Coverage for colour/models/rgb/transfer_functions/itur_bt_1886.py: 100%

1""" 

2Recommendation ITU-R BT.1886 

3============================ 

4 

5Define the *Recommendation ITU-R BT.1886* electro-optical transfer function 

6(EOTF) and its inverse. 

7 

8- :func:`colour.models.eotf_inverse_BT1886` 

9- :func:`colour.models.eotf_BT1886` 

10 

11References 

12---------- 

13- :cite:`InternationalTelecommunicationUnion2011h` : International 

14 Telecommunication Union. (2011). Recommendation ITU-R BT.1886 - Reference 

15 electro-optical transfer function for flat panel displays used in HDTV 

16 studio production BT Series Broadcasting service. 

17 https://www.itu.int/dms_pubrec/itu-r/rec/bt/\ 

18R-REC-BT.1886-0-201103-I!!PDF-E.pdf 

19""" 

20 

21from __future__ import annotations 

22 

23import numpy as np 

24 

25from colour.algebra import spow 

26from colour.hints import ( # noqa: TC001 

27 Domain1, 

28 Range1, 

29) 

30from colour.utilities import as_float, from_range_1, to_domain_1 

31 

32__author__ = "Colour Developers" 

33__copyright__ = "Copyright 2013 Colour Developers" 

34__license__ = "BSD-3-Clause - https://opensource.org/licenses/BSD-3-Clause" 

35__maintainer__ = "Colour Developers" 

36__email__ = "colour-developers@colour-science.org" 

37__status__ = "Production" 

38 

39__all__ = [ 

40 "eotf_inverse_BT1886", 

41 "eotf_BT1886", 

42] 

43 

44 

45def eotf_inverse_BT1886(L: Domain1, L_B: float = 0, L_W: float = 1) -> Range1: 

46 """ 

47 Apply the *Recommendation ITU-R BT.1886* inverse electro-optical 

48 transfer function (EOTF) for flat panel displays. 

49 

50 Parameters 

51 ---------- 

52 L 

53 Screen luminance in :math:`cd/m^2`. 

54 L_B 

55 Screen luminance for black in :math:`cd/m^2`. 

56 L_W 

57 Screen luminance for white in :math:`cd/m^2`. 

58 

59 Returns 

60 ------- 

61 :class:`numpy.ndarray` 

62 Input video signal level (normalised, with black at :math:`V = 0` 

63 and white at :math:`V = 1`). For content mastered per 

64 *Recommendation ITU-R BT.709*, 10-bit digital code values 

65 :math:`D` map into values of :math:`V` per the following equation: 

66 :math:`V = (D-64)/876` 

67 

68 Notes 

69 ----- 

70 +------------+-----------------------+---------------+ 

71 | **Domain** | **Scale - Reference** | **Scale - 1** | 

72 +============+=======================+===============+ 

73 | ``L`` | 1 | 1 | 

74 +------------+-----------------------+---------------+ 

75 

76 +------------+-----------------------+---------------+ 

77 | **Range** | **Scale - Reference** | **Scale - 1** | 

78 +============+=======================+===============+ 

79 | ``V`` | 1 | 1 | 

80 +------------+-----------------------+---------------+ 

81 

82 References 

83 ---------- 

84 :cite:`InternationalTelecommunicationUnion2011h` 

85 

86 Examples 

87 -------- 

88 >>> eotf_inverse_BT1886(0.11699185725296059) # doctest: +ELLIPSIS 

89 0.4090077... 

90 """ 

91 

92 L = to_domain_1(L) 

93 

94 gamma = 2.40 

95 gamma_d = 1 / gamma 

96 

97 n = L_W**gamma_d - L_B**gamma_d 

98 a = n**gamma 

99 b = L_B**gamma_d / n 

100 

101 V = spow(L / a, gamma_d) - b 

102 

103 return as_float(from_range_1(V)) 

104 

105 

106def eotf_BT1886(V: Domain1, L_B: float = 0, L_W: float = 1) -> Range1: 

107 """ 

108 Apply the *Recommendation ITU-R BT.1886* electro-optical transfer 

109 function (EOTF) for flat panel displays. 

110 

111 Parameters 

112 ---------- 

113 V 

114 Input video signal level (normalised, with black at :math:`V = 0` 

115 and white at :math:`V = 1`). For content mastered per 

116 *Recommendation ITU-R BT.709*, 10-bit digital code values 

117 :math:`D` map into values of :math:`V` per the following equation: 

118 :math:`V = (D-64)/876` 

119 L_B 

120 Screen luminance for black in :math:`cd/m^2`. 

121 L_W 

122 Screen luminance for white in :math:`cd/m^2`. 

123 

124 Returns 

125 ------- 

126 :class:`numpy.ndarray` 

127 Screen luminance in :math:`cd/m^2`. 

128 

129 Notes 

130 ----- 

131 +------------+-----------------------+---------------+ 

132 | **Domain** | **Scale - Reference** | **Scale - 1** | 

133 +============+=======================+===============+ 

134 | ``V`` | 1 | 1 | 

135 +------------+-----------------------+---------------+ 

136 

137 +------------+-----------------------+---------------+ 

138 | **Range** | **Scale - Reference** | **Scale - 1** | 

139 +============+=======================+===============+ 

140 | ``L`` | 1 | 1 | 

141 +------------+-----------------------+---------------+ 

142 

143 References 

144 ---------- 

145 :cite:`InternationalTelecommunicationUnion2011h` 

146 

147 Examples 

148 -------- 

149 >>> eotf_BT1886(0.409007728864150) # doctest: +ELLIPSIS 

150 0.1169918... 

151 """ 

152 

153 V = to_domain_1(V) 

154 

155 gamma = 2.40 

156 gamma_d = 1 / gamma 

157 

158 n = L_W**gamma_d - L_B**gamma_d 

159 a = n**gamma 

160 b = L_B**gamma_d / n 

161 L = a * spow(np.maximum(V + b, 0), gamma) 

162 

163 return as_float(from_range_1(L))