Clustered principal components for precomputed radiance transfer

Abstract

We compress storage and accelerate performance of precomputed radiance transfer (PRT), which captures the way an object shadows, scatters, and reflects light. PRT records over many surface points a transfer matrix. At run-time, this matrix transforms a vector of spherical harmonic coefficients representing distant, low-frequency source lighting into exiting radiance. Per-point transfer matrices form a high-dimensional surface signal that we compress using clustered principal component analysis (CPCA), which partitions many samples into fewer clusters each approximating the signal as an affine subspace. CPCA thus reduces the high-dimensional transfer signal to a low-dimensional set of perpoint weights on a per-cluster set of representative matrices. Rather than computing a weighted sum of representatives and applying this result to the lighting, we apply the representatives to the lighting per-cluster (on the CPU) and weight these results perpoint (on the GPU). Since the output of the matrix is lowerdimensional than the matrix itself, this reduces computation. We also increase the accuracy of encoded radiance functions with a new least-squares optimal projection of spherical harmonics onto the hemisphere. We describe an implementation on graphics hardware that performs real-time rendering of glossy objects with dynamic self-shadowing and interreflection without fixing the view or light as in previous work. Our approach also allows significantly increased lighting frequency when rendering diffuse objects and includes subsurface scattering.

View-dependent precomputed light transport using nonlinear Gaussian function approximations

“…We represent the diffuse component using 5th order linear spherical harmonics, however any other suitable technique could easily be used (e.g. [22,28]). …”

“…Current methods address this issue with compromises between bandwidth (or sharpness) of the illumination effects, storage costs, and rendering time. In this thesis we focus on view-dependent effects, such as glossy reflections or refractions, since view-independent effects like shadows can be handled with known techniques [22,28]. View-dependent effects are harder to address because they involve variation over the full 6D domain, and highlights can vary quickly over space and view direction, which may result in cross-fading artifacts when linear interpolation is used between views or mesh vertices.…”

Real-time triple product relighting using spherical local-frame parameterization

“…dering for rich lighting effects, such as precomputed radiance transfer using spherical harmonics by Sloan et al [15,16] and all-frequency relighting using wavelets by Ng et al [8,9]. The former allows changing lighting and viewpoint in real-time, but limited to low-frequency illumination.…”

“…In addition, it greatly reduces the data size compared to storing BRDF in the global frame. Local-frame parameterization has been used in spherical harmonics-based relighting [15]. For spherical harmonics, it is an obvious choice since spherical harmonics can be easily rotated and every function should just be parameterized in its natural domain, global for lighting and local for BRDFs.…”

“…Most PRT papers use spherical harmonics as the basis function [5,6,11,[15][16][17]. Using a local frame for shading is widely adopted in spherical-harmonics-based PRT techniques [5,6,15,17] because spherical harmonics basis has a good rotational property. Bump mapping [14] and anisotropic BRDFs [5] can be integrated into spherical harmonics PRT framework.…”