Merge pull request #264 from facelessuser/enhance/rec2100-hlg

Add proper handling of gamma and black level lift

coloraide/spaces/rec2100_hlg.py

@@ -19,29 +19,68 @@
 from .srgb import sRGB
 from .. import algebra as alg
 from ..types import Vector
+import math
 
-A = 0.17883277
-B = 0.28466892  # `1 - 4 * A`
-C = 0.55991073  # `0.5 - A * alg.nlog(4 * A)`
+# Sets 18% grey card to ~38% (37.7...) in order to set diffused white to 75%.
 SCALE = 0.26496256042100724
-INV_SCALE = 1 / SCALE
 
 
-def hlg_oetf(values: Vector) -> Vector:
+class Environment:
+    """Class to calculate and contain any required environmental data."""
+
+    def __init__(
+        self,
+        lw: float,
+        lb: float,
+        scale: float
+    ):
+        """Initialize environmental data."""
+
+        self.a = 0.17883277
+        self.b = 0.28466892  # `1 - 4 * a`
+        self.c = 0.55991073  # `0.5 - a * alg.nlog(4 * a)`
+        self.beta = hlg_black_level_lift(lw, lb)
+        self.scale = scale
+        self.inv_scale = 1 / scale
+
+
+def hlg_gamma(lw: float = 1000.0) -> float:
+    """
+    Return the reference HLG system gamma.
+
+    Ranges should be `lw >= 1000 cd / m^2`.
+    """
+
+    return 1.2 + 0.42 * math.log(lw / 1000.0)
+
+
+def hlg_black_level_lift(lw: float = 0.0, lb: float = 1000.0) -> float:
+    """
+    Return beta (the black level lift) using the nominal peak level luminance and display luminance for black.
+
+    Ranges should be `lw >= 1000 cd / m^2` and `lb <= 0.005 cd / m^2`.
+    """
+
+    return math.sqrt(3 * (lb / lw) ** (1 / hlg_gamma(lw)))
+
+
+def hlg_oetf(values: Vector, env: Environment) -> Vector:
     """HLG OETF."""
 
     adjusted = []  # type: Vector
     for e in values:
-        adjusted.append(alg.nth_root(3 * e, 2) if e <= 1 / 12 else A * alg.nlog(12 * e - B) + C)
+        e = alg.nth_root(3 * e, 2) if e <= 1 / 12 else env.a * alg.nlog(12 * e - env.b) + env.c
+        adjusted.append((e - env.beta) / (1 - env.beta))
     return adjusted
 
 
-def hlg_eotf(values: Vector) -> Vector:
+def hlg_eotf(values: Vector, env: Environment) -> Vector:
     """HLG EOTF."""
 
     adjusted = []  # type: Vector
     for e in values:
-        adjusted.append((e ** 2) / 3 if e <= 0.5 else (alg.nexp((e - C) / A) + B) / 12)
+        e = (1 - env.beta) * e + env.beta
+        adjusted.append((e ** 2) / 3 if e <= 0.5 else (alg.nexp((e - env.c) / env.a) + env.b) / 12)
     return adjusted
 
 
@@ -53,13 +92,14 @@ class Rec2100HLG(sRGB):
     SERIALIZE = ('--rec2100-hlg',)
     WHITE = WHITES['2deg']['D65']
     DYNAMIC_RANGE = 'hdr'
+    ENV = Environment(1000, 0, SCALE)
 
     def to_base(self, coords: Vector) -> Vector:
         """To base from Rec 2100 HLG."""
 
-        return alg.multiply(hlg_eotf(coords), INV_SCALE, dims=alg.D1_SC)
+        return [c * self.ENV.inv_scale for c in hlg_eotf(coords, self.ENV)]
 
     def from_base(self, coords: Vector) -> Vector:
         """From base to Rec. 2100 HLG."""
 
-        return hlg_oetf(alg.multiply(coords, SCALE, dims=alg.D1_SC))
+        return hlg_oetf([c * self.ENV.scale for c in coords], self.ENV)