Source code for colour.colorimetry.dominant

# -*- coding: utf-8 -*-
"""
Dominant Wavelength and Purity
==============================

Defines objects to compute the *dominant wavelength* and *purity* of a colour
and related quantities:

-   :func:`colour.dominant_wavelength`
-   :func:`colour.complementary_wavelength`
-   :func:`colour.excitation_purity`
-   :func:`colour.colorimetric_purity`

References
----------
-   :cite:`CIETC1-482004o` : CIE TC 1-48. (2004). 9.1 Dominant wavelength and
    purity. In CIE 015:2004 Colorimetry, 3rd Edition (pp. 32-33).
    ISBN:978-3-901906-33-6
-   :cite:`Erdogana` : Erdogan, T. (n.d.). How to Calculate Luminosity,
    Dominant Wavelength, and Excitation Purity (p. 7).
    http://www.semrock.com/Data/Sites/1/semrockpdfs/\
whitepaper_howtocalculateluminositywavelengthandpurity.pdf
"""

from __future__ import division, unicode_literals

import numpy as np
import scipy.spatial.distance

from colour.algebra import (euclidean_distance, extend_line_segment,
                            intersect_line_segments)
from colour.colorimetry import CMFS
from colour.models import XYZ_to_xy
from colour.utilities import as_float_array

__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__ = [
    'closest_spectral_locus_wavelength', 'dominant_wavelength',
    'complementary_wavelength', 'excitation_purity', 'colorimetric_purity'
]


def closest_spectral_locus_wavelength(xy, xy_n, xy_s, inverse=False):
    """
    Returns the coordinates and closest spectral locus wavelength index to the
    point where the line defined by the given achromatic stimulus :math:`xy_n`
    to colour stimulus :math:`xy_n` *CIE xy* chromaticity coordinates
    intersects the spectral locus.

    Parameters
    ----------
    xy : array_like
        Colour stimulus *CIE xy* chromaticity coordinates.
    xy_n : array_like
        Achromatic stimulus *CIE xy* chromaticity coordinates.
    xy_s : array_like
        Spectral locus *CIE xy* chromaticity coordinates.
    inverse : bool, optional
        The intersection will be computed using the colour stimulus :math:`xy`
        to achromatic stimulus :math:`xy_n` inverse direction.

    Returns
    -------
    tuple
        Closest wavelength index, intersection point *CIE xy* chromaticity
        coordinates.

    Raises
    ------
    ValueError
        If no closest spectral locus wavelength index and coordinates found.

    Examples
    --------
    >>> xy = np.array([0.54369557, 0.32107944])
    >>> xy_n = np.array([0.31270000, 0.32900000])
    >>> xy_s = XYZ_to_xy(CMFS['CIE 1931 2 Degree Standard Observer'].values)
    >>> ix, intersect = closest_spectral_locus_wavelength(xy, xy_n, xy_s)
    >>> print(ix) #
    256
    >>> print(intersect) # doctest: +ELLIPSIS
    [ 0.6835474...  0.3162840...]
    """

    xy = as_float_array(xy)
    xy_n = np.resize(xy_n, xy.shape)
    xy_s = as_float_array(xy_s)

    xy_e = (extend_line_segment(xy, xy_n)
            if inverse else extend_line_segment(xy_n, xy))

    # Closing horse-shoe shape to handle line of purples intersections.
    xy_s = np.vstack([xy_s, xy_s[0, :]])

    xy_wl = intersect_line_segments(
        np.concatenate((xy_n, xy_e), -1),
        np.hstack([xy_s, np.roll(xy_s, 1, axis=0)])).xy
    xy_wl = xy_wl[~np.isnan(xy_wl).any(axis=-1)]
    if not len(xy_wl):
        raise ValueError(
            'No closest spectral locus wavelength index and coordinates found '
            'for "{0}" colour stimulus and "{1}" achromatic stimulus "xy" '
            'chromaticity coordinates!'.format(xy, xy_n))

    i_wl = np.argmin(scipy.spatial.distance.cdist(xy_wl, xy_s), axis=-1)

    i_wl = np.reshape(i_wl, xy.shape[0:-1])
    xy_wl = np.reshape(xy_wl, xy.shape)

    return i_wl, xy_wl


[docs]def dominant_wavelength(xy, xy_n, cmfs=CMFS['CIE 1931 2 Degree Standard Observer'], inverse=False): """ Returns the *dominant wavelength* :math:`\\lambda_d` for given colour stimulus :math:`xy` and the related :math:`xy_wl` first and :math:`xy_{cw}` second intersection coordinates with the spectral locus. In the eventuality where the :math:`xy_wl` first intersection coordinates are on the line of purples, the *complementary wavelength* will be computed in lieu. The *complementary wavelength* is indicated by a negative sign and the :math:`xy_{cw}` second intersection coordinates which are set by default to the same value than :math:`xy_wl` first intersection coordinates will be set to the *complementary dominant wavelength* intersection coordinates with the spectral locus. Parameters ---------- xy : array_like Colour stimulus *CIE xy* chromaticity coordinates. xy_n : array_like Achromatic stimulus *CIE xy* chromaticity coordinates. cmfs : XYZ_ColourMatchingFunctions, optional Standard observer colour matching functions. inverse : bool, optional Inverse the computation direction to retrieve the *complementary wavelength*. Returns ------- tuple *Dominant wavelength*, first intersection point *CIE xy* chromaticity coordinates, second intersection point *CIE xy* chromaticity coordinates. References ---------- :cite:`CIETC1-482004o`, :cite:`Erdogana` Examples -------- *Dominant wavelength* computation: >>> from pprint import pprint >>> xy = np.array([0.54369557, 0.32107944]) >>> xy_n = np.array([0.31270000, 0.32900000]) >>> cmfs = CMFS['CIE 1931 2 Degree Standard Observer'] >>> pprint(dominant_wavelength(xy, xy_n, cmfs)) # doctest: +ELLIPSIS (array(616...), array([ 0.6835474..., 0.3162840...]), array([ 0.6835474..., 0.3162840...])) *Complementary dominant wavelength* is returned if the first intersection is located on the line of purples: >>> xy = np.array([0.37605506, 0.24452225]) >>> pprint(dominant_wavelength(xy, xy_n, cmfs)) # doctest: +ELLIPSIS (array(-509.0), array([ 0.4572314..., 0.1362814...]), array([ 0.0104096..., 0.7320745...])) """ xy = as_float_array(xy) xy_n = np.resize(xy_n, xy.shape) xy_s = XYZ_to_xy(cmfs.values) i_wl, xy_wl = closest_spectral_locus_wavelength(xy, xy_n, xy_s, inverse) xy_cwl = xy_wl wl = cmfs.wavelengths[i_wl] xy_e = (extend_line_segment(xy, xy_n) if inverse else extend_line_segment(xy_n, xy)) intersect = intersect_line_segments( np.concatenate((xy_n, xy_e), -1), np.hstack([xy_s[0], xy_s[-1]])).intersect intersect = np.reshape(intersect, wl.shape) i_wl_r, xy_cwl_r = closest_spectral_locus_wavelength( xy, xy_n, xy_s, not inverse) wl_r = -cmfs.wavelengths[i_wl_r] wl = np.where(intersect, wl_r, wl) xy_cwl = np.where(intersect[..., np.newaxis], xy_cwl_r, xy_cwl) return wl, np.squeeze(xy_wl), np.squeeze(xy_cwl)
[docs]def complementary_wavelength(xy, xy_n, cmfs=CMFS['CIE 1931 2 Degree Standard Observer']): """ Returns the *complementary wavelength* :math:`\\lambda_c` for given colour stimulus :math:`xy` and the related :math:`xy_wl` first and :math:`xy_{cw}` second intersection coordinates with the spectral locus. In the eventuality where the :math:`xy_wl` first intersection coordinates are on the line of purples, the *dominant wavelength* will be computed in lieu. The *dominant wavelength* is indicated by a negative sign and the :math:`xy_{cw}` second intersection coordinates which are set by default to the same value than :math:`xy_wl` first intersection coordinates will be set to the *dominant wavelength* intersection coordinates with the spectral locus. Parameters ---------- xy : array_like Colour stimulus *CIE xy* chromaticity coordinates. xy_n : array_like Achromatic stimulus *CIE xy* chromaticity coordinates. cmfs : XYZ_ColourMatchingFunctions, optional Standard observer colour matching functions. Returns ------- tuple *Complementary wavelength*, first intersection point *CIE xy* chromaticity coordinates, second intersection point *CIE xy* chromaticity coordinates. References ---------- :cite:`CIETC1-482004o`, :cite:`Erdogana` Examples -------- *Complementary wavelength* computation: >>> from pprint import pprint >>> xy = np.array([0.37605506, 0.24452225]) >>> xy_n = np.array([0.31270000, 0.32900000]) >>> cmfs = CMFS['CIE 1931 2 Degree Standard Observer'] >>> pprint(complementary_wavelength(xy, xy_n, cmfs)) # doctest: +ELLIPSIS (array(509.0), array([ 0.0104096..., 0.7320745...]), array([ 0.0104096..., 0.7320745...])) *Dominant wavelength* is returned if the first intersection is located on the line of purples: >>> xy = np.array([0.54369557, 0.32107944]) >>> pprint(complementary_wavelength(xy, xy_n, cmfs)) # doctest: +ELLIPSIS (array(492.0), array([ 0.0364795 , 0.3384712...]), array([ 0.0364795 , 0.3384712...])) """ return dominant_wavelength(xy, xy_n, cmfs, True)
[docs]def excitation_purity(xy, xy_n, cmfs=CMFS['CIE 1931 2 Degree Standard Observer']): """ Returns the *excitation purity* :math:`P_e` for given colour stimulus :math:`xy`. Parameters ---------- xy : array_like Colour stimulus *CIE xy* chromaticity coordinates. xy_n : array_like Achromatic stimulus *CIE xy* chromaticity coordinates. cmfs : XYZ_ColourMatchingFunctions, optional Standard observer colour matching functions. Returns ------- numeric or array_like *Excitation purity* :math:`P_e`. References ---------- :cite:`CIETC1-482004o`, :cite:`Erdogana` Examples -------- >>> xy = np.array([0.54369557, 0.32107944]) >>> xy_n = np.array([0.31270000, 0.32900000]) >>> cmfs = CMFS['CIE 1931 2 Degree Standard Observer'] >>> excitation_purity(xy, xy_n, cmfs) # doctest: +ELLIPSIS 0.6228856... """ _wl, xy_wl, _xy_cwl = dominant_wavelength(xy, xy_n, cmfs) P_e = euclidean_distance(xy_n, xy) / euclidean_distance(xy_n, xy_wl) return P_e
[docs]def colorimetric_purity(xy, xy_n, cmfs=CMFS['CIE 1931 2 Degree Standard Observer']): """ Returns the *colorimetric purity* :math:`P_c` for given colour stimulus :math:`xy`. Parameters ---------- xy : array_like Colour stimulus *CIE xy* chromaticity coordinates. xy_n : array_like Achromatic stimulus *CIE xy* chromaticity coordinates. cmfs : XYZ_ColourMatchingFunctions, optional Standard observer colour matching functions. Returns ------- numeric or array_like *Colorimetric purity* :math:`P_c`. References ---------- :cite:`CIETC1-482004o`, :cite:`Erdogana` Examples -------- >>> xy = np.array([0.54369557, 0.32107944]) >>> xy_n = np.array([0.31270000, 0.32900000]) >>> cmfs = CMFS['CIE 1931 2 Degree Standard Observer'] >>> colorimetric_purity(xy, xy_n, cmfs) # doctest: +ELLIPSIS 0.6135828... """ xy = as_float_array(xy) _wl, xy_wl, _xy_cwl = dominant_wavelength(xy, xy_n, cmfs) P_e = excitation_purity(xy, xy_n, cmfs) P_c = P_e * xy_wl[..., 1] / xy[..., 1] return P_c