#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
RGB Colourspace Derivation
==========================
Defines objects related to *RGB* colourspace derivation, essentially
calculating the normalised primary matrix for given *RGB* colourspace primaries
and whitepoint.
See Also
--------
`RGB Colourspaces IPython Notebook
<http://nbviewer.ipython.org/github/colour-science/colour-ipython/blob/master/notebooks/models/rgb.ipynb>`_ # noqa
References
----------
.. [1] SMPTE. (1993). Derivation of Basic Television Color Equations. In
RP 177:1993 (Vol. RP 177:199). doi:10.5594/S9781614821915
"""
from __future__ import division, unicode_literals
import numpy as np
__author__ = 'Colour Developers'
__copyright__ = 'Copyright (C) 2013 - 2014 - Colour Developers'
__license__ = 'New BSD License - http://opensource.org/licenses/BSD-3-Clause'
__maintainer__ = 'Colour Developers'
__email__ = 'colour-science@googlegroups.com'
__status__ = 'Production'
__all__ = ['xy_to_z',
'normalised_primary_matrix',
'RGB_luminance_equation',
'RGB_luminance']
[docs]def xy_to_z(xy):
"""
Returns the *z* coordinate using given *xy* chromaticity coordinates.
Parameters
----------
xy : array_like
*xy* chromaticity coordinates.
Returns
-------
numeric
*z* coordinate.
Examples
--------
>>> xy_to_z((0.25, 0.25))
0.5
"""
return 1 - xy[0] - xy[1]
[docs]def normalised_primary_matrix(primaries, whitepoint):
"""
Returns the *normalised primary matrix* using given *primaries* and
*whitepoint* matrices.
Parameters
----------
primaries : array_like
Primaries chromaticity coordinate matrix, (3, 2).
whitepoint : array_like
Illuminant / whitepoint chromaticity coordinates.
Returns
-------
ndarray, (3, 3)
Normalised primary matrix.
Examples
--------
>>> pms = np.array([0.73470, 0.26530, 0.00000, 1.00000, 0.00010, -0.07700])
>>> whitepoint = (0.32168, 0.33767)
>>> normalised_primary_matrix(pms, whitepoint) # doctest: +ELLIPSIS
array([[ 9.5255239...e-01, 0.0000000...e+00, 9.3678631...e-05],
[ 3.4396645...e-01, 7.2816609...e-01, -7.2132546...e-02],
[ 0.0000000...e+00, 0.0000000...e+00, 1.0088251...e+00]])
"""
# Add *z* coordinates to the primaries and transposing the matrix.
primaries = primaries.reshape((3, 2))
z = np.array([xy_to_z(np.ravel(primary)) for primary in primaries])
primaries = np.hstack((primaries, z.reshape((3, 1))))
primaries = np.transpose(primaries)
whitepoint = np.array([
whitepoint[0] / whitepoint[1],
1,
xy_to_z(whitepoint) / whitepoint[1]]).reshape((3, 1))
coefficients = np.dot(np.linalg.inv(primaries), whitepoint)
coefficients = np.diagflat(coefficients)
npm = np.dot(primaries, coefficients)
return npm
[docs]def RGB_luminance_equation(primaries, whitepoint):
"""
Returns the *luminance equation* from given *primaries* and *whitepoint*
matrices.
Parameters
----------
primaries : array_like, (3, 2)
Primaries chromaticity coordinate matrix.
whitepoint : array_like
Illuminant / whitepoint chromaticity coordinates.
Returns
-------
unicode
*Luminance* equation.
Examples
--------
>>> pms = np.array([0.73470, 0.26530, 0.00000, 1.00000, 0.00010, -0.07700])
>>> whitepoint = (0.32168, 0.33767)
>>> # Doctests skip for Python 2.x compatibility.
>>> RGB_luminance_equation(pms, whitepoint) # doctest: +SKIP
'Y = 0.3439664...(R) + 0.7281660...(G) + -0.0721325...(B)'
"""
return 'Y = {0}(R) + {1}(G) + {2}(B)'.format(
*np.ravel(normalised_primary_matrix(primaries, whitepoint))[3:6])
[docs]def RGB_luminance(RGB, primaries, whitepoint):
"""
Returns the *luminance* :math:`y` of given *RGB* components from given
*primaries* and *whitepoint* matrices.
Parameters
----------
RGB : array_like, (3,)
*RGB* chromaticity coordinate matrix.
primaries : array_like, (3, 2)
Primaries chromaticity coordinate matrix.
whitepoint : array_like
Illuminant / whitepoint chromaticity coordinates.
Returns
-------
numeric
*Luminance* :math:`y`.
Examples
--------
>>> RGB = np.array([40.6, 4.2, 67.4])
>>> pms = np.array([0.73470, 0.26530, 0.00000, 1.00000, 0.00010, -0.07700])
>>> whitepoint = (0.32168, 0.33767)
>>> RGB_luminance(RGB, pms, whitepoint) # doctest: +ELLIPSIS
12.1616018...
"""
R, G, B = np.ravel(RGB)
X, Y, Z = np.ravel(normalised_primary_matrix(primaries,
whitepoint))[3:6]
return X * R + Y * G + Z * B
Colour 0.3