Graphics Reference
In-Depth Information
B
(0,0,0)
bc2
R
bc1
G
Figure 2.2.
Base colors on the color plane.
use an algorithm, which walks around the silhouette computing the two points
in which the silhouette crosses the plane.
The key observation now is that we can represent a hue value as the angle
to the vectors spanning the plane or, alternatively, using a linear interpolation
between the two base colors. In order to compute the final color, we only have
to adjust the luminance and perform any required final color space conversions.
2.2.3 Luminance Encoding
The luminance of the color being encoded is stored directly. After colors have
been transformed into the linear RGB space, we can use a classic equation for
obtaining perceived luminance value derived from the sRGB to XYZ color space
transformation in [Stokes 96]:
L
=0
.
2126
·
R
+0
.
7152
·
G
+0
.
0722
·
B.
Because the weighting coecients sum up to 1, the luminance value ranges from
zero to one. Since the luminance has its own dedicated channel in the 2-channel
format, it can now be stored directly. However, as luminance perception is not
linear, we are using a gamma value of 2 for the luminance storage. This is close
enough to the standard gamma 2.2 and gives the same benefits—dark colors have
improved luminance resolution at the cost of unnoticeably reduced quality of
highlights. Also the gamma value of 2 means that luminance can simply have its
square root computed while encoding and will simply be squared while decoding.
2.2.4 Hue Estimation and Encoding
To encode the hue of the color, we have to find the closest suitable color on the
approximating plane and then find the proportion with which we should mix the
base colors to obtain the proper hue. The hue encoding process is demonstrated
