Hard vs. soft shadows

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The common-sense notion of shadow is a binary status, i.e. a point is either «in shadow» or not. This corresponds to hard shadows (see Figure 1a), as produced by point light sources : indeed, a point light source is either visible or occluded from any receiving point. However, point light sources do not exist in practice and hard shadows give a rather unrealistic feeling to images (see Figure 1b). Note that even the sun, probably the most common shadow-creating light source in our daily life, has a significant angular extent and does not create hard shadows. Still, point light sources are easy to model in computer graphics and we shall see that several algorithms let us compute hard shadows in real time.

In the more realistic case of a light source with finite extent, a point on the receiver can have a partial view of the light, i.e. only a fraction of the light source is visible from that point (see Figure 2b, and Animation). We distinguish the umbra region (if it exists) in which the light source is totally blocked from the receiver, and the penumbra region in which the light source is partially visible. The determination of the umbra and penumbra is a difficult task in general, as it amounts to solving visibility relationships in 3D, a notoriously hard problem. In the case of polygonal objects, the shape of the umbra and penumbra regions is embedded in a discontinuity mesh¹³ which can be constructed from the edges and vertices of the light source and the occluders (see Figure 2a).