All-frequency lighting with multiscale spherical radial basis functions

Hemispherical harmonic illumination and reflectance angular spectrum

Light scattering plays an important role in physics, with wide applications in science and engineering. However, accurate and effective modeling of scattering remains a great challenge. In this study, we exploited the rendering equation using hemispherical harmonics to demonstrate an angular frequency representation that directly depicts scattering in a two-dimensional spectrum, free from any underlying assumptions. This representation offers a compact and intuitive characterization of mirror reflection, isotropic scattering, and anisotropic emission. The robust support of theoretical proofs and data-driven experimental results establishes the broad applicability of our computational model in conducting scattering analyses across diffuse, specular, and glossy materials. With the capability to characterize the scattering in angular frequency domain, we expect our proposed model to emerge as an essential tool in various domains, including surface feature recognition, reflectance data compression, and computer rendering.

All-Frequency Direct Illumination with Vectorized Visibility

Many existing pre-computed radiance transfer (PRT) approaches for all-frequency lighting store the information of a 3D object in the pre-vertex manner. To preserve the fidelity of high frequency effects, the 3D object must be tessellated densely. Otherwise, rendering artifacts due to interpolation may appear. This paper presents an all-frequency lighting algorithm for direct illumination based on a new visibility representation which approximates a visibility function using a sequence of 3D vectors. The algorithm is able to construct the visibility function of an on-screen pixel on-the-fly. Hence even though the 3D object is not tessellated densely, the rendering artifacts can be suppressed greatly. Besides, a summed area table based rendering algorithm, which is able to handle the integration over a non-axis aligned polygon, is developed. Using our approach, we can rotate lighting environment, change view point, and adjust the shininess of the 3D object in a real-time manner. Experimental results show that our approach can render plausible all-frequency lighting effects for direct illumination in real-time, especially for specular shadows, which are difficult for other methods to obtain.

Using Radial Basis Function Networks for Function Approximation and Classification

The radial basis function (RBF) network has its foundation in the conventional approximation theory. It has the capability of universal approximation. The RBF network is a popular alternative to the well-known multilayer perceptron (MLP), since it has a simpler structure and a much faster training process. In this paper, we give a comprehensive survey on the RBF network and its learning. Many aspects associated with the RBF network, such as network structure, universal approimation capability, radial basis functions, RBF network learning, structure optimization, normalized RBF networks, application to dynamic system modeling, and nonlinear complex-valued signal processing, are described. We also compare the features and capability of the two models.