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Thin-film coating is a common practice to modify the appearance of materials. In optics for example, coating is often used on mirrors or lenses to modify their reflectance and transmittance properties. To achieve high transmittance optics or wavelength selective filters for sensors, multilayer coatings are required. Thin-film coating is an active area of research. In this paper we introduce to the rendering community the transfer matrix method to calculate the Fresnel coefficients for multilayer thin-film coating. This method, commonly used in optics, provides an easy way to calculate reflectance and transmittance coefficients for an arbitrary number of thin-film layers. Unlike previous methods [10], which relied on the infinite Airy summation, this method is based on the multiplication of \(2\times 2\) matrices which allows handling more general cases. We apply this method to simulate physically based anti-reflective coating where a single layer of thin-film coating is often not enough to obtain a good performance over the full visible spectrum.

We present a practical framework for reproducing omnidirectional incident illumination conditions with complex spectra using a light stage with multispectral LED lights. For lighting acquisition, we augment standard RGB panoramic photography with one or more observations of a color chart with numerous reflectance spectra. We then solve for how to drive the multispectral light sources so that they best reproduce the appearance of the color charts in the original lighting. Even when solving for non-negative intensities, we show that accurate lighting reproduction is achievable using just four or six distinct LED spectra for a wide range of incident illumination spectra. A significant benefit of our approach is that it does not require the use of specialized equipment (other than the light stage) such as monochromators, spectroradiometers, or explicit knowledge of the LED power spectra, camera spectral response functions, or color chart reflectance spectra. We describe two simple devices for multispectral lighting capture, one for slow measurements of detailed angular spectral detail, and one for fast measurements with coarse angular detail. We validate the approach by realistically compositing real subjects into acquired lighting environments, showing accurate matches to how the subject would actually look within the environments, even for those including complex multispectral illumination. We also demonstrate dynamic lighting capture and playback using the technique.

Verifying the correctness of intelligent embedded systems is notoriously difficult due to the use of machine learning algorithms that cannot provide guarantees of deterministic correctness. In this paper, our validation efforts demonstrate that the OpenCV Histogram of Oriented Gradients (HOG) implementation for human detection is susceptible to errors due to both malicious perturbations and naturally occurring fog phenomena. To the best of our knowledge, we are the first to explicitly employ a natural perturbation (like fog) as an adversarial attack using methods from computer graphics. Our experimental results show that computer vision algorithms are susceptible to errors under a small set of naturally occurring perturbations even if they are robust to a majority of such perturbations. Our methods and results may be of interest to the designers, developers and validation teams of intelligent cyber-physical systems such as autonomous cars.

Background Polychromatic flow cytometry is a popular technique that has wide usage in the medical sciences, especially for studying phenotypic properties of cells. The high-dimensionality of data generated by flow cytometry usually makes it difficult to visualize. The naive solution of simply plotting two-dimensional graphs for every combination of observables becomes impractical as the number of dimensions increases. A natural solution is to project the data from the original high dimensional space to a lower dimensional space while approximately preserving the overall relationship between the data points. The expert can then easily visualize and analyze this low-dimensional embedding of the original dataset. Results This paper describes a new method, SANJAY, for visualizing high-dimensional flow cytometry datasets. This technique uses a decision procedure to automatically synthesize two-dimensional and three-dimensional projections of the original high-dimensional data while trying to minimize distortion. We compare SANJAY to the popular multidimensional scaling (MDS) approach for visualization of small data sets drawn from a representative set of benchmarks, and our experiments show that SANJAY produces distortions that are 1.44 to 4.15 times smaller than those caused due to MDS. Our experimental results show that SANJAY also outperforms the Random Projections technique in terms of the distortions in the projections. Conclusions We describe a new algorithmic technique that uses a symbolic decision procedure to automatically synthesize low-dimensional projections of flow cytometry data that typically have a high number of dimensions. Our algorithm is the first application, to our knowledge, of using automated theorem proving for automatically generating highly-accurate, low-dimensional visualizations of high-dimensional data.

Mandible bone segmentation from computed tomography (CT) scans is challenging due to mandible's structural irregularities, complex shape patterns, and lack of contrast in joints. Furthermore, connections of teeth to mandible and mandible to remaining parts of the skull make it extremely difficult to identify mandible boundary automatically. This study addresses these challenges by proposing a novel framework where we define the segmentation as two complementary tasks: recognition and delineation. For recognition, we use random forest regression to localize mandible in 3D. For delineation, we propose to use 3D gradient-based fuzzy connectedness (FC) image segmentation algorithm, operating on the recognized mandible sub-volume. Despite heavy CT artifacts and dental fillings, consisting half of the CT image data in our experiments, we have achieved highly accurate detection and delineation results. Specifically, detection accuracy more than 96% (measured by union of intersection (UoI)), the delineation accuracy of 91% (measured by dice similarity coefficient), and less than 1 mm in shape mismatch (Hausdorff Distance) were found.

Uniform grids are a spatial subdivision acceleration structure well suited for ray tracing. They are known for their fast build times and ease of use, but suffer from slow traversals in the presence of empty space. To address this issue, we present macro 64-regions, a new GPU based approach for finding and storing empty volumes in an underlying uniform grid. This allows for fast traversals through regions that do not contain scene geometry. Further, unlike previous solutions to this problem, we do not store a hierarchical structure and therefore the traversal steps are simplified. Because macro 64-regions are dependent on an underlying grid, we also introduce an improvement in the grid construction process. Our method does not rely on sorting as previous methods do, but instead uses atomic operators to manage bookkeeping during the build. Using our proposed methods, we show a substantial improvement in build time, trace time, as well as an improvement in the consistency of rendering times for randomly generated views.

In this paper we propose a novel technique to perform real-time rendering of translucent inhomogeneous materials, one of the most well-known problems of computer graphics. The developed technique is based on an adaptive volumetric point sampling, done in a preprocessing stage, which associates to each sample the optical depth for a predefined set of directions. This information is then used by a rendering algorithm that combines the object's surface rasterization with a ray tracing algorithm, implemented on the graphics processor, to compose the final image. This approach allows us to simulate light scattering phenomena for inhomogeneous isotropic materials in real time with an arbitrary number of light sources. We tested our algorithm by comparing the produced images with the result of ray tracing and showed that the technique is effective. © Springer-Verlag 2010.

In the last few years, researchers in the field of High Dynamic Range (HDR) Imaging have focused on providing tools for expanding Low Dynamic Range (LDR) content for the generation of HDR images due to the growing popularity of HDR in applications, such as photography and rendering via Image-Based Lighting, and the imminent arrival of HDR displays to the consumer market. LDR content expansion is required due to the lack of fast and reliable consumer level HDR capture for still images and videos. Furthermore, LDR content expansion, will allow the re-use of legacy LDR stills, videos and LDR applications created, over the last century and more, to be widely available. The use of certain LDR expansion methods, those that are based on the inversion of Tone Mapping Operators (TMOs), has made it possible to create novel compression algorithms that tackle the problem of the size of HDR content storage, which remains one of the major obstacles to be overcome for the adoption of HDR. These methods are used in conjunction with traditional LDR compression methods and can evolve accordingly. The goal of this report is to provide a comprehensive overview on HDR Imaging, and an in depth review on these emerging topics.

Thanks to an increase in rendering efficiency, indirect illumination has recently begun to be integrated in cinematic lighting design, an application where physical accuracy is less important than careful control of scene appearance. This paper presents a comprehensive, efficient, and intuitive representation for artistic control of indirect illumination. We encode user's adjustments to indirect lighting as scale and offset coefficients of the transfer operator. We take advantage of the nature of indirect illumination and of the edits themselves to efficiently sample and compress them. A major benefit of this sampled representation, compared to encoding adjustments as procedural shaders, is the renderer-independence. This allowed us to easily implement several tools to produce our final images: an interactive relighting engine to view adjustments, a painting interface to define them, and a final renderer to render high quality results. We demonstrate edits to scenes with diffuse and glossy surfaces and animation.

Relief mapping using the secant method offers an efficient method for adding per-pixel displacement based on height fields to an arbitrary polygonal mesh in real time. The technique utilizes an interval-based method in which bounds of the interval are computed in the beginning and are refined at every iteration until the intersection point is reached. The search space defined by the interval reduces and converges to the intersection point rapidly and outperforms the currently popular method based on binary search (relief mapping) used for performing this task. We compute the bounds using a simple ray-segment intersection method. We demonstrate the algorithm and show empirical and explicit evidence of the speed-up. Source code is available online.

Polychromatic flow cytometry is a widely used technique for gathering and analyzing cellular data. The data generated is high-dimensional, and therefore notoriously difficult to visualize by a human expert. The traditional method of plotting every pair of observables of the original high-dimensional data leads to a combinatorial explosion in the number of visualizations. The usual solution is to project the data into a lower-dimensional space while approximately preserving key properties and relationships among data points. The lower dimensional data can then be easily analyzed with the help of specialized data visualization software.

Military training, concept design, and pre-acquisition studies often are carried out in virtual settings in which one can experience that which is, in the real world, too dangerous, too costly, or even beyond current technology. Purely virtual environments, however, have limitations in that they remove the participant from the physical world with its visual, auditory, and tactile complexities. In contrast, mixed reality (MR) seeks to blend the real and synthetic. How well that blending works is critical to the effectiveness of a user's experience within an MR scenario. The focus of this paper is on the visual aspects of this blending or more specifically on the interactions between the real and virtual in the contexts of proper inter-occlusion, illumination, and inter-shadowing. This means that the virtual objects must react properly to changes in real lighting and that the real must react properly to the insertion of virtual lights (e.g., a virtual flashlight or a simulated change in the time of day). Even more challenging, virtual objects must cast shadows on real objects and vice versa. The proper casting of shadows is critical to military training, in that shadows often provide clues of others' movements, and of our own to others, long before visual contact is made. Realistic shadows can improve training greatly; their omission or the insertion of physically incorrect shadowing can lead to negative training. To be effective, visual realism requires all such interactions occur at interactive rates (30+ frames per second). Our research focuses on algorithmic development and implementation of these procedures on programmable graphics units (GPUs) found commonly on today's commodity graphics cards. The algorithms we develop are tailored to take advantage of the parallel pipeline architecture of GPUs. Our primary application is training of dismounted infantry for the complexities of military operations in urban terrain (MOUT).

We have developed a system for computing a plausible global illumination solution for dynamic environments in real time on programmable graphics processors (GPUs). The entire algorithm runs on DirectX 9.0 compatible graphics hardware using vertex and fragment shaders, and computes a global illumination solution for reasonably complex scenes with moving objects and moving lights at frame rates of 10-40 fps. We present the salient steps of the algorithm that made this real time global illumination evaluation possible.

Realistic display of high-dynamic range images is a difficult problem. Previous methods for high-dynamic range image display suffer from halo artifacts or are computationally expensive. We present a novel method for computing local adaptation luminance that can be used with several different visual adaptation-based tone-reproduction operators for displaying visually accurate high-dynamic range images. The method uses fast image segmentation, grouping, and graph operations to generate local adaptation luminance. Results on several images show excellent dynamic range compression, while preserving detail without the presence of halo artifacts. With adaptive assimilation, the method can be configured to bring out a high-dynamic range appearance in the display image. The method is efficient in terms of processor and memory use.

Texture mapping has become indispensable in image synthesis as an inexpensive source of rich visual detail. Less obvious, but just as useful, is its ability to mask image errors due to inaccuracies in geometry or lighting. This ability can be used to substantially accelerate rendering by eliminating computations when the resulting errors will be perceptually insignificant. Our new method precomputes the masking ability of textures using aspects of the JPEG image compression standard. This extra information is stored as threshold elevation factors in the texture’s mip-map and interpolated at image generation time as part of the normal texture lookup process. Any algorithm which uses error tolerances or visibility thresholds can then take advantage of texture masking. Applications to adaptive shadow testing, irradiance caching, and path tracing are demonstrated. Unlike prior methods, our approach does not require that initial images be computed before masking can be exploited and incurs only negligible runtime computational overhead. Thus, it is much easier to integrate with existing rendering systems for both static and dynamic scenes and yields computational savings even when only small amounts of texture masking are present.

A new method for interactive rendering of complex lighting effects combines two algorithms. The first performs accurate ray tracing in heterogeneous refractive media to compute high-frequency phenomena. The second applies lattice-Boltzmann lighting to account for low-frequency multiple-scattering effects. The two algorithms execute in parallel on modern graphics hardware. This article includes a video animation of the authors' real-time algorithm rendering a variety of scenes.

Interest in polarization properties of rendered materials is growing, but so far discussions on polarization have been restricted only to surface reflection, and the reflection due to subsurface scattering is assumed to be unpolarized. Findings from other fields (e.g. optics and atmospheric science) show that volumetric interaction of light can contribute to polarization. We thus investigated the polarized nature of the radiance field due to subsurface scattering as a function of the thickness of the material layer for various types of materials. Though our computations show negligible polarization for material layers of high thickness, light reflected on thin layered materials show significant degrees of polarization. Consequently, polarization cannot be ignored for subsurface component of reflection from painted surfaces (particularly painted metal surfaces) or from coated materials. Reflection from such surfaces is computed by solving for light transport in the different paint layers. In this paper we employ the vector radiative transfer equation (VRTE), which is the polarized version of the radiative transfer equation, inside the material. We use and detail a discrete ordinate based method to solve the VRTE and use the solution to compute the polarized radiance field at the surface of the material layer. We generate the polarimetric BRDF from the solutions of the VRTE for incident irradiance with different polarizations. We validate our VRTE solution against a benchmark and demonstrate our results through renderings using the computed BRDF. Graphical abstractDisplay Omitted HighlightsWe model polarized light transport using the vector radiative transfer equation.We present a DOM solution to that equation to solve polarized subsurface scattering.We apply this solution to paint layers, and compute their polarized BRDF.We show that polarization is important for subsurface BRDF through an experiment.We compute polarized BRDF for a variety of paint layers on different base materials.

Interest in polarization properties of the rendered materials is growing, but so far discussions on polarization have been restricted only to surface reflection, and the reflection due to subsurface scattering is assumed to be unpolarized. Findings from other field (e.g. optics and atmospheric science) show that volumetric interaction of light can contribute to polarization. So we investigated the polarized nature of the radiance field due to subsurface scattering as a function of the thickness of the material layer for various types of materials. Though our computations shows negligible polarization for material layers of high thickness, thin layered materials show significant degree of polarization. That means polarization cannot be ignored for subsurface component of reflection from painted surfaces (particularly painted metal surfaces) or from coated materials. In this paper we employ the vector radiative transfer equation (VRTE), which is the polarized version of the radiative transfer equation inside the material. We use a discrete ordinate based method to solve the VRTE and compute the polarized radiance field at the surface of the material layer. We generate the polarimetric BRDF from the solutions of the VRTE for incident irradiance with different polarizations. We validate our VRTE solution against a benchmark and demonstrate our results through renderings using the computed BRDF.

We present a novel technique for physically based rendering of participating media like cloud, smoke, wax, marble, etc. We solve the radiative transfer equation (RTE) for participating media using the Modified Discrete Ordinate Method (MDOM), which computes the final solution as a combination of a direct and an indirect component. We propose a scalable GPU based parallel pipeline, for solving the RTE using the MDOM. This parallel RTE solver is capable of rendering intermediate results such as single scattering approximation. We overcome GPU memory size limitations by using low resolution radiance storage while doing high resolution radiance propagation. Furthermore, we achieve scalability by implementing an efficient volumetric data streaming mechanism. Our results demonstrate the ability of our method to render high quality multiple scattering effects.

Accurately modeling BRDF for real world materials is important and challenging for realistic image synthesis. For a majority of materials most of the incident light enters the material, undergoes multiple scattering under the surface before exiting the material's surface as reflection. Physically correct modeling of such BRDF must take into account of this subsurface volumetric light transport. Most of the accurate numerical solution methods (ex: Monte Carlo, Discrete Ordinate Methods (DOM)) for volumetric light transport compute radiance field for the whole volume, and are expensive. As BRDF ultimately relates only the outgoing radiation field at the boundary to the incident radiation, radiation field computed for the bulk of the material does not provide any useful information and hence the effort involved in computing them can be considered as wasteful. So for efficient BRDF computation any method that allows us to compute the radiance field only at the boundary would be a preferable choice. The search for such a method led us to the Ambartsumian's method [Sobolev 1975; Mishchenko et al. 1999].

This paper presents an accurate method to compute the bidirectional reflectance distribution function (BRDF) due to subsurface scattering inside the material of the objects. This computation requires iterating over the different lighting directions, and solving the integro-differential equation of light transport (scattering and absorption). Solving the light transport equation is expensive, and solving it independently for different directions adds even further to the expense. However most of the computations are very similar between directions. We make use of Green's function of the transport problem to have a better separation between computations that are independent of incident directions from those that are dependent. This allows us to avoid as much repetition in the computations as possible, thus gives us a faster BRDF computation method without any loss of accuracy. We validate our method against a standard light transport solver and use it to compute BRDF for a variety of materials.

International audience; In this paper, we present a novel approach to progressive photon-based volume rendering techniques. By making use of two Kd-trees (built in a preprocessing step) to store view beams (primary rays intersecting the medium) and visible points, our method allows to handle scenes with specular and refractive objects as well as homogeneous and heterogeneous participating media and does not require the storage of photon maps, which solves the memory management issue. These data structures are used to drive the photon shooting process by considering the photon visibility as an importance function (similarly to Hachisuka and Jensen in ACM Trans. Graph. 30(5):114:1–114:11, 2011) for scenes containing participating media. Finally, we demonstrate that our method can be easily combined with the most recent particle tracing approaches such as the one presented in Jarosz et al. (ACM Trans. Graph., vol. 30(6), 2011).

In spite of the number of efforts made by the computer graphics researchers, till today the computation of view-independent global illumination in an environment containing non-diffusely reflecting objects is a non-resolved problem. In general, non-deterministic techniques seem to be capable of solving this problem. In this article we propose one such non-deterministic method which will permit such calculation by using a combined technique of higher order junction approximation and particle tracing. We have used multi-wavelets as basis functions and have calculated the illumination function approximation coefficients by exploiting the adjointness between the radiance equation and the potential equation.

In this paper we introduce the potential equation that along with the rendering equation forms an adjoint system of equations and provides a mathematical frame work for all known approaches to illumination computation based on geometric optics. The potential equation is more natural for illumination computations that simulate light propagation starting from the light sources, such as progressive radiosity and particle tracing. Using the mathematical handles provided by this framework and the random-walk solution model, we present a number of importance sampling schemes for improving the computation of flux estimation. Of particular significance is the use of approximately computed potential for directing a majority of the random walks through regions of importance in the environment, thus reducing the variance in the estimates of luminous flux in these regions. Finally, results from a simple implementation are presented to demonstrate the high-efficiency improvements made possible by the use of these techniques.

Wavelet analysis has been found [1] to be very useful for functional representation and accurate global solution of radiosity. In radiosity we deal with functions in 2D and 4D spaces. Under such conditions, the biggest bottleneck in applying this wavelet analysis seems to be the large number of multidimensional inner products. In this paper, we propose (i) the use of interpolating wavelets for fast inner product computation and consequently for faster wavelet radiosity solution (ii) the use of hierarchical decomposition technique for determining the smoothness of the radiosity function for optimal adaptive subdivision.

This paper discusses techniques for the computation of global illumination in environments with a participating medium using a Monte Carlo simulation of the particle model of light. Efficient algorithms and data structures for tracking the particles inside the volume have been developed. The necessary equation for computing the illumination along any given direction has been derived for rendering a scene with a participating medium. A major issue in any Monte Carlo simulation is the uncertainty in the final simulation results. Various steps of the algorithm have been analysed to identify major sources of uncertainty. To reduce the uncertainty, suitable modifications to the simulation algorithm have been suggested using variance reduction methods of forced collision, absorption suppression and particle divergence. Some sample scenes showing the results of applying these methods are also included.

The potential equation provides a natural mathematical basis for all the illumination computation methods based on the strategy of shooting light. The particle tracing technique that physically simulates the particle model of light, can also be considered a general, random walk-based solution to the potential equation. As the complexity of the environment increases, the straightforward particle tracing method becomes inefficient. In this paper we discuss different biasing methods that could be used to increase the efficiency of the particle tracing process. In particular we present an importance-driven scheme in which we use an approximate potential value as the biasing function for directing a majority of the random walks through regions of importance in the environment, thus efficiently estimating the light flux in these regions. A straightforward simple implementation of this scheme has been carried out and the results that we have obtained show that the scheme is very promising.

An equation adjoint to the luminance equation for describing the global illumination can be formulated using the notion of a surface potential to illuminate the region of interest. This adjoint equation which we shall call as the potential equation, is fundamental to the adjoint radiosity equation used to devise the importance driven radiosity algorithm. In this paper we first briefly derive the adjoint system of integral equations and then show that the adjoint linear equations used in the above algorithm are basically discrete formulations of the same. We also show that the importance entity of the linear equations is basically the potential function integrated over a patch. Further we prove that the linear operators in the two equations are indeed transposes of each other.

International audience; We present a fast and simple method for adding high-frequency shadows into the foliage of trees rendered in real-time. When leaves of a tree project shadows onto other leaves, determining the relationships between cast shadows and the corresponding occluders is a visually difficult task. We present a method based on this assumption to quickly determine shadows cast by leaves onto other leaves. To this end, we simulate the presence of these shadows rather than projecting them exactly. The characteristics of these simulated shadows (movement, parallax, size, softness, and color) evolve realistically when the lighting conditions change. Our method is fast and supports soft shadows.

We present an approach for editing shadows in all-frequency lighting environments. To support artistic control, we propose to decouple shadowing from lighting and focus on providing intuitive controls to edit the former. To accomplish this task, we precompute and store scene visibility information separately from lighting and BRDFs and allow artists to edit visibility directly, by providing operations to select shadows and edit their shape. To facilitate a wider range of editing operations, we generalize visibility from binary to three-channel floating point quantities and introduce a novel shadow representation based on computation of visibility ratios between the original render and the edited one. We demonstrate our results for diffuse and glossy surfaces, still scenes and animations.

Smell is a key human sense which can significantly effect our perception of an environment. Although, typically not as developed as our other senses, the presence of a pleasant or unpleasant smell can alter the way we view a scene. Such a cross-modal effect can be substantial with parts of a scene literally going unnoticed as the smell dominates our senses. This paper investigates the cross-modal affect on the perception of the real-time animation of a field of grass in the presence of the smell of cut-grass. Rendering the high level of detail of a close-up view of a field of grass is computationally very demanding. In the real world the smell of grass would be present, and especially strong if the grass had just been cut, for example in preparation for a sports event. By exploiting the cross-modal interaction between smell and visuals we are able to render a lower quality version of a field of grass at a reduced computational cost, without the viewer being aware of the quality difference compared to a high quality version.

The authors present a real-time grass rendering technique that works for large, arbitrary terrains with dynamic lighting, shadows, and a good parallax effect. A novel combination of geometry and lit volume slices provides accurate, per-pixel lighting. A fast grass-density management scheme allows the rendering of arbitrarily shaped patches of grass.

The authors present an algorithm for real-time realistic rendering of translucent materials such as marble, wax, and milk. Their method captures subsurface scattering effects while maintaining interactive frame rates. The main idea of this work is that it employs the dipole diffusion model with a splatting approach to evaluate the integral over the surface area for computing illumination due to multiple scattering.

Radiance and irradiance caching are efficient global illumination algorithms based on interpolating indirect illumination from a sparse set of cached values. In this paper we propose an adaptive algorithm for guiding spatial density of the cached values in radiance and irradiance caching. The density is adapted to the rate of change of indirect illumination in order to avoid visible interpolation artifacts and produce smooth interpolated illumination. In addition, we discuss some practical problems arising in the implementation of radiance and irradiance caching, and propose techniques for solving those problems. Namely, the neighbor clamping heuristic is proposed as a robust means for detecting small sources of indirect illumination and for dealing with problems caused by ray leaking through small gaps between adjacent polygons.

High quality lighting is one of the challenges for interactive tree rendering. To this end, this paper presents a lighting model allowing real-time rendering of trees with convincing indirect lighting. Rather than defining an empirical model to mimic lighting of real trees, we work at a lower level by modeling the spatial distribution of leaves and by assigning them probabilistic properties. We focus mainly on precise low-frequency lighting that our eyes are more sensitive to and we add high-frequency details afterwards. The resulting model is efficient and simple to implement on a GPU.

This paper presents a new view-independent, energy equilibrium method for determining the light distributed in a complex 3D environment consisting of surfaces with general reflectance properties. The method does not depend on discretization of directions or discretization of surfaces to differential elements. Hence, it is a significant improvement over the earlier complete view-independent method which is computationally intractable for complex environments or the hybrid methods which include an extended view-dependent ray tracing second pass. The new method is based on an efficient data structure of order O(N2) called the spherical cover. The spherical cover elegantly captures the complex multidimensional directional nature of light distributed over surfaces. Subdivision techniques based on range estimation of various parameters using interval-arithmetic-like methods are next described for efficiently computing the spherical cover for a given 3D environment. Using the spherical cover, light is progressively propagated through the environment until energy equilibrium is reached. Complexity analysis of the propagation step is carried out to show that the method is computationally tractable. The paper also includes a comprehensive review of earlier rendering techniques viewed from the point of view of capturing the multidimensional nature of light distribution over surfaces.

The limited flexibility imposed by the physics of light transport has been a major hurdle in the use of global illumination in production rendering. It has been a common practice in computer cinematography to write custom shaders [Christensen 2003] or manually edit rendered images [Thacker 2006] to achieve lighting effects desired by directors. This process is lengthy, cumbersome and too technical for artists. To remove this hurdle, we propose a novel interface that allows users to modify light transport in a scene. Users can adjust effects of indirect lighting cast by one object onto another or paint indirect illumination on surfaces. As opposed to previous approaches such as [Schoeneman et al. 1993] our work departs from solving optimization problems in favor of more user control.

Particle systems are visualized by rendering some fixed number of particles per frame, where particle information is sampled from emitters represented by a location, and a range of potential initial particle parameters, such as origin, size, etc. For some complicated effects, especially for such effects where there are many potential emitters, where the location of the emitter is not well-defined, or when particle origins or other parameters can not be easily defined by an analytic boundary, the problem of generating new particle samples becomes difficult. One concrete example of such a scenario is the modelling of rain or hail splattering from visible objects as particles, where every point on a surface that can receive rain is a potential emitter. Another example comes in the form of a large-scale detailed forest fire simulation, where each leaf (or portion of leaf) that is burning is an emitter of flame particles, and there are potentially thousands of leaves visible at any given time.

In this paper, we present a simple and practical technique for real-time rendering of caustics from reflective and refractive objects. Our algorithm, conceptually similar to shadow mapping, consists of two main parts: creation of a caustic map texture, and utilization of the map to render caustics onto nonshiny surfaces. Our approach avoids performing any expensive geometric tests, such as ray-object intersection, and involves no precomputation; both of which are common features in previous work. The algorithm is well suited for the standard rasterization pipeline and runs entirely on the graphics hardware.