Accurate computation of depth-of-field effects in computer graphics rendering is generally very time consuming, creating a problematic work flow for film authoring. The computation is particularly challenging because it depends on large-scale spatially-varying filtering that must accurately respect complex boundaries. A variety of real-time algorithms have been proposed for games, but the compromises required to achieve the necessary frame rates have made them unsuitable for film. Here we introduce an approximate depth-of-field computation that is good enough for film preview, yet can be computed interactively on a GPU. The computation creates depth-of-field blurs by simulating the heat equation for a nonuniform medium. Our alternating direction implicit solution gives rise to separable spatially varying recursive filters that can compute large-kernel convolutions in constant time per pixel while respecting the boundaries between in-focus and out-of-focus objects. Recursive filters have traditionally been viewed as problematic for GPUs, but using the well-established method of cyclic reduction of tridiagonal systems, we are able to vectorize the computation and achieve interactive frame rates.