One of the limitations of ray tracing is the hard edges computed for shadows. In addition to aesthetic reasons, there is evidence that soft edged shadows aid in accurate spatial perception [19]. Ray tracing methods that produce accurate soft shadows such as ray tracing with cones [1] or probabilistic ray tracing [5] stress accurate soft shadows, but dramatically increase computation time relative to hard shadow computation. In this section we examine how to compute soft-edged shadows approximately so that interactivity can be maintained.
One option to improve performance is to do explicit multi-sampling of the light with a ``beam'' made up of a small number of rays [15]. Since the number of rays is small, there will be visual artifacts but interactive performance will be possible (Figure 10). To speed up this computation we can precompute the rays in the beam if we assume the luminaire is far away, and we can vectorize the intersection computation against each geometric primitive. This is similar to traversing efficiency structures using bundles rather than single rays [9]. Although this optimization gives us a factor of two performance over the unvectorized version, it is still too slow for many shadow rays.
An alternative to computing accurate soft shadows is to soften the edges of hard shadows. This is essentially the technique used in depth buffer algorithms [25] where the binary shadow raster can be filtered. However we want to simulate the change in penumbra width we see in real shadows. Such an effect requires more sophisticated filtering. This means shadow penumbra width should behave in a believable way, starting at zero at the occluder and increasing linearly with distance from the occluder.
It is hard for observers to tell the difference between shadows cast by differently shaped lights. For this reason we assume spherical lights. We do a rough calculation at each illuminated point of what fraction s of the light is visible, and attenuate the unshadowed illumination by s. Thus our goal is to estimate s in efficiently and to visually plausible results.
Rather than creating a correct shadow created by an area source, the algorithm creates a shadow of a soft-edged object from a point source (Figure 11). The penumbra is the shadow of the semi-opaque (outer) object that is not also shadowed by the opaque (inner) object. The transparency of the outer object increases from no transparency at the inner object to full transparency at the boundary of the outer object. For an isolated object, we can use inner and outer offsets of the real object to achieve believable results. We also need to make the intensity gradient in the penumbra natural. This can be achieved by computing the shadowing variable s beginning at s=0 on the penumbra/umbra boundary (the surface of the inner object) and increasing non-linearly with distance to s=1 on the outer boundary of the penumbra (the surface of the outer object).
The above approach will give an approximate soft shadow. The size of the penumbra is based on the size of the offsets used to create the inner and outer objects. In order to have the penumbra width change plausibly, the offsets need to change based on the distance along the shadow ray and the size of the light source, as illustrated in Figure 12. This requires modifying the intersection tests for shadow rays. The details of this approach, including solutions to light leaking between two objects and the intersection tests and bounding box construction for polygons and spheres with varying offsets are discussed in more depth by Parker et al.[#!park98b!#]. The results are shown in Figure 13.
