def lightness_scale(steps: Integer) -> NDArray:
"""
Create a non-linear lightness scale, as described in *Jakob and Hanika
(2019)*. The spacing between very dark and very bright (and saturated)
colours is made smaller, because in those regions coefficients tend to
change rapidly and a finer resolution is needed.
Parameters
----------
steps
Samples/steps count along the non-linear lightness scale.
Returns
-------
:class:`numpy.ndarray`
Non-linear lightness scale.
Examples
--------
>>> lightness_scale(5) # doctest: +ELLIPSIS
array([ 0. , 0.0656127..., 0.5 , 0.9343872..., \
1. ])
"""
linear = np.linspace(0, 1, steps)
return smoothstep_function(smoothstep_function(linear))
def test_smoothstep_function(self):
"""Test :func:`colour.algebra.common.smoothstep_function` definition."""
self.assertEqual(smoothstep_function(0.5), 0.5)
self.assertEqual(smoothstep_function(0.25), 0.15625)
self.assertEqual(smoothstep_function(0.75), 0.84375)
x = np.linspace(-2, 2, 5)
np.testing.assert_almost_equal(
smoothstep_function(x),
np.array([28.00000, 5.00000, 0.00000, 1.00000, -4.00000]),
)
np.testing.assert_almost_equal(
smoothstep_function(x, -2, 2, clip=True),
np.array([0.00000, 0.15625, 0.50000, 0.84375, 1.00000]),
)