[Figure 36] (figure is in two parts) Earth render on the top, and cloud shadow element added on the bottom.

Because this is not what is needed in this situation, another alpha channel must be created. One way to do this is with a luminance key operator, called a luma key for short. The luma key creates an alpha channel for an element based on the luminance value calculated from the combined color channels. The luma key creates more opaque alpha values for brighter portions of the image, with pure white areas being completely opaque, whereas pure black areas are completely transparent.

Cloud Layers
The alpha channel from the luma key operation on the clouds is then translated slightly down and to the right (because the sun is above and to the left). A new element is created by placing the Earth inside the translated cloud alpha and darkened with a brightness function. This layer is now clouds of darkened Earth. By placing this cloud shadow layer back over the original earth, cloud shadows are simulated (see Figure 36). Before placing the cloud shadow layer back over the Earth, it is necessary to perform an inside operation, to limit the cloud shadows to the Earth. Otherwise, because the clouds shadow layer is translated down and to the right, the shadows would extend past the Earth’s edge. This method of creating shadows is not technically accurate (the fact that the offset shadow would extend beyond the Earth’s edge instead of wrapping around is a clear sign of this), but at this distance it is a very good trick. It is much faster and easier than rendering an actual shadow pass of clouds onto the Earth (and it also saves disk space). Because the most inaccurate portion of the shadows is to the lower right of the Earth, which is the darker side opposite the sun, it works well.

[Figure 37] (figure is in two parts) Cloud render on the top, and slightly blurred cloud render on the bottom.

The next step is to add the clouds that are casting the shadows. The clouds are rendered separately as their own layer, and are simply a texture map applied to the same sphere as the Earth element (see Figure 37). The cloud render is fairly hard edged, so a slight blur is performed on the element (see Figure 37). Notice that the blur not only softens the edges, but also reduces the contrast. The amount of blur is slight to maintain the distinctive shape of the clouds, yet slightly reduce their harshness and contrast.