Many real-life materials have sparkling appearances. Some small flakes on the surface of an object can make a considerable contribution by reflecting or refracting light at a particular angle, eventually causing a sparkling appearance. Most existing approaches have focused on the glinty effects on reflective surfaces. However, transparent glint rendering has not been well studied, even though there are many natural phenomena (e.g., frost) in the real world. Recent studies have proposed the simulation of transparent glints under specific constraints (e.g., limited to the Beckmann distribution and V-groove shadowing-masking function). In this study, we propose a more general transparent glint model by performing a four-dimensional hierarchical search to count the particles located in the pixel footprint and cone around the refracted ray. Our method can produce transparent glint appearances for arbitrary normal distribution functions (e.g., GGX or Beckmann) and converge to a smooth microfacet model with a large particle count.

Specular surfaces, by focusing the light that is being reflected or refracted, cause bright spots in the scene, called caustics. These caustics are challenging to compute for global illumination algorithms. Manifold-based methods (Manifold Exploration, Manifold Next-Event Estimation, Specular Next Event Estimation) compute these caustics as the zeros of an objective function, using the Newton-Raphson method. They are efficient, but require computing the derivatives of the objective function, which in turn requires local surface derivatives around the reflection point, which can be challenging to implement. In this paper, we leverage the Nelder-Mead method to compute caustics using Manifold Next-Event Estimation without having to compute local derivatives. Our method only requires local evaluations of the objective function, making it an easy addition to any path-tracing algorithm.

Caustics are interesting patterns caused by the light being focused when reflecting off glossy materials. Rendering them in computer graphics is still challenging: they correspond to high luminous intensity focused over a small area. Finding the paths that contribute to this small area is difficult, and even more difficult when using camera-based path tracing instead of bidirectional approaches. Recent improvements in path guiding are still unable to compute efficiently the light paths that contribute to a caustic. In this paper, we present a novel path guiding approach to enable reliable rendering of caustics. Our approach relies on computing representative specular paths, then extending them using a chain of spherical Gaussians. We use these extended paths to estimate the incident radiance distribution and guide path tracing. We combine this approach with several practical strategies, such as spatial reusing and parallax-aware representation for arbitrarily curved reflectors. Our path-guided algorithm using extended specular paths outperforms current state-of-the-art methods and handles multiple bounces of light and a variety of scenes.

Abstract Spatially varying bi‐directional reflectance distribution functions (SVBRDFs) are crucial for designers to incorporate new materials in virtual scenes, making them look more realistic. Reconstruction of SVBRDFs is a long‐standing problem. Existing methods either rely on an extensive acquisition system or require huge datasets, which are non‐trivial to acquire. We aim to recover SVBRDFs from a single image, without any datasets. A single image contains incomplete information about the SVBRDF, making the reconstruction task highly ill‐posed. It is also difficult to separate between the changes in colour that are caused by the material and those caused by the illumination, without the prior knowledge learned from the dataset. In this paper, we use an unsupervised generative adversarial neural network (GAN) to recover SVBRDFs maps with a single image as input. To better separate the effects due to illumination from the effects due to the material, we add the hypothesis that the material is stationary and introduce a new loss function based on Fourier coefficients to enforce this stationarity. For efficiency, we train the network in two stages: reusing a trained model to initialize the SVBRDFs and fine‐tune it based on the input image. Our method generates high‐quality SVBRDFs maps from a single input photograph, and provides more vivid rendering results compared to the previous work. The two‐stage training boosts runtime performance, making it eight times faster than the previous work.

The detailed glinty appearance from complex surface microstructures enhances the level of realism but is both - and time-consuming to render, especially when viewed from far away (large spatial coverage) and/or illuminated by area lights (large angular coverage). In this article, we formulate the glinty appearance rendering process as a spatio-angular range query problem of the Normal Distribution Functions (NDFs), and introduce an efficient spatio-angular prefiltering solution to it. We start by exhaustively precomputing all possible NDFs with differently sized positional coverages. Then we compress the precomputed data using tensor rank decomposition, which enables accurate and fast angular range queries. With our spatio-angular prefiltering scheme, we are able to solve both the storage and performance issues at the same time, leading to efficient rendering of glinty appearance with both constant storage and constant performance, regardless of the range of spatio-angular queries. Finally, we demonstrate that our method easily applies to practical rendering applications that were traditionally considered difficult. For example, efficient bidirectional reflection distribution function evaluation accurate NDF importance sampling, fast global illumination between glinty objects, high-frequency preserving rendering with environment lighting, and tile-based synthesis of glinty appearance.

Bidirectional Scattering Distribution Functions (BSDFs) encode how a material reflects or transmits the incoming light. The most commonly used model is the microfacet BSDF. It computes the material response from the microgeometry of the surface assuming a single bounce on specular microfacets. The original model ignores multiple bounces on the microgeometry, resulting in an energy loss, especially for rough materials. In this paper, we present a new method to compute the multiple bounces inside the microgeometry, eliminating this energy loss. Our method relies on a position-free formulation of multiple bounces inside the microgeometry. We use an explicit mathematical definition of the path space that describes single and multiple bounces in a uniform way. We then study the behavior of light on the different vertices and segments in the path space, leading to a reciprocal multiple-bounce description of BSDFs. Furthermore, we present practical, unbiased Monte Carlo estimators to compute multiple scattering. Our method is less noisy than existing algorithms for computing multiple scattering. It is almost noise-free with a very-low sampling rate, from 2 to 4 samples per pixel (spp).

Rendering participating media is important to the creation of photorealistic images. Participating media has a translucent aspect that comes from light being scattered inside the material. For materials with a small mean-free-path (mfp), multiple scattering effects dominate. Simulating these effects is computationally intensive, as it requires tracking a large number of scattering events inside the material. Existing approaches precompute multiple scattering events inside the material and store the results in a table. During rendering time, this table is used to compute the scattering effects. While these methods are faster than explicit scattering computation, they incur higher storage costs. In this paper, we present a new representation for double and multiple scattering effects that uses a neural network model. The scattering response from all homogeneous participating media is encoded into a neural network in a preprocessing step. At run time, the neural network is then used to predict the double and multiple scattering effects. We demonstrate the effects combined with Virtual Ray Lights (VRL), although our approach can be integrated with other rendering algorithms. Our algorithm is implemented on GPU. Double and multiple scattering effects for the entire participating media space are encoded using only 23.6 KB of memory. Our method achieves 50 ms per frame in typical scenes and provides results almost identical to the reference.

Abstract Many real‐life materials have a sparkling appearance. Examples include metallic paints, sparkling fabrics and snow. Simulating these sparkles is important for realistic rendering but expensive. As sparkles come from small shiny particles reflecting light into a specific direction, they are very challenging for illumination simulation. Existing approaches use a four‐dimensional hierarchy, searching for light‐reflecting particles simultaneously in space and direction. The approach is accurate, but extremely expensive. A separable model is much faster, but still not suitable for real‐time applications. The performance problem is even worse when illumination comes from environment maps, as they require either a large sample count per pixel or pre‐filtering. Pre‐filtering is incompatible with the existing sparkle models, due to the discrete multi‐scale representation. In this paper, we present a GPU‐friendly, pre‐filtered model for real‐time simulation of sparkles and glints. Our method simulates glints under both environment maps and point light sources in real time, with an added cost of just 10 ms per frame with full high‐definition resolution. Editing material properties requires extra computations but is still real time, with an added cost of 10 ms per frame.

Abstract Several fast global illumination algorithms rely on the Virtual Point Lights framework. This framework separates illumination into two steps: first, propagate radiance in the scene and store it in virtual lights, then gather illumination from these virtual lights. To accelerate the second step, virtual lights and receiving points are grouped hierarchically, for example using Multi‐Dimensional Lightcuts. Computing visibility between clusters of virtual lights and receiving points is a bottleneck. Separately, matrix completion algorithms reconstruct completely a low‐rank matrix from an incomplete set of sampled elements. In this paper, we use adaptive matrix completion to approximate visibility information after an initial clustering step. We reconstruct visibility information using as little as 10 % to 20 % samples for most scenes, and combine it with shading information computed separately, in parallel on the GPU. Overall, our method computes global illumination 3 or more times faster than previous state‐of‐the‐art methods.

Rendering translucent materials is costly: light transport algorithms need to simulate a large number of scattering events inside the material before reaching convergence. The cost is especially high for materials with a large albedo or a small mean-free- path, where higher-order scattering effects dominate. In simple terms, the paths get lost in the medium. Path guiding has been proposed for surface rendering to make convergence faster by guiding the sampling process. In this paper, we introduce a path guiding solution for translucent materials. We learn an adaptive approximate representation of the radiance distribution in the volume and use it to sample the scattering direction, combining it with phase function sampling by resampled importance sampling. The proposed method significantly improves the performance of light transport simulation in participating media, especially for small lights and media with refractive boundaries. Our method can handle any homogeneous participating medium, with high or low scattering, with high or low absorption, and from isotropic to highly anisotropic.

Monte Carlo based methods such as path tracing are widely used in movie production. To achieve low noise, they require many samples per pixel, resulting in long rendering time. To reduce the cost, one solution is Monte Carlo denoising, which renders the image with fewer samples per pixel (as little as 128) and then denoises the resulting image. Many Monte Carlo denoising methods rely on deep learning: they use convolutional neural networks to learn the relationship between noisy images and reference images, using auxiliary features such as position and normal together with image color as inputs. The network predicts kernels which are then applied to the noisy input. These methods show powerful denoising ability, but tend to lose geometric or lighting details and to blur sharp features during denoising. In this paper, we solve this issue by proposing a novel network structure, a new input feature—light transport covariance from path space—and an improved loss function. Our network separates feature buffers from the color buffer to enhance detail effects. The features are extracted separately and then integrated into a shallow kernel predictor. Our loss function considers perceptual loss, which also improves detail preservation. In addition, we use a light transport covariance feature in path space as one of the features, which helps to preserve illumination details. Our method denoises Monte Carlo path traced images while preserving details much better than previous methods.

Monte Carlo light transport simulations often lack robustness in scenes containing specular or near-specular materials. Widely used uni- and bidirectional sampling strategies tend to find light paths involving such materials with insufficient probability, producing unusable images that are contaminated by significant variance. This article addresses the problem of sampling a light path connecting two given scene points via a single specular reflection or refraction, extending the range of scenes that can be robustly handled by unbiased path sampling techniques. Our technique enables efficient rendering of challenging transport phenomena caused by such paths, such as underwater caustics or caustics involving glossy metallic objects. We derive analytic expressions that predict the total radiance due to a single reflective or refractive triangle with a microfacet BSDF and we show that this reduces to the well known Lambert boundary integral for irradiance. We subsequently show how this can be leveraged to efficiently sample connections on meshes comprised of vast numbers of triangles. Our derivation builds on the theory of off-center microfacets and involves integrals in the space of surface slopes. Our approach straightforwardly applies to the related problem of rendering glints with high-resolution normal maps describing specular microstructure. Our formulation alleviates problems raised by singularities in filtering integrals and enables a generalization of previous work to perfectly specular materials. We also extend previous work to the case of GGX distributions and introduce new techniques to improve accuracy and performance.

Rendering glinty details from specular microstructure enhances the level of realism, but previous methods require heavy storage for the high-resolution height field or normal map and associated acceleration structures. In this article, we aim at dynamically generating theoretically infinite microstructure, preventing obvious tiling artifacts, while achieving constant storage cost. Unlike traditional texture synthesis, our method supports arbitrary point and range queries, and is essentially generating the microstructure implicitly. Our method fits the widely used microfacet rendering framework with multiple importance sampling (MIS), replacing the commonly used microfacet normal distribution functions (NDFs) like ground glass distribution (GGX) by a detailed local solution, with a small amount of runtime performance overhead.

Many materials combine a refractive boundary and a participating media on the interior. If the material has a low opacity, single scattering effects dominate in its appearance. Refraction at the boundary concentrates the incoming light, resulting in an important phenomenon called volume caustics. This phenomenon is hard to simulate. Previous methods used point-based light transport, but attributed point samples inefficiently, resulting in long computation time. In this paper, we use frequency analysis of light transport to allocate point samples efficiently. Our method works in two steps: in the first step, we compute volume samples along with their covariance matrices, encoding the illumination frequency content in a compact way. In the rendering step, we use the covariance matrices to compute the kernel size for each volume sample: small kernel for high-frequency single scattering, large kernel for lower frequencies. Our algorithm computes volume caustics with fewer volume samples, with no loss of quality. Our method is both faster and uses less memory than the original method. It is roughly twice as fast and uses one fifth of the memory. The extra cost of computing covariance matrices for frequency information is negligible.

Rendering translucent materials is costly: light transport algorithms need to simulate a large number of scattering events inside the material before reaching convergence. The cost is especially high for materials with a large albedo or a small mean-free-path, where higher-order scattering effects dominate. We present a new method for fast computation of global illumination with participating media. Our method uses precomputed multiple scattering effects, stored in two compact tables. These precomputed multiple scattering tables are easy to integrate with any illumination simulation algorithm. We give examples for virtual ray lights (VRL), photon mapping with beams and paths (UPBP), Metropolis Light Transport with Manifold Exploration (MEMLT). The original algorithms are in charge of low-order scattering, combined with multiple scattering computed using our table. Our results show significant improvements in convergence speed and memory costs, with negligible impact on accuracy.

Differentiable rendering has recently opened the door to a number of challenging inverse problems involving photorealistic images, such as computational material design and scattering-aware reconstruction of geometry and materials from photographs. Differentiable rendering algorithms strive to estimate partial derivatives of pixels in a rendered image with respect to scene parameters, which is difficult because visibility changes are inherently non-differentiable. We propose a new technique for differentiating path-traced images with respect to scene parameters that affect visibility, including the position of cameras, light sources, and vertices in triangle meshes. Our algorithm computes the gradients of illumination integrals by applying changes of variables that remove or strongly reduce the dependence of the position of discontinuities on differentiable scene parameters. The underlying parameterization is created on the fly for each integral and enables accurate gradient estimates using standard Monte Carlo sampling in conjunction with automatic differentiation. Importantly, our approach does not rely on sampling silhouette edges, which has been a bottleneck in previous work and tends to produce high-variance gradients when important edges are found with insufficient probability in scenes with complex visibility and high-resolution geometry. We show that our method only requires a few samples to produce gradients with low bias and variance for challenging cases such as glossy reflections and shadows. Finally, we use our differentiable path tracer to reconstruct the 3D geometry and materials of several real-world objects from a set of reference photographs.

Abstract Many real‐life materials have a sparkling appearance, whether by design or by nature. Examples include metallic paints, sparkling varnish but also snow. These sparkles correspond to small, isolated, shiny particles reflecting light in a specific direction, on the surface or embedded inside the material. The particles responsible for these sparkles are usually small and discontinuous. These characteristics make it difficult to integrate them efficiently in a standard rendering pipeline, especially for indirect illumination. Existing approaches use a 4‐dimensional hierarchy, searching for light‐reflecting particles simultaneously in space and direction. The approach is accurate, but still expensive. In this paper, we show that this 4‐dimensional search can be approximated using separate 2‐dimensional steps. This approximation allows fast integration of glint contributions for large footprints, reducing the extra cost associated with glints be an order of magnitude.

Illumination effects in translucent materials are a combination of several physical phenomena: refraction at the surface, absorption and scattering inside the material. Because refraction can focus light deep inside the material, where it will be scattered, practical illumination simulation inside translucent materials is difficult. In this paper, we present an a Point-Based Global Illumination method for light transport on homogeneous translucent materials with refractive boundaries. We start by placing light samples inside the translucent material and organizing them into a spatial hierarchy. At rendering, we gather light from these samples for each camera ray. We compute separately the sample contributions for single, double and multiple scattering, and add them. We present two implementations of our algorithm: an offline version for high-quality rendering and an interactive GPU implementation. The offline version provides significant speed-ups and reduced memory footprints compared to state-of-the-art algorithms, with no visible impact on quality. The GPU version yields interactive frame rates: 30 fps when moving the viewpoint, 25 fps when editing the light position or the material parameters.

Adequate reflectance models are essential for the production of photorealistic images. Microfacet reflectance models predict the appearance of a material at the macroscopic level based on microscopic surface details. They provide a good match with measured reflectance in some cases, but not always. This discrepancy between the behavior predicted by microfacet models and the observed behavior has puzzled researchers for a long time. In this paper, we show that diffraction effects in the micro-geometry provide a plausible explanation. We describe a two-scale reflectance model, separating between geometry details much larger than wavelength and those of size comparable to wavelength. The former model results in the standard Cook-Torrance model. The latter model is responsible for diffraction effects. Diffraction effects at the smaller scale are convolved by the micro-geometry normal distribution. The resulting two-scale model provides a very good approximation to measured reflectances.

Reflectance parameters condition the appearance of objects in photorealistic rendering. Practical acquisition of reflectance parameters is still a difficult problem. Even more so for spatially varying or anisotropic materials, which increase the number of samples required. In this paper, we present an algorithm for acquisition of spatially varying anisotropic materials, sampling only a small number of directions. Our algorithm uses Fourier analysis to extract the material parameters from a sub-sampled signal. We are able to extract diffuse and specular reflectance, direction of anisotropy, surface normal and reflectance parameters from as little as 20 sample directions. Our system makes no assumption about the stationarity or regularity of the materials, and can recover anisotropic effects at the pixel level.

Abstract Volume caustics are high‐frequency effects appearing in participating media with low opacity, when refractive interfaces are focusing the light rays. Refractions make them hard to compute, since screen locality does not correlate with spatial locality in the medium. In this paper, we give a new method for accurate computation of single scattering effects in a participating media enclosed by refractive interfaces. Our algorithm is based on the observation that although radiance along each camera ray is irregular, contributions from individual triangles are smooth. Our method gives more accurate results than existing methods, faster. It uses minimal information and requires no pre‐computation or additional data structures.

The rendering of effects such as motion blur and depth-of-field requires costly 5D integrals. We accelerate their computation through adaptive sampling and reconstruction based on the prediction of the anisotropy and bandwidth of the integrand. For this, we develop a new frequency analysis of the 5D temporal light-field, and show that first-order motion can be handled through simple changes of coordinates in 5D. We further introduce a compact representation of the spectrum using the covariance matrix and Gaussian approximations. We derive update equations for the 5 × 5 covariance matrices for each atomic light transport event, such as transport, occlusion, BRDF, texture, lens, and motion. The focus on atomic operations makes our work general, and removes the need for special-case formulas. We present a new rendering algorithm that computes 5D covariance matrices on the image plane by tracing paths through the scene, focusing on the single-bounce case. This allows us to reduce sampling rates when appropriate and perform reconstruction of images with complex depth-of-field and motion blur effects.

Shading acquired materials with high-frequency illumination is computationally expensive. Estimating the shading integral requires multiple samples of the incident illumination. The number of samples required may vary across the image, and the image itself may have high- and low-frequency variations, depending on a combination of several factors. Adaptively distributing computational budget across the pixels for shading is a challenging problem. In this paper, we depict complex materials such as acquired reflectances, interactively, without any precomputation based on geometry. In each frame, we first estimate the frequencies in the local light field arriving at each pixel, as well as the variance of the shading integrand. Our frequency analysis accounts for combinations of a variety of factors: the reflectance of the object projecting to the pixel, the nature of the illumination, the local geometry and the camera position relative to the geometry and lighting. We then exploit this frequency information (bandwidth and variance) to adaptively sample for reconstruction and integration. For example, fewer pixels per unit area are shaded for pixels projecting onto diffuse objects, and fewer samples are used for integrating illumination incident on specular objects.

Shading complex materials such as acquired reflectances in multi-light environments is computationally expensive. Estimating the shading integral requires multiple samples of the incident illumination. The number of samples required varies across the image, depending on a combination of several factors. Adaptively distributing computational budget across the pixels for shading is a challenging problem. In this paper we depict complex materials such as acquired reflectances, interactively, without any precomputation based on geometry. We first estimate the approximate spatial and angular variation in the local light field arriving at each pixel. This local bandwidth accounts for combinations of a variety of factors: the reflectance of the object projecting to the pixel, the nature of the illumination, the local geometry and the camera position relative to the geometry and lighting. We then exploit this bandwidth information to adaptively sample for reconstruction and integration. For example, fewer pixels per area are shaded for pixels projecting onto diffuse objects, and fewer samples are used for integrating illumination incident on specular objects.

Abstract Material models are essential to the production of photo‐realistic images. Measured BRDFs provide accurate representation with complex visual appearance, but have larger storage cost. Analytical BRDFs such as Cook‐Torrance provide a compact representation but fail to represent the effects we observe with measured appearance. Accurately fitting an analytical BRDF to measured data remains a challenging problem. In this paper we introduce the SGD micro‐facet distribution for Cook‐Torrance BRDF. This distribution accurately models the behavior of most materials. As a consequence, we accurately represent all measured BRDFs using a single lobe. Our fitting procedure is stable and robust, and does not require manual tweaking of the parameters.

We present an algorithm to render objects made of transparent materials with rough surfaces in real-time, under all-frequency distant illumination. Rough surfaces cause wide scattering as light enters and exits objects, which significantly complicates the rendering of such materials. We present two contributions to approximate the successive scattering events at interfaces, due to rough refraction: First, an approximation of the Bidirectional Transmittance Distribution Function (BTDF), using spherical Gaussians, suitable for real-time estimation of environment lighting using preconvolution; second, a combination of cone tracing and macrogeometry filtering to efficiently integrate the scattered rays at the exiting interface of the object. We demonstrate the quality of our approximation by comparison against stochastic ray tracing. Furthermore we propose two extensions to our method for supporting spatially varying roughness on object surfaces and local lighting for thin objects.

We present an algorithm to render objects of transparent materials with rough surfaces in real-time, under distant illumination. Rough surfaces cause wide scattering as light enters and exits objects, which significantly complexifies the rendering of such materials. We present two contributions to approximate the successive scattering events at interfaces, due to rough refraction: First, an approximation of the bidirectional scattering function (BSDF = BRDF + BTDF), using spherical Gaussians, suitable for real-time estimation of environment lighting using pre-convolution; second, a combination of cone tracing and macro-geometry filtering to efficiently integrate the scattered rays at the exiting interface of the object. We demonstrate the quality of our approximation by comparison against stochastic raytracing.

Texturing an animated fluid is a useful way to augment the visual complexity of pictures without increasing the simulation time. But texturing flowing fluids is a complex issue, as it creates conflicting requirements: we want to keep the key texture properties (features, spectrum) while advecting the texture with the underlying flow-which distorts it. In this paper, we present a new, Lagrangian, method for advecting textures: the advected texture is computed only locally and follows the velocity field at each pixel. The texture retains its local properties, including its Fourier spectrum, even though it is accurately advected. Due to its Lagrangian nature, our algorithm can perform on very large, potentially infinite scenes in real time. Our experiments show that it is well suited for a wide range of input textures, including, but not limited to, noise textures.

Abstract Realistic animation and rendering of the ocean is an important aspect for simulators, movies and video games. By nature, the ocean is a difficult problem for Computer Graphics: it is a dynamic system, it combines wave trains at all scales, ranging from kilometric to millimetric. Worse, the ocean is usually viewed at several distances, from very close to the viewpoint to the horizon, increasing the multi‐scale issue, and resulting in aliasing problems. The illumination comes from natural light sources (the Sun and the sky dome), is also dynamic, and often underlines the aliasing issues. In this paper, we present a new algorithm for modelling, animation, illumination and rendering of the ocean, in real‐time, at all scales and for all viewing distances. Our algorithm is based on a hierarchical representation, combining geometry, normals and BRDF. For each viewing distance, we compute a simplified version of the geometry, and encode the missing details into the normal and the BRDF, depending on the level of detail required. We then use this hierarchical representation for illumination and rendering. Our algorithm runs in real‐time, and produces highly realistic pictures and animations.

Abstract We present a real‐time algorithm for rendering translucent objects of arbitrary shapes. We approximate the scattering of light inside the objects using the diffusion equation, which we solve on‐the‐fly using the GPU. Our algorithm is general enough to handle arbitrary geometry, heterogeneous materials, deformable objects and modifications of lighting, all in real‐time. In a pre‐processing step, we discretize the object into a regular 4‐connected structure (QuadGraph). Due to its regular connectivity, this structure is easily packed into a texture and stored on the GPU. At runtime, we use the QuadGraph stored on the GPU to solve the diffusion equation, in real‐time, taking into account the varying input conditions: Incoming light, object material and geometry. We handle deformable objects, provided the deformation does not change the topological structure of the objects.

Abstract Many recent games and applications target the interactive exploration of realistic large scale worlds. These worlds consist mostly of static terrain models, as the simulation of animated fluids in these virtual worlds is computationally expensive. Adding flowing fluids, such as rivers, to these virtual worlds would greatly enhance their realism, but causes specific issues: as the user is usually observing the world at close range, small scale details such as waves and ripples are important. However, the large scale of the world makes classical methods impractical for simulating these effects. In this paper, we present an algorithm for the interactive simulation of realistic flowing fluids in large virtual worlds. Our method relies on two key contributions: the local computation of the velocity field of a steady flow given boundary conditions, and the advection of small scale details on a fluid, following the velocity field, and uniformly sampled in screen space.

Motion blur is crucial for high-quality rendering, but is also very expensive. Our first contribution is a frequency analysis of motion-blurred scenes, including moving objects, specular reflections, and shadows. We show that motion induces a shear in the frequency domain, and that the spectrum of moving scenes can be approximated by a wedge. This allows us to compute adaptive space-time sampling rates, to accelerate rendering. For uniform velocities and standard axis-aligned reconstruction, we show that the product of spatial and temporal bandlimits or sampling rates is constant, independent of velocity. Our second contribution is a novel sheared reconstruction filter that is aligned to the first-order direction of motion and enables even lower sampling rates. We present a rendering algorithm that computes a sheared reconstruction filter per pixel, without any intermediate Fourier representation. This often permits synthesis of motion-blurred images with far fewer rendering samples than standard techniques require.

Optical systems used in photography and cinema produce depth-of-field effects, that is, variations of focus with depth. These effects are simulated in image synthesis by integrating incoming radiance at each pixel over the lense aperture. Unfortunately, aperture integration is extremely costly for defocused areas where the incoming radiance has high variance, since many samples are then required for a noise-free Monte Carlo integration. On the other hand, using many aperture samples is wasteful in focused areas where the integrand varies little. Similarly, image sampling in defocused areas should be adapted to the very smooth appearance variations due to blurring. This article introduces an analysis of focusing and depth-of-field in the frequency domain, allowing a practical characterization of a light field's frequency content both for image and aperture sampling. Based on this analysis we propose an adaptive depth-of-field rendering algorithm which optimizes sampling in two important ways. First, image sampling is based on conservative bandwidth prediction and a splatting reconstruction technique ensures correct image reconstruction. Second, at each pixel the variance in the radiance over the aperture is estimated and used to govern sampling. This technique is easily integrated in any sampling-based renderer, and vastly improves performance.

Light scattering in refractive media is an important optical phenomenon for computer graphics. While recent research has focused on multiple scattering, there has been less work on accurate solutions for single or low-order scattering. Refraction through a complex boundary allows a single external source to be visible in multiple directions internally with different strengths; these are hard to find with existing techniques. This paper presents techniques to quickly find paths that connect points inside and outside a medium while obeying the laws of refraction. We introduce: a half-vector based formulation to support the most common geometric representation, triangles with interpolated normals; hierarchical pruning to scale to triangular meshes; and, both a solver with strong accuracy guarantees, and a faster method that is empirically accurate. A GPU version achieves interactive frame rates in several examples.

Linear perspective projections are used extensively in graphics. They provide a non-distorted view, with simple computations that map easily to hardware. Non-linear projections, such as the view given by a fish-eye lens are also used, either for artistic reasons or in order to provide a larger field of view, e.g. to approximate environment reflections or omnidirectional shadow maps. As the computations related to non-linear projections are more involved, they are harder to implement, especially in hardware, and have found little use so far in practical applications. In this paper, we apply existing methods for non-linear projections [Lloyd et al. 2006; Hou et al. 2006; Fournier 2005] to a specific class: non-linear projections with a single center of projection, radial symmetry and convexity. This class includes, but is not limited to, paraboloid projections, hemispherical projections and fish-eye lenses. We show that, for this class, the projection of a 3D triangle is a single curved triangle, and we give a mathematical analysis of the curved edges of the triangle; this analysis allows us to reduce the computations involved, and to provide a faster implementation. The overhead for non-linearity is bearable and can be balanced with the fact that a single nonlinear projection can replaces as many as five linear projections (in a hemicube), with less discontinuities and a smaller memory cost, thus making non-linear projections a practical alternative.

In this paper, we present a new algorithm for interactive rendering of animated scenes with Whitted Ray-Tracing, running on the GPU. We focus our attention on the secondary rays (the rays generated by one or more bounces on specular objects), and use the GPU rasterizer for primary rays. Our algorithm is based on a ray-space hierarchy, allowing us to handle truly dynamic scenes without the need to rebuild or update the scene hierarchy. The rayspace hierarchy is entirely built on the GPU for every frame, using a very fast process. Traversing the ray-space hierarchy is also done on the GPU; one of the benefits of using a ray-space hierarchy is that we have a single shader, and a fixed number of passes. After traversing each level of the hierarchy, we prune empty branches using a stream reduction method. We present two different stream reduction methods, a fast one using a hierarchical algorithm, and an easy one using the Geometry shaders. Our algorithm results in interactive rendering with specular reflections and shadows for moderately complex scenes (~ 700K triangles), handles any kind of dynamic or unstructured scenes without any pre-processing, and scales well with both the scene complexity and the image resolution.

Abstract Shadows, particularly soft shadows, play an important role in the visual perception of a scene by providing visual cues about the shape and position of objects. Several recent algorithms produce soft shadows at interactive rates, but they do not scale well with the number of polygons in the scene or only compute the outer penumbra. In this paper, we present a new algorithm for computing interactive soft shadows on the GPU. Our new approach provides both inner‐ and outer‐penumbra for a modest computational cost, providing interactive frame‐rates for models with hundreds of thousands of polygons. Our technique is based on a sampled image of the occluders, as in shadow map techniques. These shadow samples are used in a novel manner, computing their effect on a second projective shadow texture using fragment programs. In essence, the fraction of the light source area hidden by each sample is accumulated at each texel position of this Soft Shadow Map. We include an extensive study of the approximations caused by our algorithm, as well as its computational costs.

Abstract Specular reflections provide many important visual cues in our daily environment. They inform us of the shape of objects, of the material they are made of, of their relative positions, etc. Specular reflections on curved objects are usually approximated using environment maps. In this paper, we present a new algorithm for real‐time computation of specular reflections on curved objects, based on an exact computation for the reflection of each scene vertex. Our method exhibits all the required parallax effects and can handle arbitrary proximity between the reflector and the reflected objects. Categories and Subject Descriptors (according to ACM CCS): I.3.7 [Computer Graphics]: Three‐Dimensional Graphics and Realism

We propose an automatic method for finding symmetries of 3D shapes, that is, isometric transforms which leave a shape globally unchanged. These symmetries are deterministically found through the use of an intermediate quantity: the generalized moments. By examining the extrema and spherical harmonic coefficients of these moments, we recover the parameters of the symmetries of the shape. The computation for large composite models is made efficient by using this information in an incremental algorithm capable of recovering the symmetries of a whole shape using the symmetries of its subparts. Applications of this work range from coherent remeshing of geometry with respect to the symmetries of a shape to geometric compression, intelligent mesh editing, and automatic instantiation.

We present a signal-processing framework for light transport. We study the frequency content of radiance and how it is altered by phenomena such as shading, occlusion, and transport. This extends previous work that considered either spatial or angular dimensions, and it offers a comprehensive treatment of both space and angle.We show that occlusion, a multiplication in the primal, amounts in the Fourier domain to a convolution by the spectrum of the blocker. Propagation corresponds to a shear in the space-angle frequency domain, while reflection on curved objects performs a different shear along the angular frequency axis. As shown by previous work, reflection is a convolution in the primal and therefore a multiplication in the Fourier domain. Our work shows how the spatial components of lighting are affected by this angular convolution.Our framework predicts the characteristics of interactions such as caustics and the disappearance of the shadows of small features. Predictions on the frequency content can then be used to control sampling rates for rendering. Other potential applications include precomputed radiance transfer and inverse rendering.

Abstract We address in this paper the issue of computing diffuse global illumination solutions for animation sequences. The principal difficulties lie in the computational complexity of global illumination, emphasized by the movement of objects and the large number of frames to compute, as well as the potential for creating temporal discontinuities in the illumination, a particularly noticeable artifact. We demonstrate how space‐time hierarchical radiosity, i.e. the application to the time dimension of a hierarchical decomposition algorithm, can be effectively used to obtain smooth animations: first by proposing the integration of spatial clustering in a space‐time hierarchy; second, by using a higher‐order wavelet basis adapted for the temporal dimension. The resulting algorithm is capable of creating time‐dependent radiosity solutions efficiently.

Abstract ACM CSS: I.3.3 Computer Graphics Picture/Image Generation—Bitmap and framebuffer operations

Since wavelets were introduced in the radiosity algorithm 5, surprisingly little research has been devoted to higher order wavelets and their use in radiosity algorithms. A previous study 13 has shown that wavelet radiosity, and especially higher order wavelet radiosity was not bringing significant improvements over hierarchical radiosity and was having a very important extra memory cost, thus prohibiting any effective computation. In this paper, we present a new implementation of wavelets in the radiosity algorithm, that is substantially different from previous implementations in several key areas (refinement oracle, link storage, resolution algorithm). We show that, with this implementation, higher order wavelets are actually bringing an improvement over standard hierarchical radiosity and lower order wavelets.

This paper presents a complete algorithm for the evaluation and control of error in radiosity calculations. Providing such control is both extremely important for industrial applications andd one of the most challenging issues remaining in global illumination research. In order to control the error, we need to estimate the accuracy of the calculation while computing the energy exchanged between two objects. Having this information for each radiosity interaction allows to allocate more resources to refine interactions with greater potential error, and to avoid spending more time to refine interactions already represented with sufficient accuracy. Until now, the accuracy of the computed energy exchange could only be approximated using heuristic algorithms. This paper presents the first exhaustive algorithm to compute fully reliable upper and lower bounds on the energy being exchanged in each interaction. This is accomplished by computing first and second derivatives of the radiosity function where appropriate, and making use of two concavity conjectures. These bounds are then used in a refinement criterion for hierarchical radiosity, resulting in a global illumination algorithm with complete control of the error incurred. Results are presented, demonstrating the possibility to create radiosity solutions with guaranteed precision. We then extend our algorithm to consider linear bounding functions instead of constant functions, thus creating simpler meshes in regions where the function is concave, without loss of precision. Our experiments show that the computation of radiosity derivatives along with the radiosity values only requires a modest extra cost, with the advantage of a much greater precision.