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.
The traditional approach for parametrizing a surface involves cutting it into charts and mapping these piecewise onto a planar domain. We introduce a robust technique for directly parametrizing a genus-zero surface onto a spherical domain. A key ingredient for making such a parametrization practical is the minimization of a stretch-based measure, to reduce scale-distortion and thereby prevent undersampling. Our second contribution is a scheme for sampling the spherical domain using uniformly subdivided polyhedral domains, namely the tetrahedron, octahedron, and cube. We show that these particular semi-regular samplings can be conveniently represented as completely regular 2D grids, i.e. geometry images. Moreover, these images have simple boundary extension rules that aid many processing operations. Applications include geometry remeshing, level-of-detail, morphing, compression, and smooth surface subdivision. 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.