We therefore introduce "virtual" light sources that do not exist in reality, but are used during the calculation to direct shadow rays in the appropriate directions to find reflected or otherwise transferred light sources. This works for any planar surface, and has been implemented for mirrors as well as prismatic glazings (used in daylighting systems ). For example, a planar mirror might result in a virtual sun in the mirror direction from the real sun. When a shadow ray is sent towards the virtual sun, it will be reflected off the mirror to intersect the real sun. An example is shown in Figure 7a. This approach is essentially the same as the "virtual worlds" idea put forth by Rushmeier  and exploited by Wallace , but it is only carried out for light sources and not for all contributing surfaces. Thus, multiple transfers between specular surfaces can be made practical with this method using intelligent optimization techniques.
The first optimization we apply is to limit the scope of a virtual light source to its affected volume. Given a specific source and a specific specular surface, the influence is usually limited to a certain projected volume. Points that fall outside this volume are not affected and thus it is not necessary to consider the source everywhere. Furthermore, multiple reflections of the source are possible only within this volume. We can thus avoid creating virtual-virtual sources in cases where the volume of one virtual source fails to intersect the second reflecting surface, as shown in Figure 7b. The same holds for thrice redirected sources and so on, and the likelihood that virtual source volumes intersect becomes less likely each time, provided that the reflecting surfaces do not occupy a majority of the space.
To minimize the creation of useless virtual light sources, we check very carefully to confirm that the light in fact has some free path between the source and the reflecting surface before creating the virtual source. For example, we might have an intervening surface that prevents all rays from reaching a reflecting surface from a specific light source, such as the situation shown in Figure 7c. We can test for this condition by sending a number of presampling rays between the light source and the reflecting surface, assuming if none of the rays arrives that the reflecting path must be completely obstructed. Conversely, if none of the rays is obstructed, we can save time during shadow testing later by assuming that any ray arriving at the reflecting surface in fact has a free path to the source, and further ray intersection tests are unnecessary. We have found presampling to be very effective in avoiding wasteful testing of completely blocked or unhindered virtual light source paths.
Figure 8 shows a cross-section of an office space with a light shelf having a mirrored top surface. Exterior to this office is a building with a mirrored glass facade. Figure 9a shows the interior of the office with sunlight reflected by the shelf onto the ceiling. Light has also been reflected by the exterior, glazed building. Light shelf systems utilize daylight very effectively and are finding increasing popularity among designers.
To make our calculation more efficient overall, we have made additional use of "secondary" light sources, described in the next section.