Source code for colour.models.ipt

"""
IPT Colourspace
===============

Define the *IPT* colourspace transformations:

-   :func:`colour.XYZ_to_IPT`
-   :func:`colour.IPT_to_XYZ`

And computation of correlates:

-   :func:`colour.IPT_hue_angle`

References
----------
-   :cite:`Fairchild2013y` : Fairchild, M. D. (2013). IPT Colourspace. In
    Color Appearance Models (3rd ed., pp. 6197-6223). Wiley. ISBN:B00DAYO8E2
"""

from __future__ import annotations

from functools import partial

import numpy as np

from colour.algebra import spow
from colour.hints import ArrayLike, NDArrayFloat
from colour.models import Iab_to_XYZ, XYZ_to_Iab
from colour.utilities import as_float, from_range_degrees, to_domain_1, tsplit

__author__ = "Colour Developers"
__copyright__ = "Copyright 2013 Colour Developers"
__license__ = "BSD-3-Clause - https://opensource.org/licenses/BSD-3-Clause"
__maintainer__ = "Colour Developers"
__email__ = "colour-developers@colour-science.org"
__status__ = "Production"

__all__ = [
    "MATRIX_IPT_XYZ_TO_LMS",
    "MATRIX_IPT_LMS_TO_XYZ",
    "MATRIX_IPT_LMS_P_TO_IPT",
    "MATRIX_IPT_IPT_TO_LMS_P",
    "XYZ_to_IPT",
    "IPT_to_XYZ",
    "IPT_hue_angle",
]

MATRIX_IPT_XYZ_TO_LMS: NDArrayFloat = np.array(
    [
        [0.4002, 0.7075, -0.0807],
        [-0.2280, 1.1500, 0.0612],
        [0.0000, 0.0000, 0.9184],
    ]
)
"""*CIE XYZ* tristimulus values to normalised cone responses matrix."""

MATRIX_IPT_LMS_TO_XYZ: NDArrayFloat = np.linalg.inv(MATRIX_IPT_XYZ_TO_LMS)
"""Normalised cone responses to *CIE XYZ* tristimulus values matrix."""

MATRIX_IPT_LMS_P_TO_IPT: NDArrayFloat = np.array(
    [
        [0.4000, 0.4000, 0.2000],
        [4.4550, -4.8510, 0.3960],
        [0.8056, 0.3572, -1.1628],
    ]
)
"""Normalised non-linear cone responses to *IPT* colourspace matrix."""

MATRIX_IPT_IPT_TO_LMS_P: NDArrayFloat = np.linalg.inv(MATRIX_IPT_LMS_P_TO_IPT)
"""*IPT* colourspace to normalised non-linear cone responses matrix."""


[docs] def XYZ_to_IPT(XYZ: ArrayLike) -> NDArrayFloat: """ Convert from *CIE XYZ* tristimulus values to *IPT* colourspace. Parameters ---------- XYZ *CIE XYZ* tristimulus values. Returns ------- :class:`numpy.ndarray` *IPT* colourspace array. Notes ----- +------------+-----------------------+-----------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+=================+ | ``XYZ`` | [0, 1] | [0, 1] | +------------+-----------------------+-----------------+ +------------+-----------------------+-----------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+=================+ | ``IPT`` | ``I`` : [0, 1] | ``I`` : [0, 1] | | | | | | | ``P`` : [-1, 1] | ``P`` : [-1, 1] | | | | | | | ``T`` : [-1, 1] | ``T`` : [-1, 1] | +------------+-----------------------+-----------------+ - Input *CIE XYZ* tristimulus values must be adapted to *CIE Standard Illuminant D Series* *D65*. References ---------- :cite:`Fairchild2013y` Examples -------- >>> XYZ = np.array([0.20654008, 0.12197225, 0.05136952]) >>> XYZ_to_IPT(XYZ) # doctest: +ELLIPSIS array([ 0.3842619..., 0.3848730..., 0.1888683...]) """ return XYZ_to_Iab( XYZ, partial(spow, p=0.43), MATRIX_IPT_XYZ_TO_LMS, MATRIX_IPT_LMS_P_TO_IPT, )
[docs] def IPT_to_XYZ(IPT: ArrayLike) -> NDArrayFloat: """ Convert from *IPT* colourspace to *CIE XYZ* tristimulus values. Parameters ---------- IPT *IPT* colourspace array. Returns ------- :class:`numpy.ndarray` *CIE XYZ* tristimulus values. Notes ----- +------------+-----------------------+-----------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+=================+ | ``IPT`` | ``I`` : [0, 1] | ``I`` : [0, 1] | | | | | | | ``P`` : [-1, 1] | ``P`` : [-1, 1] | | | | | | | ``T`` : [-1, 1] | ``T`` : [-1, 1] | +------------+-----------------------+-----------------+ +------------+-----------------------+-----------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+=================+ | ``XYZ`` | [0, 1] | [0, 1] | +------------+-----------------------+-----------------+ References ---------- :cite:`Fairchild2013y` Examples -------- >>> IPT = np.array([0.38426191, 0.38487306, 0.18886838]) >>> IPT_to_XYZ(IPT) # doctest: +ELLIPSIS array([ 0.2065400..., 0.1219722..., 0.0513695...]) """ return Iab_to_XYZ( IPT, partial(spow, p=1 / 0.43), MATRIX_IPT_IPT_TO_LMS_P, MATRIX_IPT_LMS_TO_XYZ, )
[docs] def IPT_hue_angle(IPT: ArrayLike) -> NDArrayFloat: """ Compute the hue angle in degrees from *IPT* colourspace. Parameters ---------- IPT *IPT* colourspace array. Returns ------- :class:`numpy.ndarray` Hue angle in degrees. Notes ----- +------------+-----------------------+-----------------+ | **Domain** | **Scale - Reference** | **Scale - 1** | +============+=======================+=================+ | ``IPT`` | ``I`` : [0, 1] | ``I`` : [0, 1] | | | | | | | ``P`` : [-1, 1] | ``P`` : [-1, 1] | | | | | | | ``T`` : [-1, 1] | ``T`` : [-1, 1] | +------------+-----------------------+-----------------+ +------------+-----------------------+-----------------+ | **Range** | **Scale - Reference** | **Scale - 1** | +============+=======================+=================+ | ``hue`` | [0, 360] | [0, 1] | +------------+-----------------------+-----------------+ References ---------- :cite:`Fairchild2013y` Examples -------- >>> IPT = np.array([0.96907232, 1, 1.12179215]) >>> IPT_hue_angle(IPT) # doctest: +ELLIPSIS 48.2852074... """ _I, P, T = tsplit(to_domain_1(IPT)) hue = np.degrees(np.arctan2(T, P)) % 360 return as_float(from_range_degrees(hue))