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.
@cite_11 parameterized the spherical functions using geometry maps @cite_132 and provided a solution for wavelet rotation using precomputed rotation matrices. They precomputed and stored the rotation matrices and used them to rotate the light coefficients into the local space of the BRDF. However, their solution was brute force rather than analytic, since it would be impossible to derive rotation formulae for the frequency domain with the geometry map representation.
@cite_132 @cite_11
2026173400 2111999986 2171798031 2076669957
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. 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. In some applications, it is reasonable to assume that geodesics (rays) have a consistent orientation so that the Helmholtz equation may be viewed as an evolution equation in one of the spatial directions. With such applications in mind, we propose a new Eulerian computational geometrical-optics method, dubbed the fast Huygens sweeping method, for computing Green functions of Helmholtz equations in inhomogeneous media in the high-frequency regime and in the presence of caustics. The first novelty of the new method is that the Huygens–Kirchhoff secondary source principle is used to integrate many locally valid asymptotic solutions to yield a globally valid asymptotic solution so that caustics associated with the usual geometrical-optics ansatz can be treated automatically. The second novelty is that a butterfly algorithm is adapted to carry out the matrix–vector products induced by the Huygens–Kirchhoff integration in O(NlogN) operations, where N is the total number of mesh points, and the proportionality constant depends on the desired accuracy and is independent of the frequency parameter. To reduce the storage of the resulting traveltime and amplitude tables, we compress each table into a linear combination of tensor-product based multivariate Chebyshev polynomials so that the information of each table is encoded into a small number of Chebyshev coefficients. The new method enjoys the following desired features: (1) it precomputes a set of local traveltime and amplitude tables; (2) it automatically takes care of caustics; (3) it constructs Green functions of the Helmholtz equation for arbitrary frequencies and for many point sources; (4) for a specified number of points per wavelength it constructs each Green function in nearly optimal complexity in terms of the total number of mesh points, where the prefactor of the complexity only depends on the specified accuracy and is independent of the frequency parameter. Both two-dimensional (2-D) and three-dimensional (3-D) numerical experiments are presented to demonstrate the performance and accuracy of the new method. 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.