A representation used for 3-D graphical objects, the "octree," has been applied to the geometrical calculations needed to perform photon beam does calculations for radiotherapy treatment planning. This representation allows the algorithm to attempt to minimize the number of distinct geometrical calculations that are needed to perform dose calculations to a particular resolution. In this way, the calculational time can be minimized, since the geometrical part of the dose calculations is often the most time-intensive part of the calculation process. The octree-like system used here has sped up the photon dose calculations described here by up to a factor of 10.