This paper focuses on real-time all-frequency image-based rendering using an innovative solution for run-time computation of light transport. The approach is based on new results derived for non-linear phase shifting in the Haar wavelet domain. Although image-based methods for real-time rendering of dynamic glossy objects have been proposed, they do not truly scale to all possible frequencies and high sampling rates without trading storage, glossiness, or computational time, while varying both lighting and viewpoint. This is due to the fact that current approaches are limited to precomputed radiance transfer (PRT), which is prohibitively expensive in terms of memory requirements and real-time rendering when both varying light and viewpoint changes are required together with high sampling rates for high frequency lighting of glossy material. On the other hand, current methods cannot handle object rotation, which is one of the paramount issues for all PRT methods using wavelets. This latter problem arises because the precomputed data are defined in a global coordinate system and encoded in the wavelet domain, while the object is rotated in a local coordinate system. At the root of all the above problems is the lack of efficient run-time solution to the nontrivial problem of rotating wavelets (a non-linear phase-shift), which we solve in this paper.
Imposing constraints to simplify the integral to achieve real-time or interactive rates is a necessity with spherical harmonics, when glossy or general BRDF's are used. One method is to use low sampling rates, which is equivalent to band-limiting the illumination. This approach is used by in @cite_159 , @cite_0 and @cite_52 . However, band-limiting removes high frequency components, which blurs lighting detail. For diffuse materials, the error can be very low @cite_166 . However, this approach is not suitable for glossy materials, which need the high frequency for an efficient representation. Another approach is to reduce the dimensionality of the problem by fixing the light or the viewing direction as in @cite_2 . This approach, however, restricts the dynamics of the scene.
@cite_159 @cite_52 @cite_0 @cite_166 @cite_2
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This paper focuses on efficient rendering based on pre-computed light transport, with realistic materials and shadows under all-frequency direct lighting such an environment maps. The basic difficulty is representation and computation in the 6D space of light direction, view direction, and surface position. While image-based and synthetic methods for real-time rendering have been proposed, they do not scale to high sampling rates with variation of both lighting and viewpoint. Current approaches are therefore limited to lower dimensionality (only lighting or viewpoint variation, not both) or lower sampling rates (low frequency lighting and materials). We propose a new mathematical and computational analysis of pre-computed light transport. We use factored forms, separately pre-computing and representing visibility and material properties. Rendering then requires computing triple product integrals at each vertex, involving the lighting, visibility and BRDF. Our main contribution is a general analysis of these triple product integrals, which are likely to have broad applicability in computer graphics and numerical analysis. We first determine the computational complexity in a number of bases like point samples, spherical harmonics and wavelets. We then give efficient linear and sublinear-time algorithms for Haar wavelets, incorporating non-linear wavelet approximation of lighting and BRDFs. Practically, we demonstrate rendering of images under new lighting and viewing conditions in a few seconds, significantly faster than previous techniques. Real-time shading with environment maps requires the ability to rotate the global lighting to each surface point's local coordinate frame. Although extensive previous work has studied rotation of functions represented by spherical harmonics, little work has investigated efficient rotation of wavelets. Wavelets are superior at approximating high frequency signals such as detailed high dynamic range lighting and very shiny BRDFs, but present difficulties for interactive rendering due to the lack of an analytic solution for rotation. In this paper we present an efficient computational solution for wavelet rotation using precomputed matrices. Each matrix represents the linear transformation of source wavelet bases defined in the global coordinate frame to target wavelet bases defined in sampled local frames. Since wavelets have compact support, these matrices are very sparse, enabling efficient storage and fast computation at run-time. In this paper, we focus on the application of our technique to interactive environment map rendering. We show that using these matrices allows us to evaluate the integral of dynamic lighting with dynamic BRDFs at interactive rates, incorporating efficient non-linear approximation of both illumination and reflection. Our technique improves on previous work by eliminating the need for prefiltering environment maps, and is thus significantly faster for accurate rendering of dynamic environment lighting with high frequency reflection effects. We present a new, real-time method for rendering diffuse and glossy objects in low-frequency lighting environments that captures 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. Real-time shading using general (e.g., anisotropic) BRDFs has so far been limited to a few point or directional light sources. We extend such shading to smooth, area lighting using a low-order spherical harmonic basis for the lighting environment. We represent the 4D product function of BRDF times the cosine factor (dot product of the incident lighting and surface normal vectors) as a 2D table of spherical harmonic coefficients. Each table entry represents, for a single view direction, the integral of this product function times lighting on the hemisphere expressed in spherical harmonics. This reduces the shading integral to a simple dot product of 25 component vectors, easily evaluatable on PC graphics hardware. Non-trivial BRDF models require rotating the lighting coefficients to a local frame at each point on an object, currently forming the computational bottleneck. Real-time results can be achieved by fixing the view to allow dynamic lighting or vice versa. We also generalize a previous method for precomputed radiance transfer to handle general BRDF shading. This provides shadows and interreflections that respond in real-time to lighting changes on a preprocessed object of arbitrary material (BRDF) type.