This paper proposes a lightweight bidirectional scattering distribution function (BSDF) model for layered materials with anisotropic reflection and refraction properties. In our method, each layer of the materials can be described by a microfacet BSDF using an anisotropic normal distribution function (NDF). Furthermore, the NDFs of layers can be defined on tangent vector fields, which differ from layer to layer. Our method is based on a previous study in which isotropic BSDFs are approximated by projecting them onto base planes. However, the adequateness of this previous work has not been well investigated for anisotropic BSDFs. In this paper, we demonstrate that the projection is also applicable to anisotropic BSDFs and that the BSDFs are approximated by elliptical distributions using covariance matrices.

Shading filtering proposed by Kaplanyan et al. [2016] is a simple solution for specular aliasing. It filters a distribution of microfacet normals in the domain of microfacet slopes by estimating the filtering kernel using derivatives of a halfway vector between incident and outdoing directions. However, for real-time rendering, this approach can produce noticeable artifacts because of an estimation error of derivatives. For forward rendering, this estimation error is increased significantly at grazing angles and near edges. The present work improves the quality of the original technique, while decreasing the complexity of the code at the same time. To reduce the error, we introduce a more efficient kernel bandwidth that takes the angle of the halfvector into account. In addition, we optimize the calculation of an isotropic filter kernel used for deferred rendering by applying the proposed kernel bandwidth. As our implementation is simpler than the original method, it is easier to integrate in time-sensitive applications, such as game engines, while at the same time improving the filtering quality.

While bidirectional path tracing is a well-established light transport algorithm, many samples are required to obtain high-quality results for specular-diffuse-glossy or glossy-diffuse-glossy reflections especially when they are highly glossy. To improve the efficiency for such light path configurations, we propose a hierarchical Russian roulette technique for vertex connections. Our technique accelerates a huge number of Russian roulette operations according to an approximate scattering lobe at an eye-subpath vertex for many cached light-subpath vertices. Our method dramatically reduces the number of random number generations needed for Russian roulette by introducing a hierarchical rejection algorithm which assigns random numbers in a top-down fashion. To efficiently reject light vertices in each hierarchy, we also introduce an efficient approximation of anisotropic scattering lobes used for the probability of Russian roulette. Our technique is easy to integrate into some existing bidirectional path tracing-based algorithms which cache light-subpath vertices (e.g., probabilistic connections, and vertex connection and merging). In addition, unlike existing many-light methods, our method does not restrict multiple importance sampling strategies thanks to the simplicity of Russian roulette. Although the proposed technique does not support perfectly specular surfaces, it significantly improves the efficiency for caustics reflected on extremely glossy surfaces in an unbiased fashion.

Abstract This paper introduces a real‐time rendering method for single‐bounce glossy caustics created by GGX microsurfaces. Our method is based on stochastic light culling of virtual point lights (VPLs), which is an unbiased culling method that randomly determines the range of influence of light for each VPL. While the original stochastic light culling method uses a bounding sphere defined by that light range for coarse culling (e.g., tiled culling), we have further extended the method by calculating a tighter bounding ellipsoid for glossy VPLs. Such bounding ellipsoids can be calculated analytically under the classic Phong reflection model which cannot be applied to physically plausible materials used in modern computer graphics productions. In order to use stochastic light culling for such modern materials, this paper derives a simple analytical solution to generate a tighter bounding ellipsoid for VPLs on GGX microsurfaces. This paper also presents an efficient implementation for culling bounding ellipsoids in the context of tiled culling. When stochastic light culling is combined with interleaved sampling for a scene with tens of thousands of VPLs, this tiled culling is faster than conservative rasterization‐based clustered shading which is a state‐of‐the‐art culling technique that supports bounding ellipsoids. Using these techniques, VPLs are culled efficiently for completely dynamic single‐bounce glossy caustics reflected from GGX microsurfaces.

This paper proposes a modification of the filtered importance sampling method, and improves the quality of virtual spherical Gaussian light (VSGL)-based real-time glossy indirect illumination using this modification. The original filtered importance sampling method produces large overlaps of and gaps between filtering kernels for high-frequency probability density functions (PDFs). This is because the size of the filtering kernel is determined using the PDF at the sampled center of the kernel. To reduce those overlaps and gaps, this paper determines the kernel size using the integral of the PDF within the filtering kernel. Our key insight is that these integrals are approximately constant, if kernel centers are sampled using stratified sampling. Therefore, an appropriate kernel size can be obtained by solving this integral equation. Using the proposed kernel size for filtered importance sampling-based VSGL generation, undesirable artifacts are significantly reduced with a negligibly small overhead.

Abstract Although geometry‐aware filtering and upsampling have often been used for interactive or real‐time rendering, they are unsuitable for glossy surfaces because shading results strongly depend on the bidirectional reflectance distribution functions. This paper proposes a novel weighting function of cross bilateral filtering and upsampling to measure the similarity of specular lobes. The difficulty is that a specular lobe is represented with a distribution function in directional space, whereas conventional cross bilateral filtering evaluates similarities using the distance between two points in a Euclidean space. Therefore, this paper first generalizes cross bilateral filtering for the similarity of distribution functions in a non‐Euclidean space. Then, the weighting function is specialized for specular lobes. Our key insight is that the weighting function of bilateral filtering can be represented with the product integral of two distribution functions corresponding to two pixels. In addition, we propose spherical Gaussian‐based approximations to calculate this weighting function analytically. Our weighting function detects the edges of glossiness, and adapts to all‐frequency materials using only a camera position and G‐buffer. These features are not only suitable for path tracing, but also deferred shading and non‐ray tracing–based methods such as voxel cone tracing.

Virtual point lights (VPLs) are well established for real-time global illumination. However, this method suffers from spiky artifacts and flickering caused by singularities of VPLs, highly glossy materials, high-frequency textures, and discontinuous geometries. To avoid these artifacts, this paper introduces a virtual spherical Gaussian light (VSGL) which roughly represents a set of VPLs. For a VSGL, the total radiant intensity and positional distribution of VPLs are approximated using spherical Gaussians and a Gaussian distribution, respectively. Since this approximation can be computed using summations of VPL parameters, VSGLs can be dynamically generated using mipmapped reflective shadow maps. Our VSGL generation is simple and independent from any scene geometries. In addition, reflected radiance for a VSGL is calculated using an analytic formula. Hence, we are able to render one-bounce glossy interreflections at real-time frame rates with smaller artifacts.

Abstract This paper proposes an adaptive rendering technique for ray‐bundle tracing. Ray‐bundle tracing can be done by per‐pixel linked‐list construction on a GPU rasterization pipeline. This rasterization based approach offers significant benefits for the efficient generation of light maps (e.g., hardware acceleration, tessellation, and recycling of shaders used in real‐time graphics). However, it is inapplicable to large and complex scenes due to the limited capacity of the GPU memory because it requires a high‐resolution frame buffer and high‐capacity node buffer for the linked‐lists. In addition, memory overflow can potentially occur on the per‐pixel linked‐list since the memory usage of the lists is usually unknown before the rendering process. We introduce an adaptive tiling technique with memory usage prediction. Our method uses an appropriately tiled frame buffer, thus eliminating almost all of the overflow risks thanks to our adaptive tile subdivision scheme. Using this technique, we are able to render high‐quality light maps of large and complex scenes which cannot be computed using previous ray‐bundle based methods.

Global illumination drastically improves visual realism of interactive applications. Although many interactive techniques are available, they have some limitations or employ coarse approximations. For example, general instant radiosity often has numerical error, because the sampling strategy fails in some cases. This problem can be reduced by a bidirectional sampling strategy that is often used in off-line rendering. However, it has been complicated to implement in real-time applications. This paper presents a simple real-time global illumination system based on bidirectional path tracing. The proposed system approximates bidirectional path tracing by using rasterization on a commodity DirectX® 11 capable GPU. Moreover, for glossy surfaces, a simple and efficient artifact suppression technique is also introduced.

In interactive applications such as video games, light maps are often used to generate realistic images. However, baking light maps is time consuming because it is necessary to compute global illumination. This sketch presents a simple and fast rendering system for light maps. Our system exploits ray-bundles on DirectX®11 capable GPUs and outperforms ray tracing based methods. Furthermore, it supports tessellation for DirectX 11 games.

Abstract There are two major ways of calculating ray and parametric surface intersections in rendering. The first is through the use of tessellated triangles, and the second is to use parametric surfaces together with numerical methods such as Newton's method. Both methods are computationally expensive and complicated to implement. In this paper, we focus on Phong Tessellation and introduce a simple direct ray tracing method for Phong Tessellation. Our method enables rendering smooth surfaces in a computationally inexpensive yet robust way.

Many shading models have been proposed for human hair fibers (see, for example, [Marschner et al. 2003]) and they are used successfully in film productions. Not much attention, however, has been paid to animal furs. The models developed for human hair fibers may not be suitable for animal fur since the scale patterns, medullary types, and pigments are different from those of humans, and greatly different between animals [Deedrick and Koch 2004b]. In this paper we propose an empirical shader to reproduce the detailed appearance of animal fur.

This paper presents an efficient technique for global illumination rendering of a scene with participating media. The rendering handling participating media is performed by ray marching method, which requires sampling along each view direction. The step size of the ray marching must be taken short to generate a high quality image and thus leads to very long computational time. One possible method to improve the computational cost is to exploit importance sampling. In this paper, we propose a method to determine the step size based on the importance sampling technique. For efficient sampling, the probability density function which is "close" to the radiance distribution is required. In our method, 3D space is divided into a set of uniform grids. The radiance distribution is approximated using the grid structure. To deal with the participating media which has anisotropic scattering property, we use spherical harmonics to represent directional dependence of radiance distribution. Using this grid-based representation, fast calculation of good approximation of desirable probability density is made possible. Using this probability, high quality image can be rendered with fewer number of sampling compared to the conventional methods.