Precomputed Radiance Transfer for Real-Time Rendering in Dynamic, Low-Frequency Lighting Environments Peter-Pike Sloan Jan Kautz John Snyder Microsoft Research [email protected] Max-Planck-Institut für Informatik [email protected] Microsoft Research [email protected] Abstract We present a new, real-time method for rendering diffuse and glossy objects in low-frequency lighting environments that cap-tures soft shadows, interreflections, and caustics. As a preprocess, a novel global transport simulator creates functions over the object’s surface representing transfer of arbitrary, low-frequency incident lighting into transferred radiance which includes global effects like shadows and interreflections from the object onto itself. At run-time, these transfer functions are applied to actual incident lighting. Dynamic, local lighting is handled by sampling it close to the object every frame; the object can also be rigidly rotated with respect to the lighting and vice versa. Lighting and transfer functions are represented using low-order spherical harmonics. This avoids aliasing and evaluates efficiently on graphics hardware by reducing the shading integral to a dot product of 9 to 25 element vectors for diffuse receivers. Glossy objects are handled using matrices rather than vectors. We further introduce functions for radiance transfer from a dynamic lighting environment through a preprocessed object to neighboring points in space. These allow soft shadows and caustics from rigidly moving objects to be cast onto arbitrary, dynamic receivers. We demonstrate real-time global lighting effects with this approach. Keywords: Graphics Hardware, Illumination, Monte Carlo Techniques, Rendering, Shadow Algorithms. 1. Introduction Lighting from area sources, soft shadows, and interreflections are important effects in realistic image synthesis. Unfortunately, general methods for integrating over large-scale lighting environ-ments [8], including Monte Carlo ray tracing [7][21][25], rad-iosity [6], or multi-pass rendering that sums over multiple point light sources [17][27][36], are impractical for real-time rendering. Real-time, realistic global illumination encounters three difficul-ties – it must model the complex, spatially-varying BRDFs of real materials (BRDF complexity), it requires integration over the hemisphere of lighting directions at each point (light integration), and it must account for bouncing/occlusion effects, like shadows, due to intervening matter along light paths from sources to receiv-ers (light transport complexity). Much research has focused on extending BRDF complexity (e.g., glossy and anisotropic reflec-tions), solving the light integration problem by representing incident lighting as a sum of directions or points. Light integra-tion thus tractably reduces to sampling an analytic or tabulated BRDF at a few points, but becomes intractable for large light sources. A second line of research samples radiance and pre-convolves it with kernels of various sizes [5][14][19][24][34]. This solves the light integration problem but ignores light trans-port complexities like shadows since the convolution assumes the incident radiance is unoccluded and unscattered. Finally, clever techniques exist to simulate more complex light transport, espe-cially shadows. Light integration becomes the problem; these techniques are impractical for very large light sources. Our goal is to better account for light integration and light trans-port complexity in real-time. Our compromise is to focus on low-frequency lighting environments, using a low-order spherical harmonic (SH) basis to represent such environments efficiently without aliasing. The main idea is to represent how an object scatters this light onto itself or its neighboring space. To describe our technique, assume initially we have a convex, diffuse object lit by an infinitely distant environment map. The object’s shaded “response” to its environment can be viewed as a transfer function, mapping incoming to outgoing radiance, which in this case simply performs a cosine-weighted integral. A more complex integral captures how a concave object shadows itself, where the integrand is multiplied by an additional transport factor representing visibility along each direction. Our approach is to precompute for a given object the expensive transport simulation required by complex transfer functions like shadowing. The resulting transfer functions are represented as a dense set of vectors or matrices over its surface. Meanwhile, incident radiance need not be precomputed. The graphics hard-ware can dynamically sample incident radiance at a number of points. Analytic models, such as skylight models [33] or simple geometries like circles, can also be used. By representing both incident radiance and transfer functions in a linear basis (in our case, SH), we exploit the linearity of light transport to reduce the light integral to a simple dot product between their coefficient vectors (diffuse receivers) or a simple linear transform of the lighting coefficient vector through a small transfer matrix (glossy receivers). Low-frequency lighting envi-ronments require few coefficients (9-25), enabling graphics hardware to compute the result in a single pass (Figure 1, right). Unlike Monte-Carlo and multi-pass light integration methods, our run-time computation stays constant no matter how many or how big the light sources, and in fact relies on large-scale, smooth lighting to limit the number of SH coefficients necessary. We represent complex transport effects like interreflections and caustics in the transfer function. Since these are simulated as a preprocess, only the transfer function’s basis coefficients are affected, not the run-time computation. Our approach handles both surface and volume-based geometry. With more SH coeffi-cients, we can even handle glossy (but not highly specular) receivers as well as diffuse, including interreflection. 25 coeffi-cients suffice for useful glossy effects. In addition to transfer from a rigid object to itself, called self-transfer, we generalize the technique to neighborhood-transfer from a rigid object to its neighboring space, allowing cast soft shadows, glossy reflections, and caustics on dynamic receivers, see Figure 7. Figure 1: Precomputed, unshadowed irradiance from [34] (left) vs. our precomputed transfer (right). The right model can
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