Multiple shadows

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While the creation of a shadow is easily described for a (light source, occluder, receiver) triple, care must be taken to allow for more complex situations.

Shadows from several light sources Shadows produced by multiple light sources are relatively easy to obtain if we know how to deal with a single source (see Figure 1a). Due to the linear nature of light transfer we simply sum the contribution of each light for each wavelength or color band (see Figure 1b and Animation).

Shadows from several objects For point light sources, shadows due to different occluders can be easily combined since the shadow area (where the light source is invisible) is the union of all individual shadows.

With an area light source, combining the shadows of several occluders is more complicated. Recall that the lighting contribution of the light source on the receiver involves a partial visibility function: a major issue is that no simple combination of the partial visibility functions of distinct occluders can yield the partial visibility function of the set of occluders considered together. For instance there may be points in the scene where the light source is not occluded by any object taken separately, but is totally occluded by the set of objects taken together. The correlation between the partial visibility functions of different occluders cannot be predicted easily, but can sometimes be approximated or bounded^{45, 5}.

As a consequence, the shadow of the union of the objects can be larger than the union of the shadows of the objects (see Figure 2). This effect is quite real, but is not very visible on typical scenes, especially if the objects casting shadows are animated.