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More solveCubic() hardening

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It really should be quite solid this time. :-)
This commit is contained in:
Behdad Esfahbod 2016-08-13 16:29:49 -07:00
parent 5bea5f4fd6
commit 8701fedcfe
1 changed files with 3 additions and 2 deletions
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5
Lib/fontTools/misc/bezierTools.py
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@ -342,8 +342,9 @@ def solveCubic(a, b, c, d):
if R2 == 0. and Q3 == 0.: if R2 == 0. and Q3 == 0.:
x = round(-a1/3.0, epsilonDigits) x = round(-a1/3.0, epsilonDigits)
return [x, x, x] return [x, x, x]
elif R2_Q3 <= epsilon: elif R2_Q3 <= epsilon * .5:
theta = acos(max(min(R/sqrt(Q*Q*Q), 1.0), -1.0)) # The epsilon * .5 above ensures that Q3 is not zero.
theta = acos(max(min(R/sqrt(Q3), 1.0), -1.0))
rQ2 = -2.0*sqrt(Q) rQ2 = -2.0*sqrt(Q)
a1_3 = a1/3.0 a1_3 = a1/3.0
x0 = rQ2*cos(theta/3.0) - a1_3 x0 = rQ2*cos(theta/3.0) - a1_3