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[bezier] Add cubicPointAtTC

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This commit is contained in:
Behdad Esfahbod 2023-02-13 14:19:45 -07:00
parent 16ee5ca195
commit 8dde7fef90
1 changed files with 26 additions and 0 deletions
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26
Lib/fontTools/misc/bezierTools.py
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@ -30,6 +30,7 @@ __all__ = [
"solveCubic",
"quadraticPointAtT",
"cubicPointAtT",
"cubicPointAtTC",
"linePointAtT",
"segmentPointAtT",
"lineLineIntersections",
@ -860,6 +861,31 @@ def cubicPointAtT(pt1, pt2, pt3, pt4, t):
return (x, y)
@cython.returns(cython.complex)
@cython.locals(
t=cython.double,
pt1=cython.complex,
pt2=cython.complex,
pt3=cython.complex,
pt4=cython.complex,
)
@cython.locals(t2=cython.double, t_1 = cython.double, t_1_2 = cython.double)
def cubicPointAtTC(pt1, pt2, pt3, pt4, t):
"""Finds the point at time `t` on a cubic curve.
Args:
pt1, pt2, pt3, pt4: Coordinates of the curve as complex numbers.
t: The time along the curve.
Returns:
A complex number with the coordinates of the point.
"""
t2 = t * t
t_1 = 1 - t
t_1_2 = t_1 * t_1
return t_1_2 * t_1 * pt1 + 3 * (t_1_2 * t * pt2 + t_1 * t2 * pt3) + t2 * t * pt4
def segmentPointAtT(seg, t):
if len(seg) == 2:
return linePointAtT(*seg, t)