Extending PRT Framework for Lowly-Tessellated and Continuous Surfaces

Abstract

Precomputed Radiance Transfer (PRT) is widely used for real-time photorealistic effects. PRT disentangles the rendering equation into transfer and lighting, enabling their precomputation. Transfer accounts for the cosine-weighted visibility of points in the scene, while Lighting is usually a distant emitted lighting, e.g., environment. Transfer computation involves tracing several rays into the scene from every point on the surface. For every ray, the binary visibility is calculated, and a spherical function is obtained. The spherical function is projected into Spherical Harmonic(SH) domain. SH is a band-limited representation of spherical functions, and the order of SH decides the representation capacity of the SH (the higher the SH order better the approximation of a spherical function). The SH domain also facilitates fast and efficient integral computation by simplifying the integral into simple dot products and convolutions. The original formulation of PRT by Sloan et al. 2002 provides different storage requirements for the transfer—vectors in the case of diffuse materials and matrices in the case of glossy materials. Using matrices for Transfer representation makes it infeasible as the SH orders increase. The work of Triple Product Formulation by Ng et al. in 2004 extended the formulation to allow simple vector-based Transfer storage even for the case of glossy materials. Prior art stored precomputed transfer in a tabulated manner in vertex space. These values are fetched with interpolation at each point for shading. Since the barycentric interpolation is finally employed to calculate the final color across the geometry apart from the vertex locations, the vertex space methods require densely tessellated mesh vertices to obtain accurate radiance. Sometimes high-density(tessellated) meshes adversely affect runtimes and memory requirements. This is mainly observed in simple geometries with no additional detailing but still demanding higher triangle counts (e.g., planes, walls, etc.). The first work provides a solution by leveraging Texture space, which is more continuous than the Vertex space. We also added additional functionality to obtain inter-reflection effects in the texture space. While Texture space methods provide faithful results in meshes, they require non-overlapping, areapreserving UV mapping, and a high-resolution texture to avoid artifacts. In the subsequent work, we propose a compact transfer representation that is learnt directly on scene geometry points. Specifically, we train a small multi-layer perceptron (MLP) to predict the transfer at sampled surface points. Our approach is most beneficial where inherent mesh storage structure and natural UV mapping are unavailable, such as Implicit Surfaces, as it learns the transfer values directly on the surface. Using our approach, we demonstrate real-time, photorealistic renderings of diffuse and glossy materials on SDF geometries with PRT.