Abstract Voxel‐based rendering has recently received significant attention due to its potential in the context of efficiently rendering massively large and highly detailed scenes. Unfortunately, few scenes are available in the form of sparse voxel octrees. In this paper, we present an out‐of‐core algorithm for constructing a sparse voxel octree from a triangle mesh. Our algorithm allows the input triangle mesh, the output sparse voxel octree and, most importantly, the intermediate high‐resolution 3D voxel grid, to be larger than available memory. We demonstrate that our out‐of‐core algorithm can construct sparse voxel octrees from triangle meshes using only a fraction of the memory required by an in‐core algorithm in roughly the same time, and that our out‐of‐core algorithm can also handle extremely large triangle meshes.

Abstract Evaluating the visibility between two points is a fundamental problem for ray‐tracing and path‐tracing algorithms. Ideally, visibility computations are organized such that a minimum number of geometric primitives need to be checked for each ray. Replacing complex geometric shapes by a simpler set of primitives is one strategy to control the amount of intersection calculations. However, approximating the original geometry introduces inaccuracies in e.g. shadow regions when shadow rays are intersected with the approximate geometry. This paper presents a theoretical framework for probabilistic visibility evaluation. When intersecting a shadow ray with the scene, we randomly select the original geometry, the approximated geometry, or one of several correction terms, to be tested. Not all shadow rays will therefore intersect the original geometry, but our method is able to produce unbiased images that converge to the correct solution. Although probabilistic visibility evaluation is an experimental idea, we show several example scenes that highlight the potential for future improvements.

Abstract The efficient evaluation of visibility in a three‐dimensional scene is a longstanding problem in computer graphics. Visibility evaluations come in many different forms: figuring out what object is visible in a pixel; determining whether a point is visible to a light source; or evaluating the mutual visibility between 2 surface points. This paper provides a new, experimental view on visibility, based on a probabilistic evaluation of the visibility function. Instead of checking the visibility against all possible intervening geometry the visibility between 2 points is now evaluated by testing only a random subset of objects. The result is not a Boolean value that is either 0 or 1, but a numerical value that can even be negative. Because we use the visibility evaluation as part of the integrand in illumination computations, the probabilistic evaluation of visibility becomes part of the Monte Carlo procedure of estimating the illumination integral, and results in an unbiased computation of illumination values in the scene. Moreover, the number of intersections tests for any given ray is decreased, since only a random selection of geometric primitives is tested. Although probabilistic visibility is an experimental and new idea, we present a practical algorithm for direct illumination that uses the probabilistic nature of visibility evaluations.

Procedural noise is a fundamental tool in Computer Graphics. However, designing noise patterns is hard. In this paper, we present Gabor noise by example , a method to estimate the parameters of bandwidth-quantized Gabor noise, a procedural noise function that can generate noise with an arbitrary power spectrum, from exemplar Gaussian textures, a class of textures that is completely characterized by their power spectrum. More specifically, we introduce (i) bandwidth-quantized Gabor noise, a generalization of Gabor noise to arbitrary power spectra that enables robust parameter estimation and efficient procedural evaluation; (ii) a robust parameter estimation technique for quantized-bandwidth Gabor noise, that automatically decomposes the noisy power spectrum estimate of an exemplar into a sparse sum of Gaussians using non-negative basis pursuit denoising; and (iii) an efficient procedural evaluation scheme for bandwidth-quantized Gabor noise, that uses multi-grid evaluation and importance sampling of the kernel parameters. Gabor noise by example preserves the traditional advantages of procedural noise, including a compact representation and a fast on-the-fly evaluation, and is mathematically well-founded.

Abstract Recent work in interactive global illumination addresses diffuse and moderately glossy indirect lighting effects, but high‐frequency effects such as multi‐bounce reflections on highly glossy surfaces are often ignored. Accurately simulating such effects is important to convey the realistic appearance of materials such as chrome and shiny metal. In this paper, we present an efficient method for visualizing multi‐bounce glossy reflections at interactive rates under environment lighting. Our main contribution is a pre‐computation–based method which efficiently gathers subsequent highly glossy reflection passes modelled with a non‐linear transfer function representation based on the von Mises–Fisher distribution. We show that our gathering method is superior to scattered sampling. To exploit the sparsity of the pre‐computed data, we apply perfect spatial hashing. As a result, we are able to visualize multi‐bounce glossy reflections at interactive rates at a low pre‐computation cost.

Solid noise is a fundamental tool in computer graphics. Surprisingly, no existing noise function supports both high-quality antialiasing and continuity across sharp edges. In this paper we show that a slicing approach is required to preserve continuity across sharp edges, and we present a new noise function that supports anisotropic filtering of sliced solid noise. This is made possible by individually filtering the slices of Gabor kernels, which requires the proper treatment of phase. This in turn leads to the introduction of the phase-augmented Gabor kernel and random-phase Gabor noise, our new noise function. We demonstrate that our new noise function supports both high-quality anti-aliasing and continuity across sharp edges, as well as anisotropy.

We have recently proposed a new procedural noise function, Gabor noise, which offers a combination of properties not found in the existing noise functions. In this paper, we present three significant improvements to Gabor noise: 1) an isotropic kernel for Gabor noise, which speeds up isotropic Gabor noise with a factor of roughly two, 2) an error analysis of Gabor noise, which relates the kernel truncation radius to the relative error of the noise, and 3) spatially varying Gabor noise, which enables spatial variation of all noise parameters. These improvements make Gabor noise an even more attractive alternative for the existing noise functions.

Abstract We present a new solution for temporal coherence in non‐photorealistic rendering (NPR) of animations. Given the conflicting goals of preserving the 2D aspect of the style and the 3D scene motion, any such solution is a tradeoff. We observe that primitive‐based methods in NPR can be seen as texture‐based methods when using large numbers of primitives, leading to our key insight, namely that this process is similar to sparse convolution noise in procedural texturing. Consequently, we present a new primitive for NPR based on Gabor noise, that preserves the 2D aspect of noise, conveys the 3D motion of the scene, and is temporally continuous. We can thus use standard techniques from procedural texturing to create various styles, which we show for interactive NPR applications. We also present a user study to evaluate this and existing solutions, and to provide more insight in the trade‐off implied by temporal coherence. The results of the study indicate that maintaining coherent motion is important, but also that our new solution provides a good compromise between the 2D aspect of the style and 3D motion.

Abstract Procedural noise functions are widely used in computer graphics, from off‐line rendering in movie production to interactive video games. The ability to add complex and intricate details at low memory and authoring cost is one of its main attractions. This survey is motivated by the inherent importance of noise in graphics, the widespread use of noise in industry and the fact that many recent research developments justify the need for an up‐to‐date survey. Our goal is to provide both a valuable entry point into the field of procedural noise functions, as well as a comprehensive view of the field to the informed reader. In this report, we cover procedural noise functions in all their aspects. We outline recent advances in research on this topic, discussing and comparing recent and well‐established methods. We first formally define procedural noise functions based on stochastic processes and then classify and review existing procedural noise functions. We discuss how procedural noise functions are used for modelling and how they are applied to surfaces. We then introduce analysis tools and apply them to evaluate and compare the major approaches to noise generation. We finally identify several directions for future work.

Noise is an essential tool for texturing and modeling. Designing interesting textures with noise calls for accurate spectral control, since noise is best described in terms of spectral content. Texturing requires that noise can be easily mapped to a surface, while high-quality rendering requires anisotropic filtering. A noise function that is procedural and fast to evaluate offers several additional advantages. Unfortunately, no existing noise combines all of these properties. In this paper we introduce a noise based on sparse convolution and the Gabor kernel that enables all of these properties. Our noise offers accurate spectral control with intuitive parameters such as orientation, principal frequency and bandwidth. Our noise supports two-dimensional and solid noise, but we also introduce setup-free surface noise. This is a method for mapping noise onto a surface, complementary to solid noise, that maintains the appearance of the noise pattern along the object and does not require a texture parameterization. Our approach requires only a few bytes of storage, does not use discretely sampled data, and is nonperiodic. It supports anisotropy and anisotropic filtering. We demonstrate our noise using an interactive tool for noise design.

Abstract Poisson disk distributions have many applications in the field of computer graphics. Besides sampling, Poisson disk distributions are used in object distribution, non‐photorealistic rendering and procedural texturing. Over the years, a large number of methods for generating Poisson disk distributions have been proposed, making it difficult to choose the right method for a given application. In this paper, we present a detailed comparison of most techniques for generating Poisson disk distributions. The methods we study include dart throwing, relaxation dart throwing, Lloyd's relaxation, Shade's Poisson disk tiles, tiled blue noise samples, fast hierarchical importance sampling with blue noise properties, edge‐based Poisson disk tiles, template Poisson disk tiles, corner‐based Poisson disk tiles and recursive Wang tiles for real‐time blue noise. Analysing all of these methods within a single framework is one of the major contributions of this work .

Abstract The focus of research in acceleration structures for ray tracing recently shifted from render time to time to image, the sum of build time and render time, and also the memory footprint of acceleration structures now receives more attention. In this paper we revisit the grid acceleration structure in this setting. We present two efficient methods for representing and building a grid. The compact grid method consists of a static data structure for representing a grid with minimal memory requirements, more specifically exactly one index per grid cell and exactly one index per object reference, and an algorithm for building that data structure in linear time. The hashed grid method reduces memory requirements even further, by using perfect hashing based on row displacement compression. We show that these methods are more efficient in both time and space than traditional methods based on linked lists and dynamic arrays. We also present a more robust grid traversal algorithm. We show that, for applications where time to image or memory usage is important, such as interactive ray tracing and rendering large models, the grid acceleration structure is an attractive alternative.

Abstract In this paper we introduce the constrained tetrahedralization as a new acceleration structure for ray tracing. A constrained tetrahedralization of a scene is a tetrahedralization that respects the faces of the scene geometry. The closest intersection of a ray with a scene is found by traversing this tetrahedralization along the ray, one tetrahedron at a time. We show that constrained tetrahedralizations are a viable alternative to current acceleration structures, and that they have a number of unique properties that set them apart from other acceleration structures: constrained tetrahedralizations are not hierarchical yet adaptive; the complexity of traversing them is a function of local geometric complexity rather than global geometric complexity; constrained tetrahedralizations support deforming geometry without any effort; and they have the potential to unify several data structures currently used in global illumination.

In this article we revisit the concept of Wang tiles and introduce corner tiles, square tiles with colored corners. During past years, Wang tiles have become a valuable tool in computer graphics. Important applications of Wang tiles include texture synthesis, tile-based texture mapping, and generating Poisson disk distributions. Through their colored edges, Wang tiles enforce continuity with their direct neighbors. However, Wang tiles do not directly constrain their diagonal neighbors. This leads to continuity problems near tile corners, a problem commonly known as the corner problem. Corner tiles, on the other hand, do impose restrictions on their diagonal neighbors, and thus are not subject to the corner problem. In this article we show that previous applications of Wang tiles can also be done using corner tiles, but that corner tiles have distinct advantages for each of these applications. Compared to Wang tiles, corner tiles are easier to tile, textures synthesized with corner tiles contain more samples from the original texture, corner tiles reduce the required texture memory by a factor of two for tile-based texture mapping, and Poisson disk distributions generated with corner tiles have better spectral properties. Corner tiles result in cleaner, simpler, and more efficient applications.

In this paper we present a method for geometry synthesis by example, inspired by techniques from texture synthesis. Given an example of input geometry, we synthesize new output geometry that is perceived similar to the input geometry, but at the same time differs in its local appearance. We assume the input geometry satisfies the constraints of a Markov Random Field model, and represent the input geometry by a hierarchical distance field. This allows us to perform fast matching between a target distance field that is partially synthesized, and the input distance field. Once the target distance field is completed, we copy the original corresponding geometry elements to the synthesized result. We show that automatically generating geometry by example can be achieved within reasonable computing times, and is able to produce convincing results.

In this article, we present a procedural object distribution function, a new texture basis function that distributes procedurally generated objects over a procedurally generated texture. The objects are distributed uniformly over the texture, and are guaranteed not to overlap. The scale, size, and orientation of the objects can be easily manipulated. The texture basis function is efficient to evaluate, and is suited for real-time applications. The new texturing primitive we present extends the range of textures that can be generated procedurally.The procedural object distribution function we propose is based on Poisson disk tiles and a direct stochastic tiling algorithm for Wang tiles. Poisson disk tiles are square tiles filled with a precomputed set of Poisson disk distributed points, inspired by Wang tiles. A single set of Poisson disk tiles enables the real-time generation of an infinite amount of Poisson disk distributions of arbitrary size. With the direct stochastic tiling algorithm, these Poisson disk distributions can be evaluated locally, at any position in the Euclidean plane.Poisson disk tiles and the direct stochastic tiling algorithm have many other applications in computer graphics. We briefly explore applications in object distribution, primitive distribution for illustration, and environment map sampling.

Abstract We propose a new technique for efficiently rendering bidirectional texture functions (BTFs). A 6D BTF describesthe appearance of a material as a texture that depends on the lighting and viewing directions. As such, a BTFaccommodates self‐shadowing, interreflection, and masking effects of a complex material without needing anexplicit representation of the small scale geometry. Our method represents the BTF as a set of spatially varyingapparent BRDFs, that each encode the reflectance field of a single pixel in the BTF. Each apparent BRDF isdecomposed into a product of three or more two‐dimensional positive factors using a novel factorization technique,which we call chained matrix factorization (CMF). The proposed factorization technique is fully automatic andsuitable for both BRDFs and apparent BRDFs (which typically exhibit off‐specular peaks and non‐reciprocity).The main benefit of CMF is that it delivers factors well suited for the limited dynamic range of conventionaltexture maps. After factorization, an efficient representation of the BTF is obtained by clustering the factors intoa compact set of 2D textures. With this compact representation, BTFs can be rendered on recent consumer levelhardware with arbitrary viewing and lighting directions at interactive rates. Categories and Subject Descriptors (according to ACM CCS): I.3.7 [Computer Graphics]: Three‐DimensionalGraphics and Realism