"""
Rösch-MacAdam colour solid - Visible Spectrum Volume Computations
=================================================================
Defines the objects related to *Rösch-MacAdam* colour solid, visible spectrum
volume computations.
References
----------
- :cite:`Lindbloom2015` : Lindbloom, B. (2015). About the Lab Gamut.
Retrieved August 20, 2018, from
http://www.brucelindbloom.com/LabGamutDisplayHelp.html
- :cite:`Mansencal2018` : Mansencal, T. (2018). How is the visible gamut
bounded? Retrieved August 19, 2018, from
https://stackoverflow.com/a/48396021/931625
- :cite:`Martinez-Verdu2007` : Martínez-Verdú, F., Perales, E., Chorro, E.,
de Fez, D., Viqueira, V., & Gilabert, E. (2007). Computation and
visualization of the MacAdam limits for any lightness, hue angle, and light
source. Journal of the Optical Society of America A, 24(6), 1501.
doi:10.1364/JOSAA.24.001501
"""
from __future__ import annotations
import numpy as np
from colour.colorimetry import (
MultiSpectralDistributions,
SpectralDistribution,
SpectralShape,
handle_spectral_arguments,
msds_to_XYZ,
)
from colour.constants import DEFAULT_FLOAT_DTYPE
from colour.hints import (
Any,
ArrayLike,
Boolean,
Dict,
Floating,
Integer,
Literal,
NDArray,
Optional,
Union,
)
from colour.volume import is_within_mesh_volume
from colour.utilities import CACHE_REGISTRY, zeros, validate_method
__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 Colour Developers"
__license__ = "New BSD License - https://opensource.org/licenses/BSD-3-Clause"
__maintainer__ = "Colour Developers"
__email__ = "colour-developers@colour-science.org"
__status__ = "Production"
__all__ = [
"SPECTRAL_SHAPE_OUTER_SURFACE_XYZ",
"generate_pulse_waves",
"XYZ_outer_surface",
"solid_RoschMacAdam",
"is_within_visible_spectrum",
]
SPECTRAL_SHAPE_OUTER_SURFACE_XYZ: SpectralShape = SpectralShape(360, 780, 5)
"""
Default spectral shape according to *ASTM E308-15* practise shape but using an
interval of 5.
"""
_CACHE_OUTER_SURFACE_XYZ: Dict = CACHE_REGISTRY.register_cache(
f"{__name__}._CACHE_OUTER_SURFACE_XYZ"
)
_CACHE_OUTER_SURFACE_XYZ_POINTS: Dict = CACHE_REGISTRY.register_cache(
f"{__name__}._CACHE_OUTER_SURFACE_XYZ_POINTS"
)
[docs]def generate_pulse_waves(
bins: Integer,
pulse_order: Union[Literal["Bins", "Pulse Wave Width"], str] = "Bins",
filter_jagged_pulses: Boolean = False,
) -> NDArray:
"""
Generate the pulse waves of given number of bins necessary to totally
stimulate the colour matching functions and produce the *Rösch-MacAdam*
colour solid.
Assuming 5 bins, a first set of SPDs would be as follows::
1 0 0 0 0
0 1 0 0 0
0 0 1 0 0
0 0 0 1 0
0 0 0 0 1
The second one::
1 1 0 0 0
0 1 1 0 0
0 0 1 1 0
0 0 0 1 1
1 0 0 0 1
The third:
1 1 1 0 0
0 1 1 1 0
0 0 1 1 1
1 0 0 1 1
1 1 0 0 1
Etc...
Parameters
----------
bins
Number of bins of the pulse waves.
pulse_order
Method for ordering the pulse waves. *Bins* is the default order, with
*Pulse Wave Width* ordering, instead of iterating over the pulse wave
widths first, iteration occurs over the bins, producing blocks of pulse
waves with increasing width.
filter_jagged_pulses
Whether to filter jagged pulses. When ``pulse_order`` is set to
*Pulse Wave Width*, the pulses are ordered by increasing width. Because
of the discrete nature of the underlying signal, the resulting pulses
will be jagged. For example assuming 5 bins, the center block with
the two extreme values added would be as follows::
0 0 0 0 0
0 0 1 0 0
0 0 1 1 0 <--
0 1 1 1 0
0 1 1 1 1 <--
1 1 1 1 1
Setting the ``filter_jagged_pulses`` parameter to `True` will result
in the removal of the two marked pulse waves above thus avoiding jagged
lines when plotting and having to resort to excessive ``bins`` values.
Returns
-------
:class:`numpy.ndarray`
Pulse waves.
References
----------
:cite:`Lindbloom2015`, :cite:`Mansencal2018`, :cite:`Martinez-Verdu2007`
Examples
--------
>>> generate_pulse_waves(5)
array([[ 0., 0., 0., 0., 0.],
[ 1., 0., 0., 0., 0.],
[ 0., 1., 0., 0., 0.],
[ 0., 0., 1., 0., 0.],
[ 0., 0., 0., 1., 0.],
[ 0., 0., 0., 0., 1.],
[ 1., 1., 0., 0., 0.],
[ 0., 1., 1., 0., 0.],
[ 0., 0., 1., 1., 0.],
[ 0., 0., 0., 1., 1.],
[ 1., 0., 0., 0., 1.],
[ 1., 1., 1., 0., 0.],
[ 0., 1., 1., 1., 0.],
[ 0., 0., 1., 1., 1.],
[ 1., 0., 0., 1., 1.],
[ 1., 1., 0., 0., 1.],
[ 1., 1., 1., 1., 0.],
[ 0., 1., 1., 1., 1.],
[ 1., 0., 1., 1., 1.],
[ 1., 1., 0., 1., 1.],
[ 1., 1., 1., 0., 1.],
[ 1., 1., 1., 1., 1.]])
>>> generate_pulse_waves(5, 'Pulse Wave Width')
array([[ 0., 0., 0., 0., 0.],
[ 1., 0., 0., 0., 0.],
[ 1., 1., 0., 0., 0.],
[ 1., 1., 0., 0., 1.],
[ 1., 1., 1., 0., 1.],
[ 0., 1., 0., 0., 0.],
[ 0., 1., 1., 0., 0.],
[ 1., 1., 1., 0., 0.],
[ 1., 1., 1., 1., 0.],
[ 0., 0., 1., 0., 0.],
[ 0., 0., 1., 1., 0.],
[ 0., 1., 1., 1., 0.],
[ 0., 1., 1., 1., 1.],
[ 0., 0., 0., 1., 0.],
[ 0., 0., 0., 1., 1.],
[ 0., 0., 1., 1., 1.],
[ 1., 0., 1., 1., 1.],
[ 0., 0., 0., 0., 1.],
[ 1., 0., 0., 0., 1.],
[ 1., 0., 0., 1., 1.],
[ 1., 1., 0., 1., 1.],
[ 1., 1., 1., 1., 1.]])
>>> generate_pulse_waves(5, 'Pulse Wave Width', True)
array([[ 0., 0., 0., 0., 0.],
[ 1., 0., 0., 0., 0.],
[ 1., 1., 0., 0., 1.],
[ 0., 1., 0., 0., 0.],
[ 1., 1., 1., 0., 0.],
[ 0., 0., 1., 0., 0.],
[ 0., 1., 1., 1., 0.],
[ 0., 0., 0., 1., 0.],
[ 0., 0., 1., 1., 1.],
[ 0., 0., 0., 0., 1.],
[ 1., 0., 0., 1., 1.],
[ 1., 1., 1., 1., 1.]])
"""
pulse_order = validate_method(
pulse_order,
["Bins", "Pulse Wave Width"],
'"{0}" pulse order is invalid, it must be one of {1}!',
)
square_waves = []
square_waves_basis = np.tril(
np.ones((bins, bins), dtype=DEFAULT_FLOAT_DTYPE)
)[0:-1, :]
if pulse_order.lower() == "bins":
for square_wave_basis in square_waves_basis:
for i in range(bins):
square_waves.append(np.roll(square_wave_basis, i))
else:
for i in range(bins):
for j, square_wave_basis in enumerate(square_waves_basis):
square_waves.append(np.roll(square_wave_basis, i - j // 2))
if filter_jagged_pulses:
square_waves = square_waves[::2]
return np.vstack(
[
zeros(bins),
np.vstack(square_waves),
np.ones(bins, dtype=DEFAULT_FLOAT_DTYPE),
]
)
[docs]def XYZ_outer_surface(
cmfs: Optional[MultiSpectralDistributions] = None,
illuminant: Optional[SpectralDistribution] = None,
point_order: Union[Literal["Bins", "Pulse Wave Width"], str] = "Bins",
filter_jagged_points: Boolean = False,
**kwargs: Any,
) -> NDArray:
"""
Generate the *Rösch-MacAdam* colour solid, i.e. *CIE XYZ* colourspace
outer surface, for given colour matching functions using multi-spectral
conversion of pulse waves to *CIE XYZ* tristimulus values.
Parameters
----------
cmfs
Standard observer colour matching functions, default to the
*CIE 1931 2 Degree Standard Observer*.
illuminant
Illuminant spectral distribution, default to *CIE Illuminant E*.
point_order
Method for ordering the underlying pulse waves used to generate the
*Rösch-MacAdam* colour solid. *Bins* is the default order, with
*Pulse Wave Width* ordering, instead of iterating over the pulse wave
widths first, iteration occurs over the bins, producing blocks of pulse
waves with increasing width.
filter_jagged_points
Whether to filter the underlying jagged pulses. When ``point_order`` is
set to *Pulse Wave Width*, the pulses are ordered by increasing width.
Because of the discrete nature of the underlying signal, the resulting
pulses will be jagged. For example assuming 5 bins, the center block
with the two extreme values added would be as follows::
0 0 0 0 0
0 0 1 0 0
0 0 1 1 0 <--
0 1 1 1 0
0 1 1 1 1 <--
1 1 1 1 1
Setting the ``filter_jagged_points`` parameter to `True` will result
in the removal of the two marked pulse waves above thus avoiding jagged
lines when plotting and having to resort to excessive ``bins`` values.
Other Parameters
----------------
kwargs
{:func:`colour.msds_to_XYZ`},
See the documentation of the previously listed definition.
Returns
-------
:class:`numpy.ndarray`
*Rösch-MacAdam* colour solid, *CIE XYZ* outer surface tristimulus
values.
References
----------
:cite:`Lindbloom2015`, :cite:`Mansencal2018`, :cite:`Martinez-Verdu2007`
Examples
--------
>>> from colour import MSDS_CMFS, SPECTRAL_SHAPE_DEFAULT
>>> shape = SpectralShape(
... SPECTRAL_SHAPE_DEFAULT.start, SPECTRAL_SHAPE_DEFAULT.end, 84
... )
>>> cmfs = MSDS_CMFS['CIE 1931 2 Degree Standard Observer']
>>> XYZ_outer_surface(cmfs.copy().align(shape)) # doctest: +ELLIPSIS
array([[ 0.0000000...e+00, 0.0000000...e+00, 0.0000000...e+00],
[ 9.6361381...e-05, 2.9056776...e-06, 4.4961226...e-04],
[ 2.5910529...e-01, 2.1031298...e-02, 1.3207468...e+00],
[ 1.0561021...e-01, 6.2038243...e-01, 3.5423571...e-02],
[ 7.2647980...e-01, 3.5460869...e-01, 2.1005149...e-04],
[ 1.0971874...e-02, 3.9635453...e-03, 0.0000000...e+00],
[ 3.0792572...e-05, 1.1119762...e-05, 0.0000000...e+00],
[ 2.5920165...e-01, 2.1034203...e-02, 1.3211965...e+00],
[ 3.6471551...e-01, 6.4141373...e-01, 1.3561704...e+00],
[ 8.3209002...e-01, 9.7499113...e-01, 3.5633622...e-02],
[ 7.3745167...e-01, 3.5857224...e-01, 2.1005149...e-04],
[ 1.1002667...e-02, 3.9746651...e-03, 0.0000000...e+00],
[ 1.2715395...e-04, 1.4025439...e-05, 4.4961226...e-04],
[ 3.6481187...e-01, 6.4141663...e-01, 1.3566200...e+00],
[ 1.0911953...e+00, 9.9602242...e-01, 1.3563805...e+00],
[ 8.4306189...e-01, 9.7895467...e-01, 3.5633622...e-02],
[ 7.3748247...e-01, 3.5858336...e-01, 2.1005149...e-04],
[ 1.1099028...e-02, 3.9775708...e-03, 4.4961226...e-04],
[ 2.5923244...e-01, 2.1045323...e-02, 1.3211965...e+00],
[ 1.0912916...e+00, 9.9602533...e-01, 1.3568301...e+00],
[ 1.1021671...e+00, 9.9998597...e-01, 1.3563805...e+00],
[ 8.4309268...e-01, 9.7896579...e-01, 3.5633622...e-02],
[ 7.3757883...e-01, 3.5858626...e-01, 6.5966375...e-04],
[ 2.7020432...e-01, 2.5008868...e-02, 1.3211965...e+00],
[ 3.6484266...e-01, 6.4142775...e-01, 1.3566200...e+00],
[ 1.1022635...e+00, 9.9998888...e-01, 1.3568301...e+00],
[ 1.1021979...e+00, 9.9999709...e-01, 1.3563805...e+00],
[ 8.4318905...e-01, 9.7896870...e-01, 3.6083235...e-02],
[ 9.9668412...e-01, 3.7961756...e-01, 1.3214065...e+00],
[ 3.7581454...e-01, 6.4539130...e-01, 1.3566200...e+00],
[ 1.0913224...e+00, 9.9603645...e-01, 1.3568301...e+00],
[ 1.1022943...e+00, 1.0000000...e+00, 1.3568301...e+00]])
"""
cmfs, illuminant = handle_spectral_arguments(
cmfs,
illuminant,
"CIE 1931 2 Degree Standard Observer",
"E",
SPECTRAL_SHAPE_OUTER_SURFACE_XYZ,
)
settings = dict(kwargs)
settings.update({"shape": cmfs.shape})
key = (
hash(cmfs),
hash(illuminant),
point_order,
filter_jagged_points,
str(settings),
)
XYZ = _CACHE_OUTER_SURFACE_XYZ.get(key)
if XYZ is None:
pulse_waves = generate_pulse_waves(
len(cmfs.wavelengths), point_order, filter_jagged_points
)
XYZ = (
msds_to_XYZ(
pulse_waves, cmfs, illuminant, method="Integration", **settings
)
/ 100
)
_CACHE_OUTER_SURFACE_XYZ[key] = XYZ
return XYZ
solid_RoschMacAdam = XYZ_outer_surface
[docs]def is_within_visible_spectrum(
XYZ: ArrayLike,
cmfs: Optional[MultiSpectralDistributions] = None,
illuminant: Optional[SpectralDistribution] = None,
tolerance: Optional[Floating] = None,
**kwargs: Any,
) -> NDArray:
"""
Return whether given *CIE XYZ* tristimulus values are within the visible
spectrum volume, i.e. *Rösch-MacAdam* colour solid, for given colour
matching functions and illuminant.
Parameters
----------
XYZ
*CIE XYZ* tristimulus values.
cmfs
Standard observer colour matching functions, default to the
*CIE 1931 2 Degree Standard Observer*.
illuminant
Illuminant spectral distribution, default to *CIE Illuminant E*.
tolerance
Tolerance allowed in the inside-triangle check.
Other Parameters
----------------
kwargs
{:func:`colour.msds_to_XYZ`},
See the documentation of the previously listed definition.
Returns
-------
:class:`numpy.ndarray`
Are *CIE XYZ* tristimulus values within the visible spectrum volume,
i.e. *Rösch-MacAdam* colour solid.
Notes
-----
+------------+-----------------------+---------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+===============+
| ``XYZ`` | [0, 1] | [0, 1] |
+------------+-----------------------+---------------+
Examples
--------
>>> import numpy as np
>>> is_within_visible_spectrum(np.array([0.3205, 0.4131, 0.51]))
array(True, dtype=bool)
>>> a = np.array([[0.3205, 0.4131, 0.51],
... [-0.0005, 0.0031, 0.001]])
>>> is_within_visible_spectrum(a)
array([ True, False], dtype=bool)
"""
cmfs, illuminant = handle_spectral_arguments(
cmfs,
illuminant,
"CIE 1931 2 Degree Standard Observer",
"E",
SPECTRAL_SHAPE_OUTER_SURFACE_XYZ,
)
key = (hash(cmfs), hash(illuminant), str(kwargs))
vertices = _CACHE_OUTER_SURFACE_XYZ_POINTS.get(key)
if vertices is None:
_CACHE_OUTER_SURFACE_XYZ_POINTS[key] = vertices = solid_RoschMacAdam(
cmfs, illuminant, **kwargs
)
return is_within_mesh_volume(XYZ, vertices, tolerance)