We present a signal-processing framework for light transport. We study the frequency content of radiance and how it is affected by phenomena such as shading, occlusion, and travel in free space. This extends previous work that considered either spatial or angular dimensions, and offers a comprehensive treatment of both space and angle.

We characterize how the radiance signal is modified as light propagates and interacts with objects. In particular, we show that occlusion (a multiplication in the primal space) amounts in the Fourier domain to a convolution by the frequency content of the blocker. Propagation in free space corresponds to a shear in the space-angle frequency domain, while reflection on curved objects performs a different shear along the angular frequency axis. As described by previous work, reflection is a convolution in the primal space, and therefore amounts to a multiplication in the Fourier domain. Our extension shows how the spatial components of lighting are affected by this angular convolution.

We show that our signal-processing framework predicts the characteristics of interactions such as caustics, and the disappearance of the shadows of small features. Predictions on the frequency spectrum of the radiance function can then be used to control sampling rates or the choice of reconstruction kernels for rendering. Other potential applications include pre-computed radiance transfer and inverse rendering.

We present a hybrid algorithm for rendering hard shadows accurately and efficiently. Our method combines the strengths of shadow maps and shadow volumes. We first use a shadow map to identify the pixels in the image that lie near shadow discontinuities. Then, we perform the shadow volume algorithm only at these pixels to ensure accurate shadow edges. This approach simultaneously avoids the edge aliasing artifacts of standard shadow maps and avoids the high fillrate consumption of standard shadow volumes. The algorithm relies on a hardware mechanism for rapidly rejecting non-silhouette pixels during rasterization. Since current graphics hardware does not directly provide this mechanism, we simulate it using available features related to occlusion culling and show that dedicated hardware support requires minimal changes to existing technology.

We present a new method for real-time rendering of shadows in dynamic scenes. Our approach builds on the shadow map algorithm by attaching geometric primitives that we call "smoothies" to the objects' silhouettes. The smoothies give rise to fake shadows that appear qualitatively like soft shadows, without the cost of densely sampling an area light source. The soft shadow edges hide objectionable aliasing artifacts that are noticeable with ordinary shadow maps. Our algorithm computes shadows efficiently in image space and maps well to programmable graphics hardware. We present results from several example scenes rendered in real-time.

Real-time programmable graphics hardware has resource constraints that prevent complex shaders from rendering in a single pass. One way to virtualize these resources is to partition shading computations into multiple passes, each of which satisfies the given constraints. Many such partitions exist for a shader, but it is important to find one that renders efficiently. We present Recursive Dominator Split (RDS), a polynomial-time algorithm that uses a cost model to find near-optimal partitions of arbitrarily complex shaders. Using a simulator, we analyze partitions for architectures with different resource constraints and show that RDS performs well on different graphics architectures. We also demonstrate that shader partitions computed by RDS can run efficiently on programmable graphics hardware available today.