Abstract We introduce a discrete polydisperse micrograin BSDF model for the rendering of porous surface materials composed of microscopic elements of different size, shape and reflectance distributed on a bulk medium. Our approach generalizes the anisotropic monodisperse micrograin model We first reformulate it in a non‐axis‐aligned configuration, allowing for the later combination of different micrograin types elongated in arbitrary directions. We then extend the monodisperse model to the polydisperse case, deriving its three key components: (i) a general filling factor that controls the mix between micrograins and the bulk medium; (ii) an exact normal distribution function for surfaces composed of polydisperse micrograin distributions; and (iii) the corresponding fully‐correlated shadowing and masking term. This results in an analytical single‐scattering BSDF for discrete polydisperse surface materials, validated over ground truth simulations, for which we also derive a dedicated importance sampling procedure. Our model supports varying heights and anisotropy orientations of different micrograin types as input, giving additional control to simulate phenomena like retro‐reflection from mixed materials, color mixture depending on lighting and observation directions, multiple directions of anisotropy, etc.

Abstract Real‐time rendering of complex environments and detailed objects is challenging due to the geometric generation cost and its associated memory requirements. Traditional methods often rely on precomputed procedural details, limiting flexibility and realtime interaction. Although state‐of‐the‐art approaches have addressed these questions, they frequently fall short in providing dynamic, high‐fidelity surface transformations. This article presents a novel real‐time procedural mesh resurfacing method that utilizes GPU mesh shaders to generate a wide range of geometrical appearances directly in place of a base control mesh. Our approach enables on‐the‐fly procedural geometry generation, allowing for the creation of new explicit geometric surfaces, fine control over geometric adjustments, and dynamic level of detail management. Procedural parameters can be accurately driven in real time by explicit control maps or arbitrary user inputs. The proposed technique reduces VRAM usage and power consumption, offering competitive performance compared to traditional pipelines. Comparative evaluations demonstrate that it enables a significantly higher number of primitives to be rendered in real‐time without being limited by GPU memory. The key advantage of the proposed resurfacing framework lies in its ability to fully control dynamic generation of surfaces at rendertime.

Reflectance models capture many types of visual appearances. The most plausible reflectance models follow the Microfacet theory, which is specifically based on statistical representations, with an analytic visibility term. This visibility term has a significant impact on appearance. Visibility computed with the masking term proposed by Smith (1967), and revisited by Ashikhmin et al. (2000), is nowadays considered as the most plausible in the literature. It is simple and efficient to evaluate for statistical distributions, but it relies on assumptions that are not necessarily respected by real surfaces. This article proposes an in-depth study of masking for meshed height-field surfaces, generated either from measured real-world materials or from functions derived from distributions of surface normals. We experimentally estimate the masking (and shadowing) of surfaces using a ray-casting technique, and compare their measurements with the theoretical model from Smith and Ashikhmin et al. We show that their assumptions are too restrictive for a majority of real-world surfaces. We propose a model capable of predicting how close the theoretical masking term can be from the masking term estimated by a ray-casting approach. Although most surfaces break their assumptions, our results show that the term from Smith and Ashikhmin et al. can still be reasonably employed for a fraction in a set of more than 400 measured surfaces, with low errors compared to a ray-casting masking estimation, much lower computation times, and very similar visual appearances. Our model can be used to predict the incurred error on a physically-based rendering simulation with a microfacet-based BRDF created from real-world surfaces, instead of explicitly calculating the masking term from its height field.

We introduce an improved version of the micrograin BSDF model [Lucas et al. 2023] for the rendering of anisotropic porous layers. Our approach leverages the properties of micrograins to take into account the correlation between their height and normal, as well as the correlation between the light and view directions. This allows us to derive an exact analytical expression for the Geometrical Attenuation Factor (GAF), summarizing shadowing and masking inside the porous layer. This fully-correlated GAF is then used to define appropriate mixing weights to blend the BSDFs of the porous and base layers. Furthermore, by generalizing the micrograins shape to anisotropy, combined with their fully-correlated GAF, our improved BSDF model produces effects specific to porous layers such as retro-reflection visible on dust layers at grazing angles or height and color correlation that can be found on rusty materials. Finally, we demonstrate very close matches between our BSDF model and light transport simulations realized with explicit instances of micrograins, thus validating our model.

We introduce a new BSDF model for the rendering of porous layers, as found on surfaces covered by dust, rust, dirt, or sprayed paint. Our approach is based on a distribution of elliptical opaque micrograins, extending the Trowbridge-Reitz (GGX) distribution [Trowbridge and Reitz 1975; Walter et al. 2007] to handle pores (i.e., spaces between micrograins). We use distance field statistics to derive the corresponding Normal Distribution Function (NDF) and Geometric Attenuation Factor (GAF), as well as a view- and light-dependent filling factor to blend between the porous and base layers. All the derived terms show excellent agreement when compared against numerical simulations.

Abstract Man‐made objects commonly exhibit rounded edges and corners generated through their manufacturing processes. The variation of surface normals at these confined locations produces shading details that are visually essential to the realism of synthetic scenes. The more specular the surface, the finer and more prominent its highlights. However, most geometric modellers represent rounded edges and corners with dense polygonal meshes that are limited in terms of smoothness, while tremendously increasing scene complexity. This paper proposes a non‐invasive method (i.e. that does not modify the original geometry) for the modelling and rendering of smooth edges and corners from any input polygonal geometry defined with infinitely sharp edges. At the heart of our contribution is a geometric structure that automatically and accurately defines the geometry of edge and corner rounded areas, as well as the topological relationships at edges and vertices. This structure, called SREC‐RT, is integrated in a ray‐tracing‐based acceleration structure in order to determine the region of interest of each rounded edge and corner. It allows systematic rounding of all edges and vertices without increasing the 3D scene geometric complexity. While the underlying rounded geometry can be of any type, we propose a practical ray‐edge and ray‐corner intersection based on parametric surfaces. We analyse comparisons generated with existing methods. Our results present the advantages of our method, including extreme close‐up views of surfaces with a much higher quality for very little additional memory, and reasonable computation time overhead.

Microfacet distributions are considered nowadays as a reference for physically plausible BSDF representations. Many authors have focused on their physical and mathematical correctness, while introducing means to enlarge the range of possible appearances. This article is dedicated to Normal Distribution Functions (NDFs) and the influence of their shape on the rendered material aspect. We provide a complete framework for studying the impact of NDFs on the observed Bidirectional Scattering Distribution Functions (BSDFs). To explore very general NDFs, manually controlled by the user, and including anisotropic materials, we propose to use a piecewise continuous representation. It is derived with its associated Smith shadowing-masking function and importance sampling formulations for ensuring efficient global illumination computations. A new procedure is also proposed in this article for generating an explicit geometric micro-surface, used to evaluate the validity of analytic models and multiple scattering effects. The results are produced with a computer-generated process using path tracing. They show that this generation procedure is suitable with any NDF model, independently from its shape complexity.

Specular microfacet distributions have been successfully employed by many authors for representing glossiness of materials. They are generally combined with a Lambertian term to account for the colored aspect. These representations make use of the Fresnel reflectance factor at the interface, but the transmission factor at the interface should also be managed. One solution is to employ a multi-layered model with a single layer for the rough interface, which requires a numerical simulation for handling the multiple reflections of light between the substrate and the interface. In this paper, we propose rather to use a representation corresponding to a Fresnel interface lying on a Lambertian substrate, for which the multiple reflections of light between the interface and the substrate can be expressed analytically. With this interfaced Lambertian model, we show how Fresnel transmission affects the material appearance for flat and rough surfaces with isotropic and anisotropic distributions, that produce light backscattering effects. We also propose a methodology for using such materials in any physically based Monte Carlo rendering system, as well as an approximate representation, suitable for GPU applications or measured data fitting. Our approach generalizes several previous models, including flat Lambertian materials as well as specular and Lambertian microfacets. Our results illustrate the wide range of materials that can be rendered with this representation.

This paper focuses on microfacet reflectance models, and more precisely on the definition of a new and more general distribution function, which includes both Beckmann's and GGX distributions widely used in the computer graphics community. Therefore, our model makes use of an additional parameter γ, which controls the distribution function slope and tail height. It actually corresponds to a bivariate Student's t-distribution in slopes space and it is presented with the associated analytical formulation of the geometric attenuation factor derived from Smith representation. We also provide the analytical derivations for importance sampling isotropic and anisotropic materials. As shown in the results, this new representation offers a finer control of a wide range of materials, while extending the capabilities of fitting parameters with captured data.

The human visual system is sensitive to relative differences in luminance, but light transport simulation algorithms based on Metropolis sampling often result in a highly nonuniform relative error distribution over the rendered image. Although this issue has previously been addressed in the context of the Metropolis light transport algorithm, our work focuses on Metropolis photon tracing. We present a new target function (TF) for Metropolis photon tracing that ensures good stratification of photons leading to pixel estimates with equalized relative error. We develop a hierarchical scheme for progressive construction of the TF from paths sampled during rendering. In addition to the approach taken in previous work, where the TF is defined in the image plane, ours can be associated with compact spatial regions. This allows us to take advantage of illumination coherence to more robustly estimate the TF while adapting to geometry discontinuities. To sample from this TF, we design a new replica exchange Metropolis scheme. We apply our algorithm in progressive photon mapping and show that it often outperforms alternative approaches in terms of image quality by a large margin.

Abstract Color adaptation is a well known ability of the human visual system (HVS). Colors are perceived as constant even though the illuminant color changes. Indeed, the perceived color of a diffuse white sheet of paper is still white even though it is illuminated by a single orange tungsten light, whereas it is orange from a physical point of view. Unfortunately global illumination algorithms only focus on the physics aspects of light transport. The ouput of a global illuminantion engine is an image which has to undergo chromatic adaptation to recover the color as perceived by the HVS. In this paper, we propose a new color adaptation method well suited to global illumination. This method estimates the adaptation color by averaging the irradiance color arriving at the eye. Unlike other existing methods, our approach is not limited to the view frustrum, as it considers the illumination from all the scene. Experiments have shown that our method outperforms the state of the art methods.

Abstract Quasi‐Monte Carlo (QMC) methods exhibit a faster convergence rate than that of classic Monte Carlo methods. This feature has made QMC prevalent in image synthesis, where it is frequently used for approximating the value of spherical integrals (e.g. illumination integral). The common approach for generating QMC sampling patterns for spherical integration is to resort to unit square low‐discrepancy sequences and map them to the hemisphere. However such an approach is suboptimal as these sequences do not account for the spherical topology and their discrepancy properties on the unit square are impaired by the spherical projection. In this paper we present a strategy for producing high‐quality QMC sampling patterns for spherical integration by resorting to spherical Fibonacci point sets. We show that these patterns, when applied to illumination integrals, are very simple to generate and consistently outperform existing approaches, both in terms of root mean square error (RMSE) and image quality. Furthermore, only a single pattern is required to produce an image, thanks to a scrambling scheme performed directly in the spherical domain.

The Monte Carlo method has proved to be very powerful to cope with global illumination problems but it remains costly in terms of sampling operations. In various applications, previous work has shown that Bayesian Monte Carlo can significantly outperform importance sampling Monte Carlo thanks to a more effective use of the prior knowledge and of the information brought by the samples set. These good results have been confirmed in the context of global illumination but strictly limited to the perfect diffuse case. Our main goal in this paper is to propose a more general Bayesian Monte Carlo solution that allows dealing with nondiffuse BRDFs thanks to a spherical Gaussian-based framework. We also propose a fast hyperparameters determination method that avoids learning the hyperparameters for each BRDF. These contributions represent two major steps toward generalizing Bayesian Monte Carlo for global illumination rendering. We show that we achieve substantial quality improvements over importance sampling at comparable computational cost.

Abstract Local Principal Component Analysis (LPCA) is one of the popular techniques for dimensionality reduction and data compression of large data sets encountered in computer graphics. The LPCA algorithm is a variant of k‐means clustering where the repetitive classification of high dimensional data points to their nearest cluster leads to long execution times. The focus of this paper is on improving the efficiency and accuracy of LPCA. We propose a novel SortCluster LPCA algorithm that significantly reduces the cost of the point‐cluster classification stage, achieving a speed‐up of up to 20. To improve the approximation accuracy, we investigate different initialization schemes for LPCA and find that the k‐means++ algorithm [ AV07 ] yields best results, however at a high computation cost. We show that similar ideas that lead to the efficiency of our SortCluster LPCA algorithm can be used to accelerate k‐means++. The resulting initialization algorithm is faster than purely random seeding while producing substantially more accurate data approximation.

Abstract Irradiance Caching is one of the most widely used algorithms to speed up global illumination. In this paper, we propose an algorithm based on the Irradiance Caching scheme that allows us (1) to adjust the density of cached records according to illumination changes and (2) to efficiently render the high‐frequency illumination changes. To achieve this, a new record footprint is presented. Although the original method uses records having circular footprints depending only on geometrical features, our record footprints have a more complex shape which accounts for both geometry and irradiance variations. Irradiance values are computed using a classical Monte Carlo ray tracing method that simplifies the determination of nearby objects and the pre‐computation of the shape of the influence zone of the current record. By gathering irradiance due to all the incident rays, illumination changes are evaluated to adjust the footprint’s records. As a consequence, the record footprints are smaller where illumination gradients are high. With this technique, the record density depends on the irradiance variations. Strong variations of irradiance (due to direct contributions for example) can be handled and evaluated accurately. Caching direct illumination is of high importance, especially in the case of scenes having many light sources with complex geometry as well as surfaces exposed to daylight. Recomputing direct illumination for the whole image can be very time‐consuming, especially for walkthrough animation rendering or for high‐resolution pictures. Storing such contributions in the irradiance cache seems to be an appropriate solution to accelerate the final rendering pass.