c, d, _1_3=1.0 / 3):
p2 = (c * _1_3) + d
p3 = (b + c) * _1_3 + p2
p4 = a + b + c + d
return (d, p2, p3, p4)
#
# Point at time
#