Abstract Global illumination computation in real time has been an objective for Computer Graphics since its inception. Unfortunately, its implementation has challenged up to now the most advanced hardware and software solutions. We propose a real‐time voxel‐based global illumination solution for a single light bounce that handles static and dynamic objects with diffuse materials under a dynamic light source. The combination of ray tracing and voxelization on the GPU offers scalability and performance. Our divide‐and‐win approach, which ray traces separately static and dynamic objects, reduces the re‐computation load with updates of any number of dynamic objects. Our results demonstrate the effectiveness of our approach, allowing the real‐time display of global illumination effects, including colour bleeding and indirect shadows, for complex scenes containing millions of polygons.

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 propose to exploit a visualization metaphor and a set of filters to assist developers grasping high-level behaviors of programs. Our interactive visualization is based on a metaphor of light-traces as part of an animation to explore execution scenarios. The animation is augmented with a set of structural and temporal filters to reduce the volume of information displayed. We showcase our visualization environment on two case studies featuring programs of a chess game and a UML diagram editor.

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.

Abstract It is notoriously difficult for artists to control liquids while generating plausible animations. We introduce a new liquid control tool that allows users to load, transform, and apply precomputed liquid simulation templates in a scene in order to control a particle‐based simulation. Each template instance generates control forces that drive the global simulated liquid to locally reproduce the templated liquid behavior. Our system is augmented with a variable proportion of temporary particles to help efficiently reproduce the templated liquid density, with fewer requirements on the surrounding environment. The resulting control strategy adds only a small computational overhead, leading to quick visual feedback for resolutions allowing interactive simulation. We demonstrate the robustness and ease of use of our method on various examples in 2D and 3D.

Lossy texture compression is increasingly used to reduce GPU memory and bandwidth consumption. However, as raised by recent studies, evaluating the quality of compressed textures is a difficult problem. Indeed using Peak Signal-to-Noise Ratio (PSNR) on texture images, like done in most applications, may not be a correct way to proceed. In particular, there is evidence that masking effects apply when the texture image is mapped on a surface and combined with other textures (e.g., affecting geometry or normal). These masking effects have to be taken into account when compressing a set of texture maps, in order to have a real understanding of the visual impact of the compression artifacts on the rendered images. In this work, we present the first psychophysical experiment investigating the perceptual impact of texture compression on rendered images. We explore the influence of compression bit rate, light direction, and diffuse and normal map content on the visual impact of artifacts. The collected data reveal huge masking effects from normal map to diffuse map artifacts and vice versa, and reveal the weakness of PSNR applied on individual textures for evaluating compression quality. The results allow us to also analyze the performance and failures of image quality metrics for predicting the visibility of these artifacts. We finally provide some recommendations for evaluating the quality of texture compression and show a practical application to approximating the distortion measured on a rendered 3D shape.

The dimension of time in software appears in both program execution and software evolution. Much research has been devoted to the understanding of either program execution or software evolution, but these two research communities have developed tools and solutions exclusively in their respective context. In this paper, we claim that a common comprehension framework should apply to the time dimension of software. We formalize this as a meta-model that we instantiate and apply to the two different comprehension problems.

Software evolution history is usually represented at fine granularity by commits in software repositories, and at coarse granularity by software releases. In order to gain insights on development activities and on software evolution, the information on releases is too general, whereas the information on commits is prohibitively large to be efficiently processed by a developer. This paper proposes an automatic technique for the identification of distinct phases of evolution. Such software evolution phases are characterized by similar development activities in terms of changes to entities. Therefore, our technique decomposes software evolution history to assist developers identify periods of different development activities. Our analysis technique is a search-based optimization of the best decomposition of commits from the software repository using heuristics such as classes changed in each commit, and the magnitude/importance of these changes. To validate our technique, we applied it on the evolution history of five case studies covering multiple releases over several years of development. An interesting outcome of the evaluation is that our automatic decomposition of software evolution history recovered the original decomposition in software releases.

Abstract We introduce a novel fitting procedure that takes as input an arbitrary material, possibly anisotropic, and automatically converts it to a microfacet BRDF. Our algorithm is based on the property that the distribution of microfacets may be retrieved by solving an eigenvector problem that is built solely from backscattering samples. We show that the eigenvector associated to the largest eigenvalue is always the only solution to this problem, and compute it using the power iteration method. This approach is straightforward to implement, much faster to compute, and considerably more robust than solutions based on nonlinear optimizations. In addition, we provide simple conversion procedures of our fits into both Beckmann and GGX roughness parameters, and discuss the advantages of microfacet slope space to make our fits editable. We apply our method to measured materials from two large databases that include anisotropic materials, and demonstrate the benefits of spatially varying roughness on texture mapped geometric models.

Abstract Combining procedural generation and user control is a fundamental challenge for the interactive design of natural scenery. This is particularly true for modelling complex waterfall scenes where, in addition to taking charge of geometric details, an ideal tool should also provide a user with the freedom to shape the running streams and falls, while automatically maintaining physical plausibility in terms of flow network, embedding into the terrain, and visual aspects of the waterfalls. We present the first solution for the interactive procedural design of coherent waterfall scenes. Our system combines vectorial editing, where the user assembles elements to create a waterfall network over an existing terrain, with a procedural model that parametrizes these elements from hydraulic exchanges; enforces consistency between the terrain and the flow; and generates detailed geometry, animated textures and shaders for the waterfalls and their surroundings. The tool is interactive, yielding visual feedback after each edit.

We present a novel approach for the interactive synthesis and editing of virtual worlds. Our method is inspired by painting operations and uses methods for statistical example-based synthesis to automate content synthesis and deformation. Our real-time approach takes a form of local inverse procedural modeling based on intermediate statistical models: selected regions of procedurally and manually constructed example scenes are analyzed, and their parameters are stored as distributions in a palette, similar to colors on a painter's palette. These distributions can then be interactively applied with brushes and combined in various ways, like in painting systems. Selected regions can also be moved or stretched while maintaining the consistency of their content. Our method captures both distributions of elements and structured objects, and models their interactions. Results range from the interactive editing of 2D artwork maps to the design of 3D virtual worlds, where constraints set by the terrain's slope are also taken into account.

We present a geometric representation of a tetrahedral mesh that is solely based on dihedral angles. We first show that the shape of a tetrahedral mesh is completely defined by its dihedral angles. This proof leads to a set of angular constraints that must be satisfied for an immersion to exist in R 3 . This formulation lets us easily specify conditions to avoid inverted tetrahedra and multiply-covered vertices, thus leading to locally injective maps. We then present a constrained optimization method that modifies input angles when they do not satisfy constraints. Additionally, we develop a fast spectral reconstruction method to robustly recover positions from dihedral angles. We demonstrate the applicability of our representation with examples of volume parameterization, shape interpolation, mesh optimization, connectivity shapes, and mesh compression.

Applying non-linear transfer functions and look-up tables to procedural functions (such as noise), surface attributes, or even surface geometry are common strategies used to enhance visual detail. Their simplicity and ability to mimic a wide range of realistic appearances have led to their adoption in many rendering problems. As with any textured or geometric detail, proper filtering is needed to reduce aliasing when viewed across a range of distances, but accurate and efficient transfer function filtering remains an open problem for several reasons: transfer functions are complex and non-linear, especially when mapped through procedural noise and/or geometry-dependent functions, and the effects of perspective and masking further complicate the filtering over a pixel's footprint. We accurately solve this problem by computing and sampling from specialized filtering distributions on the fly, yielding very fast performance. We investigate the case where the transfer function to filter is a color map applied to (macroscale) surface textures (like noise), as well as color maps applied according to (microscale) geometric details. We introduce a novel representation of a (potentially modulated) color map's distribution over pixel footprints using Gaussian statistics and, in the more complex case of high-resolution color mapped microsurface details, our filtering is view- and light-dependent, and capable of correctly handling masking and occlusion effects. Our approach can be generalized to filter other physical-based rendering quantities. We propose an application to shading with irradiance environment maps over large terrains. Our framework is also compatible with the case of transfer functions used to warp surface geometry, as long as the transformations can be represented with Gaussian statistics, leading to proper view- and light-dependent filtering results. Our results match ground truth and our solution is well suited to real-time applications, requires only a few lines of shader code (provided in supplemental material, which can be found on the Computer Society Digital Library at http://doi.ieeecomputersociety.org/10.1109/TVCG.2013.102), is high performance, and has a negligible memory footprint.

In order to interactively render large virtual worlds, the amount of 3D geometry passed to the graphics hardware must be kept to a minimum. Typical solutions to this problem include the use of potentially visible sets and occlusion culling, however, these solutions do not scale well, in time nor in memory, with the size of a virtual world. We propose a fast and inexpensive variant of occlusion culling tailored to a simple tiling scheme that improves scalability while maintaining very high performance. Tile visibilities are evaluated with hardware-accelerated occlusion queries, and in-tile rendering is rapidly computed using BVH instantiation and any visibility method, we use the CHC++ occlusion culling method for its good general performance. Tiles are instantiated only when tested locally for visibility, thus avoiding the need for a preconstructed global structure for the complete world. Our approach can render large-scale, diversified virtual worlds with complex geometry, such as cities or forests, all at high performance and with a modest memory footprint.

Color map textures applied directly to surfaces, to geometric microsurface details, or to procedural functions (such as noise), are commonly used to enhance visual detail. Their simplicity and ability to mimic a wide range of realistic appearances have led to their adoption in many rendering problems. As with any textured or geometric detail, proper filtering is needed to reduce aliasing when viewed across a range of distances, but accurate and efficient color map filtering remains an open problem for several reasons: color maps are complex non-linear functions, especially when mapped through procedural noise and/or geometry-dependent functions, and the effects of perspective and masking further complicate the filtering over a pixel's footprint. We accurately solve this problem by computing and sampling from specialized filtering distributions on-the-fly, yielding very fast performance. We filter color map textures applied to (macro-scale) surfaces, as well as color maps applied according to (micro-scale) geometric details. We introduce a novel representation of a (potentially modulated) color map's distribution over pixel footprints using Gaussian statistics and, in the more complex case of high-resolution color mapped microsurface details, our filtering is view- and light-dependent, and capable of correctly handling masking and occlusion effects. Our results match ground truth and our solution is well suited to real-time applications, requires only a few lines of shader code (provided in supplemental material), is high performance, and has a negligible memory footprint.

Interactive software visualization offers a promising support for program comprehension, including program dynamicity. We present, the extension of an existing visualization tool with heat maps to explore the time and other dimensions of software. To this end, we first propose a framework to unify the two main software dynamicities, execution and evolution. Then, this unified framework is exploited to define a visualization environment based on heat maps. We illustrate our approach on two comprehension tasks: understanding the behavior of programmers during the evolution of an application and understanding class contributions in use cases. The case studies show that the heat-map metaphor contributes to answer, more easily, many of the questions important to program comprehension.

Abstract We propose a method for mapping polynomial volumes. Given a closed surface and an initial template volume grid, our method deforms the template grid by fitting its boundary to the input surface while minimizing a volume distortion criterion. The result is a point‐to‐point map distorting linear cells into curved ones. Our method is based on several extensions of Voronoi Squared Distance Minimization (VSDM) combined with a higher‐order finite element formulation of the deformation energy. This allows us to globally optimize the mapping without prior parameterization. The anisotropic VSDM formulation allows for sharp and semi‐sharp features to be implicitly preserved without tagging. We use a hierarchical finite element function basis that selectively adapts to the geometric details. This makes both the method more efficient and the representation more compact. We apply our method to geometric modeling applications in computer‐aided design and computer graphics, including mixed‐element meshing, mesh optimization, subdivision volume fitting, and shell meshing.

We present Linear Efficient Antialiased Displacement and Reflectance (LEADR) mapping, a reflectance filtering technique for displacement mapped surfaces. Similarly to LEAN mapping, it employs two mipmapped texture maps, which store the first two moments of the displacement gradients. During rendering, the projection of this data over a pixel is used to compute a noncentered anisotropic Beckmann distribution using only simple, linear filtering operations. The distribution is then injected in a new, physically based, rough surface microfacet BRDF model, that includes masking and shadowing effects for both diffuse and specular reflection under directional, point, and environment lighting. Furthermore, our method is compatible with animation and deformation, making it extremely general and flexible. Combined with an adaptive meshing scheme, LEADR mapping provides the very first seamless and hardware-accelerated multi-resolution representation for surfaces. In order to demonstrate its effectiveness, we render highly detailed production models in real time on a commodity GPU, with quality matching supersampled ground-truth images.

Over the last two decades, much effort has been devoted to accurately measuring Bidirectional Reflectance Distribution Functions (BRDFs) of real-world materials and to use efficiently the resulting data for rendering. Because of their large size, it is difficult to use directly measured BRDFs for real-time applications, and fitting the most sophisticated analytical BRDF models is still a complex task. In this paper, we introduce Rational BRDF, a general-purpose and efficient representation for arbitrary BRDFs, based on Rational Functions (RFs). Using an adapted parametrization, we demonstrate how Rational BRDFs offer 1) a more compact and efficient representation using low-degree RFs, 2) an accurate fitting of measured materials with guaranteed control of the residual error, and 3) efficient importance sampling by applying the same fitting process to determine the inverse of the Cumulative Distribution Function (CDF) generated from the BRDF for use in Monte-Carlo rendering.

Abstract This paper presents a reformulation of bidirectional path‐tracing that adequately divides the algorithm into processes efficiently executed in parallel on both the CPU and the GPU. We thus benefit from high‐level optimization techniques such as double buffering, batch processing, and asyncronous execution, as well as from the exploitation of most of the CPU, GPU, and memory bus capabilities. Our approach, while avoiding pure GPU implementation limitations (such as limited complexity of shaders, light or camera models, and processed scene data sets), is more than ten times faster than standard bidirectional path‐tracing implementations, leading to performance suitable for production‐oriented rendering engines.

We present a general method enhancing the robustness of estimators based on multiple importance sampling (MIS) in a numerical integration context. MIS minimizes variance of estimators for a given sampling configuration, but when this configuration is less adapted to the integrand, the resulting estimator suffers from extra variance. We address this issue by introducing the notion of "representativity" of a sampling strategy, and demonstrate how it can be used to increase robustness of estimators, by adapting them to the integrand. We first show how to compute representativities using common rendering informations such as BSDF, photon maps, or caches in order to choose the best sampling strategy for MIS. We then give hints to generalize our method to any integration problem and demonstrate that it can be used successfully to enhance robustness in different common rendering algorithms.

Abstract Raytracing metaballs is a problem that has numerous applications in the rendering of dynamic soft objects such as fluids. However, current techniques are either limited in the visual effects that they can render or their performance drops as the number of metaballs and their density increase. We present a new acceleration structure based on BVH and kd‐tree for efficient raytracing of a large number of metaballs. This structure is built from an adapted SAH using a fast greedy algorithm and allows the visualization of several hundreds of thousands metaballs at interactive‐to‐real‐time framerates. Our method can handle arbitrary rays to simulate any complex secondary effects such as reflections or soft shadows, and is robust with respect to the density of metaballs. We achieve this performance thanks to a balanced CPU‐GPU (using CUDA) implementation of the animation, structure creation, and rendering.

Abstract While existing spherical parameterization algorithms are limited to genus‐0 geometrical models, we believe a wide class of models of arbitrary genus can also benefit from the spherical domain. We present a complete and robust pipeline that can generate spherical geometry images from arbitrary genus surfaces where the holes are explicitly represented. The geometrical model, represented as a triangle mesh, is first made topologically equivalent to a sphere by cutting each hole along its generators, thus performing genus reduction. The resulting genus‐0 model is then parameterized on the sphere, where it is resampled in a way to preserve connectivity between holes and to reduce the visual impact of seams due to these holes. Knowing the location of each pair of boundary components in parametric space, our novel sampling scheme can automatically choose to scale down or completely eliminate the associated hole, depending on geometry image resolution, thus lowering the genus of the reconstructed model. We found our method to scale better than other geometry image algorithms for higher genus models. We illustrate our approach on remeshing, level‐of‐detail rendering, normal mapping and topology editing.

Assessing software quality and understanding how events in its evolution have lead to anomalies are two important steps toward reducing costs in software maintenance. Unfortunately, evaluation of large quantities of code over several versions is a task too time-consuming, if not overwhelming, to be applicable in general. To address this problem, we designed a visualization framework as a semi-automatic approach to quickly investigate programs composed of thousands of classes, over dozens of versions. Programs and their associated quality characteristics for each version are graphically represented and displayed independently. Real-time navigation and animation between these representations recreate visual coherences often associated with coherences intrinsic to subsequent software versions. Exploiting such coherences can reduce cognitive gaps between the different views of software, and allows human experts to use their visual capacity and intuition to efficiently investigate and understand various quality aspects of software evolution. To illustrate the interest of our framework, we report our results on two case studies.

Motion capture data is an effective way of synthesizing human motion for many interactive applications, including games and simulations. A compact, easy-to-decode representation is needed for the motion data in order to support the real-time motion of a large number of characters with minimal memory and minimal computational overheads. We present a wavelet-based compression technique that is specially adapted to the nature of joint angle data. In particular, we define wavelet coefficient selection as a discrete optimization problem within a tractable search space adapted to the nature of the data. We further extend this technique to take into account visual artifacts such as footskate. The proposed techniques are compared to standard truncated wavelet compression and principal component analysis based compression. The fast decompression times and our focus on short, recomposable animation clips make the proposed techniques a realistic choice for many interactive applications.

We propose an approach for complex software analysis based on visualization. Our work is motivated by the fact that in spite of years of research and practice, software development and maintenance are still time and resource consuming, and high-risk activities. The most important reason in our opinion is the complexity of many phenomena related to software, such as its evolution and its reliability. In fact, there is very little theory explaining them. Today, we have a unique opportunity to empirically study these phenomena, thanks to large sets of software data available through open-source programs and open repositories. Automatic analysis techniques, such as statistics and machine learning, are usually limited when studying phenomena with unknown or poorly-understood influence factors. We claim that hybrid techniques that combine automatic analysis with human expertise through visualization are excellent alternatives to them. In this paper, we propose a visualization framework that supports quality analysis of large-scale software systems. We circumvent the problem of size by exploiting perception capabilities of the human visual system.

Caustics produce beautiful and intriguing illumination patterns. However, their complex behavior makes them difficult to simulate accurately in all but the simplest configurations. To capture their appearance, we present an adaptive approach based upon light beams. Exploiting the coherence between the light rays forming a beam greatly reduces the number of samples required for precise illumination reconstruction. The beams characterize the light distribution due to interactions with specular surfaces in 3D space. They thus allow for the treatment of illumination within single‐scattering participating media. A hierarchical structure enclosing the light beams possesses inherent properties to detect efficiently all beams reaching any 3D point, to adapt itself according to illumination effects in the final image, and to reduce memory consumption via caching.

We present an animation system that captures live facial expressions from a performance actor and uses them to animate in real time a synthetic character. Our approach is based upon a bank of 3D facial expressions of a synthetic model. Critical points on the face model are matched to live markers. A linear combination of the basic expressions obtained by minimizing Euclidean distance between corresponding points and markers is then used to construct the intermediate facial expression. Mapping the motion into a bank of expressions produces subtle motions, more dependent on the characteristics of the model itself. This is more difficult to achieve with previous techniques deforming a model without any additional information on how the model should move. Our technique draws mostly on the technical skills of an artist to model facial expressions, and on the skills of a performance actor to bring life to a face, with most animation issues being automated. We also present improvements on the control of markers, on specific details for more delicate control of the eyelids, and on the use of filters applied to the sequence of marker displacements. More flexibility in the bank of expressions is provided by subdividing some of the expressions into independent components, and by controlling accessories such as teeth and tongue only by means of the reconstructed expression. The resulting system is very flexible, intuitive to use, and the real time animations provide immediate feedback to express and refine animator and performer skills.

We introduce a new data structure in the form of a light hierarchy for efficiently ray‐tracing scenes with many light sources. An octree is constructed with the point light sources in a scene. Each node represents all the light sources it contains by means of a virtual light source. We determine bounds on the error committed with this approximation to shade a point, both for the cases of diffuse and specular reflections. These bounds are then used to guide a hierarchical shading algorithm. If the current level of the light hierarchy provides shading of sufficient quality, the approximation is used, thus avoiding the cost of shading for all the light sources contained below this level. Otherwise the descent into the light hierarchy continues. Our approach has been implemented for scenes without occlusion. The results show important acceleration compared to standard ray‐tracing (up to 90 times faster) and an important improvement compared to Ward’s adaptive shadow testing.

In inverse shading, a user provides information about the desired shading as she/he would like it to appear in the final image. The computer then interprets this information to identify the best values for the various shading parameters that would lead to the desired visual effect. The authors introduce an approach based on sketching in order to position light sources. Point light sources are positioned by sketches of shadows or highlights. Extended light sources are positioned by sketches of umbra or penumbra. The resulting system allows one to quickly position light sources and to refine their positions interactively and more intuitively.

Article Hierarchical view-dependent structures for interactive scene manipulation Share on Authors: Normand Brière Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, succ. Centre-Ville, Montréal (Qc) Canada H3C 3J7 Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, succ. Centre-Ville, Montréal (Qc) Canada H3C 3J7View Profile , Pierre Poulin Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, succ. Centre-Ville, Montréal (Qc) Canada H3C 3J7 Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128, succ. Centre-Ville, Montréal (Qc) Canada H3C 3J7View Profile Authors Info & Claims SIGGRAPH '96: Proceedings of the 23rd annual conference on Computer graphics and interactive techniquesAugust 1996 Pages 83–90https://doi.org/10.1145/237170.237211Online:01 August 1996Publication History 17citation468DownloadsMetricsTotal Citations17Total Downloads468Last 12 Months7Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

A reflection and refraction model for anisotropic surfaces is introduced. The anisotropy is simulated by small cylinders (added or subtracted) distributed on the anisotropic surface. Different levels of anisotropy are achieved by varying the distance between each cylinder and/or rising the cylinders more or less from the surface. Multidirectional anisotropy is modelled by orienting groups of cylinders in different direction. The intensity of the reflected light is computed by determining the visible and illuminated portion of the cylinders, taking self-blocking into account. We present two techniques to compute this in practice. In one the intensity is computed by sampling the surface of the cylinders. The other is an analytic solution. In the case of the diffuse component, the solution is exact. In the case of the specular component, an approximation is developed using a Chebyshev polynomial approximation of the specular term, and integrating the polynomial.This model can be implemented easily within most rendering system, given a suitable mechanism to define and alter surface tangents. The effectiveness of the model and the visual importance of anisotropy are illustrated with some pictures.