# -*- coding: utf-8 -*-
"""
:math:`I_GP_GT_G` Colourspace
=============================
Defines the :math:`I_GP_GT_G` colourspace transformations:
- :func:`colour.XYZ_to_IGPGTG`
- :func:`colour.IGPGTG_to_XYZ`
References
----------
- :cite:`Hellwig2020` : Hellwig, L., & Fairchild, M. D. (2020). Using
Gaussian Spectra to Derive a Hue-linear Color Space. Journal of Perceptual
Imaging. doi:10.2352/J.Percept.Imaging.2020.3.2.020401
"""
from __future__ import division, unicode_literals
import numpy as np
from colour.algebra import spow
from colour.utilities import (from_range_1, to_domain_1, vector_dot)
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013-2020 - 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__ = [
'MATRIX_IGPGTG_XYZ_TO_LMS', 'MATRIX_IGPGTG_LMS_TO_XYZ',
'MATRIX_IGPGTG_LMS_TO_IGPGTG', 'MATRIX_IGPGTG_IGPGTG_TO_LMS',
'XYZ_to_IGPGTG', 'IGPGTG_to_XYZ'
]
MATRIX_IGPGTG_XYZ_TO_LMS = np.array([
[2.968, 2.741, -0.649],
[1.237, 5.969, -0.173],
[-0.318, 0.387, 2.311],
])
"""
*CIE XYZ* tristimulus values to normalised cone responses matrix.
MATRIX_IGPGTG_XYZ_TO_LMS : array_like, (3, 3)
"""
MATRIX_IGPGTG_LMS_TO_XYZ = np.linalg.inv(MATRIX_IGPGTG_XYZ_TO_LMS)
"""
Normalised cone responses to *CIE XYZ* tristimulus values matrix.
MATRIX_IGPGTG_LMS_TO_XYZ : array_like, (3, 3)
"""
MATRIX_IGPGTG_LMS_TO_IGPGTG = np.array([
[0.117, 1.464, 0.130],
[8.285, -8.361, 21.400],
[-1.208, 2.412, -36.530],
])
"""
Normalised cone responses to :math:`I_GP_GT_G` colourspace matrix.
MATRIX_IGPGTG_LMS_TO_IGPGTG : array_like, (3, 3)
"""
MATRIX_IGPGTG_IGPGTG_TO_LMS = np.linalg.inv(MATRIX_IGPGTG_LMS_TO_IGPGTG)
"""
:math:`I_GP_GT_G` colourspace to normalised cone responses matrix.
MATRIX_IGPGTG_IGPGTG_TO_LMS : array_like, (3, 3)
"""
[docs]def XYZ_to_IGPGTG(XYZ):
"""
Converts from *CIE XYZ* tristimulus values to :math:`I_GP_GT_G`
colourspace.
Parameters
----------
XYZ : array_like
*CIE XYZ* tristimulus values.
Returns
-------
ndarray
:math:`I_GP_GT_G` colourspace array.
Notes
-----
+------------+-----------------------+-----------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+=================+
| ``XYZ`` | [0, 1] | [0, 1] |
+------------+-----------------------+-----------------+
+------------+-----------------------+-----------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+=================+
| ``IGPGTG`` | ``IG`` : [0, 1] | ``IG`` : [0, 1] |
| | | |
| | ``PG`` : [-1, 1] | ``PG`` : [-1, 1]|
| | | |
| | ``TG`` : [-1, 1] | ``TG`` : [-1, 1]|
+------------+-----------------------+-----------------+
- Input *CIE XYZ* tristimulus values must be adapted to
*CIE Standard Illuminant D Series* *D65*.
References
----------
:cite:`Hellwig2020`
Examples
--------
>>> XYZ = np.array([0.20654008, 0.12197225, 0.05136952])
>>> XYZ_to_IGPGTG(XYZ) # doctest: +ELLIPSIS
array([ 0.4242125..., 0.1863249..., 0.1068922...])
"""
XYZ = to_domain_1(XYZ)
LMS = vector_dot(MATRIX_IGPGTG_XYZ_TO_LMS, XYZ)
LMS_prime = spow(LMS / np.array([18.36, 21.46, 19435]), 0.427)
IGPGTG = vector_dot(MATRIX_IGPGTG_LMS_TO_IGPGTG, LMS_prime)
return from_range_1(IGPGTG)
[docs]def IGPGTG_to_XYZ(IGPGTG):
"""
Converts from :math:`I_GP_GT_G` colourspace to *CIE XYZ* tristimulus
values.
Parameters
----------
IGPGTG : array_like
:math:`I_GP_GT_G` colourspace array.
Returns
-------
ndarray
*CIE XYZ* tristimulus values.
Notes
-----
+------------+-----------------------+-----------------+
| **Domain** | **Scale - Reference** | **Scale - 1** |
+============+=======================+=================+
| ``IGPGTG`` | ``IG`` : [0, 1] | ``IG`` : [0, 1] |
| | | |
| | ``PG`` : [-1, 1] | ``PG`` : [-1, 1]|
| | | |
| | ``TG`` : [-1, 1] | ``TG`` : [-1, 1]|
+------------+-----------------------+-----------------+
+------------+-----------------------+-----------------+
| **Range** | **Scale - Reference** | **Scale - 1** |
+============+=======================+=================+
| ``XYZ`` | [0, 1] | [0, 1] |
+------------+-----------------------+-----------------+
References
----------
:cite:`Hellwig2020`
Examples
--------
>>> IGPGTG = np.array([0.42421258, 0.18632491, 0.10689223])
>>> IGPGTG_to_XYZ(IGPGTG) # doctest: +ELLIPSIS
array([ 0.2065400..., 0.1219722..., 0.0513695...])
"""
IGPGTG = to_domain_1(IGPGTG)
LMS = vector_dot(MATRIX_IGPGTG_IGPGTG_TO_LMS, IGPGTG)
LMS_prime = spow(LMS, 1 / 0.427) * np.array([18.36, 21.46, 19435])
XYZ = vector_dot(MATRIX_IGPGTG_LMS_TO_XYZ, LMS_prime)
return from_range_1(XYZ)