László Szirmay-Kalos

Approximate Ray-Tracing on the GPU with Distance Impostors

This paper presents a fast approximation method to obtain the point hit by a reflection or refraction ray. The calculation is based on the distance values stored in environment map texels. This approximation is used to localize environment mapped reflections and refractions, that is, to make them depend on where they occur. On the other hand, placing the eye into the light source, the method is also good to generate real-time caustics. Computing a map for each refractor surface, we can even evaluate multiple refractions without tracing rays. The method is fast and accurate if the scene consists of larger planar faces, when the results are similar to that of ray-tracing. On the other hand, the method suits very well to the GPU architecture, and can render ray-tracing and global illumination effects with few hundred frames per second. The primary application area of the proposed method is the introduction of these effects in games.

Displacement Mapping on the GPU — State of the Art

This paper reviews the latest developments of displacement mapping algorithms implemented on the vertex, geometry, and fragment shaders of graphics cards. Displacement mapping algorithms are classified as per‐vertex and per‐pixel methods. Per‐pixel approaches are further categorized as safe algorithms that aim at correct solutions in all cases, to unsafe techniques that may fail in extreme cases but are usually much faster than safe algorithms, and to combined methods that exploit the robustness of safe and the speed of unsafe techniques. We discuss the possible roles of vertex, geometry and fragment shaders to implement these algorithms. Then the particular GPU‐based bump, parallax, relief, sphere, horizon mapping, cone stepping, local ray tracing, pyramidal and view‐dependent displacement mapping methods, as well as their numerous variations are reviewed providing also implementation details of the shader programs. We present these methods using uniform notations and also point out when different authors called similar concepts differently. In addition to basic displacement mapping, self‐shadowing and silhouette processing are also reviewed. Based on our experiences gained having reimplemented these methods, their performance and quality are compared, and the advantages and disadvantages are fairly presented.

Compact Metallic Reflectance Models

The paper presents simple, physically plausible, but not physically based reflectance models for metals and other specular materials. So far there has been no metallic BRDF model that is easy to compute, suitable for fast importance sampling and is physically plausible. This gap is filled by appropriate modifications of the Phong, Blinn and the Ward models. The Phong and the Blinn models are known not to have metallic characteristics. On the other hand, this paper also shows that the Cook‐Torrance and the Ward models are not physically plausible, because of their behavior at grazing angles. We also compare the previous and the newly proposed models. Finally, the generated images demonstrate how the metallic impression can be provided by the new models.

Monte Carlo volume rendering

In this paper a novel volume-rendering technique based on Monte Carlo integration is presented. As a result of a preprocessing, a point cloud of random samples is generated using a normalized continuous reconstruction of the volume as a probability density function. This point cloud is projected onto the image plane, and to each pixel an intensity value is assigned which is proportional to the number of samples projected onto the corresponding pixel area. In such a way a simulated X-ray image of the volume can be obtained. Theoretically, for a fixed image resolution, there exists an M number of samples such that the average standard deviation of the estimated pixel intensities us under the level of quantization error regardless of the number of voxels. Therefore Monte Carlo Volume Rendering (MCVR) is mainly proposed to efficiently visualize large volume data sets. Furthermore, network applications are also supported, since the trade-off between image quality and interactivity can be adapted to the bandwidth of the client/server connection by using progressive refinement.

Global Ray-bundle Tracing with Hardware Acceleration

The paper presents a single-pass, view-dependent method to solve the general rendering equation, using a combined finite element and random walk approach. Applying finite element techniques, the surfaces are decomposed into planar patches that are assumed to have position independent, but not direction independent radiance. The direction dependent radiance function is then computed by random walk using bundles of parallel rays. In a single step of the walk, the radiance transfer is evaluated exploiting the hardware z-buffer of workstations, making the calculation fast. The proposed method is particularly efficient for scenes including not very specular materials illuminated by large area light-sources or sky-light. In order to increase the speed for difficult lighting situations, walks can be selected according to their importance. The importance can be explored adaptively by the Metropolis sampling method.

An Analysis of Quasi‐Monte Carlo Integration Applied to the Transillumination Radiosity Method

This paper presents an enhanced transillumination radiosity method that can provide accurate solutions at relatively low computational cost. The proposed algorithm breaks down the double integral of the gathered power to an area integral that is computed analytically and to a directional integral that is evaluated by quasi‐Monte Carlo techniques. Since the analytical integration results in a continuous function of finite variation, the quasi‐Monte Carlo integration that follows the analytical integration will be efficient and its error can be bounded by the Koksma‐Hlawka inequality. The paper also analyses the requirements of the convergence, presents theoretical error bounds and proposes error reduction techniques. The theoretical bounds are compared with simulation results.

An anisotropic BRDF model for fitting and Monte Carlo rendering

In this paper we propose a new physically plausible, anisotropic Bidirectional Reflectance Distribution Function (BRDF) for fitting and for importance sampling in global illumination rendering. We demonstrate that the new model is better in data fitting than existing BRDF models. We also describe efficient schemes for sampling the proposed anisotropic BRDF model. Furthermore, we test it on a GPU-based real-time rendering algorithm and show that material design can be done with this anisotropic BRDF model effectively. We also show that the new model has effective real-time rendering performance.

Stochastic iteration for nondiffuse global illumination

This paper presents a single‐pass, view‐dependent method to solve the rendering equation, using a stochastic iterational scheme where the transport operator is selected randomly in each iteration. The requirements of convergence are given for the general case. To demonstrate the basic idea, a very simple,continuous random transport operator is examined, which gives back the light tracing algorithm incorporating Russian roulette. Then, a new mixed continuous and finite‐element based iteration method is proposed, which uses ray‐bundles to transfer the radiance in a single random direction. The resulting algorithm is fast, it provides initial results in seconds and accurate solutions in minutes and does not suffer from the error accumulation problem and the high memory demand of other finite‐element and hierarchical approaches.

Free Path Sampling in High Resolution Inhomogeneous Participating Media

This paper presents efficient algorithms for free path sampling in heterogeneous participating media defined either by high‐resolution voxel arrays or generated procedurally. The method is based on the concept of mixing ‘virtual’ material or particles to the medium, augmenting the extinction coefficient to a function for which the free path can be sampled in a straightforward way. The virtual material is selected such that it modifies the volume density but does not alter the radiance. We define the total extinction coefficient of the real and virtual particles by a low‐resolution grid of super‐voxels that are much larger than the real voxels defining the medium. The computational complexity of the proposed method depends just on the resolution of the super‐voxel grid and does not grow with the resolution above the scale of super‐voxels. The method is particularly efficient to render large, low‐density, heterogeneous volumes, which should otherwise be defined by enormously high resolution voxel grids and where the average free path length would cross many voxels.

Volumetric Ambient Occlusion for Real-Time Rendering and Games

This new algorithm, based on GPUs, can compute ambient occlusion to inexpensively approximate global-illumination effects in real-time systems and games. The first step in deriving this algorithm is to examine how ambient occlusion relates to the physically founded rendering equation. The correspondence stems from a fuzzy membership function that defines what constitutes nearby occlusions. The next step is to develop a method to calculate ambient occlusion in real time without precomputation. The algorithm is based on a novel interpretation of ambient occlusion that measures the relative volume of the visible part of the surfaces tangent sphere. The new formulas integrand has low variation and thus can be estimated accurately with a few samples.