def test_length(self):
# A straight line:
arc = CubicBezier(complex(0, 0), complex(0, 0), complex(0, 100),
complex(0, 100))
self.assertAlmostEqual(arc.length(), 100)
# A diagonal line:
arc = CubicBezier(complex(0, 0), complex(0, 0), complex(100, 100),
complex(100, 100))
self.assertAlmostEqual(arc.length(), sqrt(2 * 100 * 100))
# A quarter circle arc with radius 100:
kappa = 4 * (
sqrt(2) -
1) / 3 # http://www.whizkidtech.redprince.net/bezier/circle/
arc = CubicBezier(complex(0, 0), complex(0, kappa * 100),
complex(100 - kappa * 100, 100), complex(100, 100))
# We can't compare with pi*50 here, because this is just an
# approximation of a circle arc. pi*50 is 157.079632679
# So this is just yet another "warn if this changes" test.
# This value is not to be seens as verified as correct.
self.assertAlmostEqual(arc.length(), 157.1016698)
def test_length(self):
# A straight line:
arc = CubicBezier(
complex(0, 0),
complex(0, 0),
complex(0, 100),
complex(0, 100)
)
self.assertAlmostEqual(arc.length(), 100)
# A diagonal line:
arc = CubicBezier(
complex(0, 0),
complex(0, 0),
complex(100, 100),
complex(100, 100)
)
self.assertAlmostEqual(arc.length(), sqrt(2 * 100 * 100))
# A quarter circle arc with radius 100:
kappa = 4 * (sqrt(2) - 1) / 3 # http://www.whizkidtech.redprince.net/bezier/circle/
arc = CubicBezier(
complex(0, 0),
complex(0, kappa * 100),
complex(100 - kappa * 100, 100),
complex(100, 100)
)
# We can't compare with pi*50 here, because this is just an
# approximation of a circle arc. pi*50 is 157.079632679
# So this is just yet another "warn if this changes" test.
# This value is not verified to be correct.
self.assertAlmostEqual(arc.length(), 157.1016698)
# A recursive solution has also been suggested, but for CubicBezier
# curves it could get a false solution on curves where the midpoint is on a
# straight line between the start and end. For example, the following
# curve would get solved as a straight line and get the length 300.
# Make sure this is not the case.
arc = CubicBezier(
complex(600, 500),
complex(600, 350),
complex(900, 650),
complex(900, 500)
)
self.assertTrue(arc.length() > 300.0)