Improved Dual-Space Bounds for Simultaneous Motion and Defocus Blur

Our previous paper on stochastic rasterization [Laine et al. 2011] presented a method for constructing time and lens bounds to accelerate stochastic rasterization by skipping the costly 5D coverage test. Although the method works for the combined case of simultaneous motion and defocus blur, its efficiency drops when significant amounts of both effects are present. In this paper, we describe a bound computation method that treats time and lens domains in a unified fashion, and yields tight bounds also for the combined case. 1 Extended Dual Space In previous work [Laine et al. 2011], time and lens bounds were considered separately, and in order to guarantee correctness, both of these domains had to be conservative with respect to the other. In other words, the lens bounds had to be valid for all instants of time, and the time bounds had to be valid for all lens positions. In situations where significant amounts of both effects occur simultaneously, this decreases the sample test efficiency (STE). Treating the time and lens domains in a unified fashion lets us derive tight bounds even when both effects occur simultaneously. It also simplifies the overall algorithm. We extend the dual-space idea of previous work into three dimensions. As before, the construction is based on parallel projection of a vertex onto camera plane, illustrated in Figure 1. The position of the projected point on camera plane is δx (resp. δy), and it is defined as a function of projection direction γx (resp. γy), lens position u (resp. v), and time t. As before, the projection formulas are δx = x ′ − w′ · γx δy = y ′ − w′ · γy