Abstract Path tracing remains the gold standard for high‐fidelity subsurface scattering despite requiring numerous paths for noise‐free estimates. We introduce a novel variance‐reduction method based on two complementary zero‐variance‐theory‐based approaches. The first one, analytical Dwivedi sampling, is lightweight but struggles with complex lighting. The second one, surface path guiding, learns incident illumination at boundaries to guide sampled paths, but it does not reduce variance from subsurface scattering. In our novel method, we enhance Dwivedi sampling by incorporating the radiance field learned only at the volume boundary. We use the average normal of points on an illuminated boundary region or directions sampled from distributions of incident light at the boundary as our analytical Dwivedi slab normals. Unlike previous methods based on Dwivedi sampling, our method is efficient even in scenes with complex light rigs typical for movie production and under indirect illumination. We achieve comparable noise reduction and even slightly improved estimates in some scenes compared to volume path guiding, and our method can be easily added on top of any existing surface path guiding system. Our method is particularly effective for homogeneous, isotropic media, bypassing the extensive training and caching inside the 3D volume that volume path guiding requires.

Abstract In the domain of wood modeling, we present a new complex appearance model, coupled with a user‐friendly NLP‐based frontend for intuitive interactivity. First , we present a procedurally generated wood model that is capable of accurately simulating intricate wood characteristics, including growth rings, vessels/pores, rays, knots, and figure. Furthermore, newly developed features were introduced, including brushiness distortion, influence points, and individual feature control. These novel enhancements facilitate a more precise matching between procedurally generated wood and ground truth images. Second , we present a text‐based user interface that relies on a trained natural language processing model that is designed to map user plain English requests into the parameter space of our procedurally generated wood model. This significantly reduces the complexity of the authoring process, thereby enabling any user, regardless of their level of woodworking expertise or familiarity with procedurally generated materials, to utilize it to its fullest potential.

Abstract Spectral representation of assets is an important precondition for achieving physical realism in rendering. However, defining assets by their spectral distribution is complicated and tedious. Therefore, it has become general practice to create RGB assets and convert them into their spectral counterparts prior to rendering. This process is called spectral uplifting. While a multitude of techniques focusing on reflectance uplifting exist, the current state of the art of uplifting emission for image‐based lighting consists of simply scaling reflectance uplifts. Although this is usable insofar as the obtained overall scene appearance is not unrealistic, the generated emission spectra are only metamers of the original illumination. This, in turn, can cause deviations from the expected appearance even if the rest of the scene corresponds to real‐world data. In a recent publication, we proposed a method capable of uplifting HDR environment maps based on spectral measurements of light sources similar to those present in the maps. To identify the illuminants, we employ an extensive set of emission measurements, and we combine the results with an existing reflectance uplifting method. In addition, we address the problem of environment map capture for the purposes of a spectral rendering pipeline, for which we propose a novel solution. We further extend this work with a detailed evaluation of the method, both in terms of improved colour error and performance.

We present a novel method for accurately calibrating the optical properties of full-color 3D printers using only a single, directly printable calibration target. Our approach is based on accurate multiple-scattering light transport and estimates the single-scattering albedo and extinction coefficient for each resin. These parameters are essential for both soft-proof rendering of 3D printouts and for advanced, scattering-aware 3D halftoning algorithms. In contrast to previous methods that rely on thin, precisely fabricated resin samples and labor-intensive manual processing, our technique achieves higher accuracy with significantly less effort. Our calibration target is specifically designed to enable algorithmic recovery of each resin's optical properties through a series of one-dimensional and two-dimensional numerical optimizations, applied first on the white and black resins, and then on any remaining resins. The method supports both RGB and spectral calibration, depending on whether a camera or spectrometer is used to capture the calibration target. It also scales linearly with the number of resins, making it well-suited for modern multi-material printers. We validate our approach extensively, first on synthetic and then on real resins across 242 color mixtures, printed thin translucent samples, printed surface textures, and fully textured 3D models with complex geometry, including an eye model and a figurine.

Abstract Realistically modelled atmospheric phenomena are a long‐standing research topic in rendering. While significant progress has been made in modelling clear skies and clouds, fog has often been simplified as a medium that is homogeneous throughout, or as a simple density gradient. However, these approximations neglect the characteristic variations real advection fog shows throughout its vertical span, and do not provide the particle distribution data needed for accurate rendering. Based on data from meteorological literature, we developed an analytical model that yields the distribution of particle size as a function of altitude within an advection fog layer. The thickness of the fog layer is an additional input parameter, so that fog layers of varying thickness can be realistically represented. We also demonstrate that based on Mie scattering, one can easily integrate this model into a Monte Carlo renderer. Our model is the first ever non‐trivial volumetric model for advection fog that is based on real measurement data, and that contains all the components needed for inclusion in a modern renderer. The model is provided as open source component, and can serve as reference for rendering problems that involve fog layers.

Abstract We propose a technique for efficient storage and importance sampling of fluorescent spectral data. Fluorescence is fully described by a re‐radiation matrix, which for a given input wavelength indicates how much energy is re‐emitted at other wavelengths. However, such representation has a considerable memory footprint. To significantly reduce memory requirements, we propose the use of Gaussian mixture models for the representation of re‐radiation matrices. Instead of the full‐resolution matrix, we work with a set of Gaussian parameters that also allow direct importance sampling. Furthermore, if accuracy is of concern, a re‐radiation matrix can be used jointly with efficient importance sampling provided by the Gaussian mixture. In this paper, we present our pipeline for efficient storage of bispectral data and provide its extensive evaluation on a large set of bispectral measurements. We show that our method is robust and colour accurate even with its comparably minor memory requirements and that it can be seamlessly integrated into a standard Monte Carlo path tracer.

Abstract We derive a general result in microfacet theory: given an arbitrary microsurface defined via standard microfacet statistics, we show how to construct the statistics of its linearly transformed counterparts. A common use case of such transformations is to generate anisotropic versions of a given surface. Traditional anisotropic derivations based on varying the roughness of an isotropic distribution in an ellipse have a general closed‐form formula only for the subclass of shape‐invariant distributions. While our formulation is equivalent to these specific constructs, it is more general in two aspects: it leads to simple closed‐form solutions for all distributions, including shape‐variant ones, and works for all invertible 2D transform matrices. The latter is of particular importance in case of deformation of the macrosurface, since it can be approximated locally by a linear transformation in the tangent plane. We demonstrate our results using the Generalized Trowbridge‐Reitz (GTR) distribution which is shape‐invariant only in the special case of the popular Trowbridge‐Reitz (GGX) distribution.

Abstract Spectral rendering is increasingly used in appearance‐critical rendering workflows due to its ability to predict colour values under varying illuminants. However, directly modelling assets via input of spectral data is a tedious process: and if asset appearance is defined via artist‐created textures, these are drawn in colour space, i.e. RGB. Converting these RGB values to equivalent spectral representations is an ambiguous problem, for which robust techniques have been proposed only comparatively recently. However, other than the resulting RGB values matching under the illuminant the RGB space is defined for (usually D65), these uplifting techniques do not provide the user with further control over the resulting spectral shape. In a recent publication, we have proposed a method for constraining the spectral uplifting process so that for a finite number of input spectra that need to be preserved, it always yields the correct uplifted spectrum for the corresponding RGB value. We extend this previous work, which supported the sRGB gamut only, by describing a method that is able to constrain any spectrum from within the gamut of realisable reflectances. Due to constraints placed on the uplifting process, target RGB values that are in close proximity to one another uplift to spectra within the same metameric family, so that textures with colour variations can be meaningfully uplifted. Renderings uplifted via our method show minimal discrepancies when compared to the original objects.

Abstract Pre‐computed models of sky radiance are a tool to rapidly determine incident solar irradiance in applications as diverse as movie VFX, lighting simulation for architecture, experimental biology, and flight simulators. Several such models exist, but most provide data only for the visible range and, in some cases, for the near‐UV. But for accurate simulations of photovoltaic plant yield and the thermal properties of buildings, a pre‐computed reference sky model which covers the entire spectral range of terrestrial solar irradiance is needed: and this range is considerably larger than what extant models provide. We deliver this, and for a ground‐based observer provide the three components of sky dome radiance, atmospheric transmittance, and polarisation. We also discuss the additional aspects that need to be taken into consideration when including the near‐infrared in such a model. Additionally, we provide a simple standalone C++ implementation as well as an implementation with a GUI.

We present a spectral measurement approach for the bulk optical properties of translucent materials using only low-cost components. We focus on the translucent inks used in full-color 3D printing, and develop a technique with a high spectral resolution, which is important for accurate color reproduction. We enable this by developing a new acquisition technique for the three unknown material parameters, namely, the absorption and scattering coefficients, and its phase function anisotropy factor, that only requires three point measurements with a spectrometer. In essence, our technique is based on us finding a three-dimensional appearance map , computed using Monte Carlo rendering, that allows the conversion between the three observables and the material parameters. Our measurement setup works without laboratory equipment or expensive optical components. We validate our results on a 3D printed color checker with various ink combinations. Our work paves a path for more accurate appearance modeling and fabrication even for low-budget environments or affordable embedding into other devices.

Abstract Accurately controllable shading detail is a crucial aspect of realistic appearance modelling. Two fundamental building blocks for this are microfacet BRDFs, which describe the statistical behaviour of infinitely small facets, and normal maps, which provide user‐controllable spatio‐directional surface features. We analyse the filtering of the combined effect of a microfacet BRDF and a normal map. By partitioning the half‐vector domain into bins we show that the filtering problem can be reduced to evaluation of an integral histogram (IH), a generalization of a summed‐area table (SAT). Integral histograms are known for their large memory requirements, which are usually proportional to the number of bins. To alleviate this, we introduce Inverse Bin Maps, a specialised form of IH with a memory footprint that is practically independent of the number of bins. Based on these, we present a memory‐efficient, production‐ready approach for filtering of high resolution normal maps with arbitrary Beckmann flake roughness. In the corner case of specular normal maps (zero, or very small roughness values) our method shows similar convergence rates to the current state of the art, and is also more memory efficient.

Abstract With the wider availability of full‐color 3D printers, color‐accurate 3D‐print preparation has received increased attention. A key challenge lies in the inherent translucency of commonly used print materials that blurs out details of the color texture. Previous work tries to compensate for these scattering effects through strategic assignment of colored primary materials to printer voxels. To date, the highest‐quality approach uses iterative optimization that relies on computationally expensive Monte Carlo light transport simulation to predict the surface appearance from subsurface scattering within a given print material distribution; that optimization, however, takes in the order of days on a single machine. In our work, we dramatically speed up the process by replacing the light transport simulation with a data‐driven approach. Leveraging a deep neural network to predict the scattering within a highly heterogeneous medium, our method performs around two orders of magnitude faster than Monte Carlo rendering while yielding optimization results of similar quality level. The network is based on an established method from atmospheric cloud rendering, adapted to our domain and extended by a physically motivated weight sharing scheme that substantially reduces the network size. We analyze its performance in an end‐to‐end print preparation pipeline and compare quality and runtime to alternative approaches, and demonstrate its generalization to unseen geometry and material values. This for the first time enables full heterogenous material optimization for 3D‐print preparation within time frames in the order of the actual printing time.

In full-color inkjet 3D printing, a key problem is determining the material configuration for the millions of voxels that a printed object is made of. The goal is a configuration that minimises the difference between desired target appearance and the result of the printing process. So far, the techniques used to find such a configuration have relied on domain-specific methods or heuristic optimization, which allowed only a limited level of control over the resulting appearance. We propose to use differentiable volume rendering in a continuous material-mixture space, which leads to a framework that can be used as a general tool for optimising inkjet 3D printouts. We demonstrate the technical feasibility of this approach, and use it to attain fine control over the fabricated appearance, and high levels of faithfulness to the specified target.

We present a fitted model of sky dome radiance and attenuation for realistic terrestrial atmospheres. Using scatterer distribution data from atmospheric measurement data, our model considerably improves on the visual realism of existing analytical clear sky models, as well as of interactive methods that are based on approximating atmospheric light transport. We also provide features not found in fitted models so far: radiance patterns for post-sunset conditions, in-scattered radiance and attenuation values for finite viewing distances, an observer altitude resolved model that includes downward-looking viewing directions, as well as polarisation information. We introduce a fully spherical model for in-scattered radiance that replaces the family of hemispherical functions originally introduced by Perez et al., and which was extended for several subsequent analytical models: our model relies on reference image compression via tensor decomposition instead.

Abstract Physically based spectral rendering has become increasingly important in recent years. However, asset textures in such systems are usually still drawn or acquired as RGB tristimulus values. While a number of RGB to spectrum upsampling techniques are available, none of them support upsampling of all colours in the full spectral locus, as it is intrinsically bigger than the gamut of physically valid reflectance spectra. But with display technology moving to increasingly wider gamuts, the ability to achieve highly saturated colours becomes an increasingly important feature. Real materials usually exhibit smooth reflectance spectra, while computationally generated spectra become more blocky as they represent increasingly bright and saturated colours. In print media, plastic or textile design, fluorescent dyes are added to extend the boundaries of the gamut of reflectance spectra. We follow the same approach for rendering: we provide a method which, given an input RGB tristimulus value, automatically provides a mixture of a regular, smooth reflectance spectrum plus a fluorescent part. For highly saturated input colours, the combination yields an improved reconstruction compared to what would be possible relying on a reflectance spectrum alone. At the core of our technique is a simple parametric spectral model for reflectance, excitation, and emission that allows for compact storage and is compatible with texture mapping. The model can then be used as a fluorescent diffuse component in an existing more complex BRDF model. We also provide importance sampling routines for practical application in a path tracer.

Commercially available full-color 3D printing allows for detailed control of material deposition in a volume, but an exact reproduction of a target surface appearance is hampered by the strong subsurface scattering that causes nontrivial volumetric cross-talk at the print surface. Previous work showed how an iterative optimization scheme based on accumulating absorptive materials at the surface can be used to find a volumetric distribution of print materials that closely approximates a given target appearance. In this work, we first revisit the assumption that pushing the absorptive materials to the surface results in minimal volumetric cross-talk. We design a full-fledged optimization on a small domain for this task and confirm this previously reported heuristic. Then, we extend the above approach that is critically limited to color reproduction on planar surfaces, to arbitrary 3D shapes. Our method enables high-fidelity color texture reproduction on 3D prints by effectively compensating for internal light scattering within arbitrarily shaped objects. In addition, we propose a content-aware gamut mapping that significantly improves color reproduction for the pathological case of thin geometric features. Using a wide range of sample objects with complex textures and geometries, we demonstrate color reproduction whose fidelity is superior to state-of-the-art drivers for color 3D printers.

Abstract We present two separate improvements to the handling of fluorescence effects in modern uni‐directional spectral rendering systems. The first is the formulation of a new distance tracking scheme for fluorescent volume materials which exhibit a pronounced wavelength asymmetry. Such volumetric materials are an important and not uncommon corner case of wavelength‐shifting media behaviour, and have not been addressed so far in rendering literature. The second one is that we introduce an extension of Hero wavelength sampling which can handle fluorescence events, both on surfaces, and in volumes. Both improvements are useful by themselves, and can be used separately: when used together, they enable the robust inclusion of arbitrary fluorescence effects in modern uni‐directional spectral MIS path tracers. Our extension of Hero wavelength sampling is generally useful, while our proposed technique for distance tracking in strongly asymmetric media is admittedly not very efficient. However, it makes the most of a rather difficult situation, and at least allows the inclusion of such media in uni‐directional path tracers, albeit at comparatively high cost. Which is still an improvement since up to now, their inclusion was not really possible at all, due to the inability of conventional tracking schemes to generate sampling points in such volume materials.

Color texture reproduction in 3D printing commonly ignores volumetric light transport (cross-talk) between surface points on a 3D print. Such light diffusion leads to significant blur of details and color bleeding, and is particularly severe for highly translucent resin-based print materials. Given their widely varying scattering properties, this cross-talk between surface points strongly depends on the internal structure of the volume surrounding each surface point. Existing scattering-aware methods use simplified models for light difusion, and often accept the visual blur as an immutable property of the print medium. In contrast, our work counteracts heterogeneous scattering to obtain the impression of a crisp albedo texture on top of the 3D print, by optimizing for a fully volumetric material distribution that preserves the target appearance. Our method employs an efficient numerical optimizer on top of a general Monte-Carlo simulation of heterogeneous scattering, supported by a practical calibration procedure to obtain scattering parameters from a given set of printer materials. Despite the inherent translucency of the medium, we reproduce detailed surface textures on 3D prints. We evaluate our system using a commercial, five-tone 3D print process and compare against the printer's native color texturing mode, demonstrating that our method preserves high-frequency features well without having to compromise on color gamut.

Abstract We present a model for growing procedural road networks in and close to cities. The main idea of our paper is that a city cannot be meaningfully simulated without taking its neighbourhood into account. A simple traffic simulation that considers this neighbourhood is then used to grow new major roads and to influence the locations of minor road growth. Waterways are introduced and used to help position the city nuclei on the map. The resulting cities are formed by allowing several smaller settlements to grow together and to form a rich road structure, much like in real world, and require only minimal per‐city input, allowing for batch generation.

Abstract We present a spectral rendering technique that offers a compelling set of advantages over existing approaches. The key idea is to propagate energy along paths for a small, constant number of changing wavelengths. The first of these, the hero wavelength, is randomly sampled for each path, and all directional sampling is solely based on it. The additional wavelengths are placed at equal distances from the hero wavelength, so that all path wavelengths together always evenly cover the visible range. A related technique, spectral multiple importance sampling, was already introduced a few years ago. We propose a simplified and optimised version of this approach which is easier to implement, has good performance characteristics, and is actually more powerful than the original method. Our proposed method is also superior to techniques which use a static spectral representation, as it does not suffer from any inherent representation bias. We demonstrate the performance of our method in several application areas that are of critical importance for production work, such as fidelity of colour reproduction, sub‐surface scattering, dispersion and volumetric effects. We also discuss how to couple our proposed approach with several technologies that are important in current production systems, such as photon maps, bidirectional path tracing, environment maps, and participating media.

In Computer Graphics, the polarisation properties of light currently play a role in several contexts: in certain forms of highly realistic ray-based image synthesis (sometimes colloquially referred to as Polarisation Ray Tracing), in some 3D display systems, and in some material acquisition technologies. The properties of light that are behind all of these applications are basically the same, although the technologies for which this property of light is being used differ considerably. Also, the notations and mathematical formalisms used in these application areas differ to some degree as well. This course aims to provide a unified resource for those areas of computer graphics which require a working knowledge of light polarisation: rendering and material acquisition. Consequently, the course is structured into three main parts: I - Background, II - Polarisation Ray Tracing, and III - Polarised Light in Acquisition Technology. Care is taken so that the information provided in Part I is applicable to both Part II and III of the course, and is formulated in a way that emphasises the underlying similarities.

Abstract High‐fidelity rendering can be used to investigate Cultural Heritage (CH) sites in a scientifically rigorous manner. However, a high degree of realism in the reconstruction of a CH site can be misleading insofar as it can be seen to imply a high degree of certainty about the displayed scene—which is frequently not the case, especially when investigating the past. So far, little effort has gone into adapting and formulating a Predictive Rendering pipeline for CH research applications. In this paper, we first discuss the goals and the workflow of CH reconstructions in general, as well as those of traditional Predictive Rendering. Based on this, we then propose a research framework for CH research, which we refer to as ‘Cultural Heritage Predictive Rendering’ (CHPR). This is an extension to Predictive Rendering that introduces a temporal component and addresses uncertainty that is important for the scene’s historical interpretation. To demonstrate these concepts, two example case studies are detailed.

We present a physically-based analytical model of the daytime sky. Based on the results of a first-principles brute force simulation of radiative transfer in the atmosphere, we use the same general approach of fitting basis function coefficients to radiance data as the Perez and Preetham models do. However, we make several modifications to this process, which together significantly improve the rendition of sunsets and high atmospheric turbidity setups -- known weak points of the Preetham model. Additionally, our model accounts for ground albedo, and handles each spectral component independently. The latter property makes it easily extensible to the near ultraviolet range of the spectrum, so that the daylight appearance of surfaces that include optical brighteners can be properly predicted. Due to its similar mathematical properties, the new model can be used as a drop-in replacement of the Preetham model.

This course serves as a guide to the considerable potential of layered surface models that are available in many commercial products. The key advantage of using such layered materials over traditional shading language constructs is that the end result is highly physically plausible because it simulates real materials more precisely. However, this does not mean that these models cannot be used for artistic purposes. Using simple layered surface models, we demonstrate how a surprisingly large number of interesting and important surface types can be efficiently represented. We also show how handy such an approach is for the end-user, whose main concern is the ease with which one can describe object appearance based only on a few intuitive parameters. We first discuss layered surface models in general and the constraints of modeling object appearance in a physically plausible fashion by explaining basic material properties. We then demonstrate the techniques that are used to analyze such materials, both for high quality offline rendering as well as in a realtime setting. We then give examples of the surface types that can be described in this way and demonstrate how we create them in our company.

Polarisation Ray Tracing is a bit like spectral rendering. You might have heard about it, but the technical details - what exactly it is all about, how it is best done, what the benefits are, where you ought to use it, and where you can safely omit it - are not that well known. At least in principle, information about all this is available already - but it is scattered across many different sources, some of which are outside graphics literature, and consequently can be a bit hard to find at first. Also, a number of these resources - in particular publications in physics literature - were not written with graphics engineering in mind, and can prove hard to directly apply to the engineering problem of getting such a Tenderer to work. This course aims to provide a unified one-stop information resource on this topic, and should enable graphics engineers with a background in physically-based rendering to properly assess whether the phenomenon has to be included in a given simulation, and what has to be done in order to properly allow for handling of the phenomenon in a ray-based Tenderer. However, the contents of the course are also potentially very relevant for other areas of graphics beyond rendering proper: polarised light is currently being used in several other contexts, such as face scanning, highlight removal, or 3D projection technologies. Engineers and researchers in these other areas might benefit from the course insofar as the knowledge needed for an outright simulation of polarised light transport presented here is a superset of the information needed for more specialised tasks. This comprehensive overview would thus be a useful repository of knowledge for other areas as well.

Abstract The emissive properties of glowing solid objects appear to be something that the graphics community has not considered in depth before. While the volumetric emission of plasma, i.e. flames, has been discussed numerous times, and while the emission characteristics of entire luminaires can be handled via IESNA profiles, the exact appearance of glowing solid objects appears to have eluded detailed scrutiny so far. In this paper, we discuss the theoretical background to thermally induced light emission of objects, describe how one can handle this behaviour with very little effort in a physically based rendering system, and provide examples for the visual importance of handling this in a plausible fashion.

Skeletal implicit modelling systems have been used to design models of both organic and man-made structures, however existing systems lack convenient and accurate methods for users to define fillets when building prototype engineering models. In this work we extend the methodology and skeletal primitives found in the BlobTree and introduce an improved method for modelling fillets. This is done by interpolating between hard-edged and soft-edged representations of a primitive, using the field to control the interpolation. Blending planes are introduced as a way of providing user control for this interpolation. The new methods are expressed as blend operators between two objects and can thus be implemented as a new node in the BlobTree. In addition we introduce an efficient methodology for modelling hard edged primitives.

Abstract In coloured media, the index of refraction does not decrease monotonically with increasing wavelength, but behaves in a quite non‐monotonical way. This behaviour is called anomalous dispersion and results from the fact that the absorption of a material influences its index of refraction. So far, this interesting fact has not been widely acknowledged by the graphics community. In this paper, we demonstrate how to calculate the correct refractive index for a material based on its absorption spectrum with the Kramers‐Kronig relation, and we discuss for which types of objects this effect is relevant in practice.

Abstract We propose a method that improves automatic colour correction operations for rendered images. In particular, we propose a robust technique for estimating the visible and pertinent illumination in a given scene. We do this at very low computational cost by mostly re‐using information that is already being computed during the image synthesis process. Conventional illuminant estimations either operate only on 2D image data, or, if they do go beyond pure image analysis, only use information on the luminaires found in the scene. The latter is usually done with little or no regard for how the light sources actually affect the part of the scene that is being viewed. Our technique goes beyond that, and also takes object reflectance into account, as well as the incident light that is actually responsible for the colour of the objects that one sees. It is therefore able to cope with difficult cases, such as scenes with mixed illuminants, complex scenes with many light sources of varying colour, or strongly coloured indirect illumination.

In this article we derive the complete set of formulas needed to generate physically plausible images of uniaxial crystals. So far no computer graphics publication contains all the formulas one needs to compute the interaction of light with such crystals in a form that is useable by a graphics application, especially if a polarization-aware rendering system is being used. This paper contains the complete derivation of the Fresnel coefficients for birefringent transparent materials, as well as for the direction cosines of the extraordinary ray and the Mueller matrices necessary to describe polarization effects. The formulas we derive can be directly used in a ray based renderer, and we demonstrate these capabilities in test scenes.

Abstract Within computer graphics, the field of predictive rendering is concerned with those methods of image synthesis that yield results that do not only look real, but are also radiometrically correct renditions of nature, i.e. which are accurate predictions of what a real scene would look like under given lighting conditions. In order to guarantee the correctness of the results obtained by such techniques, three stages of such a rendering system have to be verified with particular care: the light reflection models, the light transport simulation and the perceptually based calculations used at display time. In this report, we will concentrate on the state of the art with respect to the second step in this chain. Various approaches for experimental verification of the implementation of a physically based rendering system have been proposed so far. However, the problem of proving that the results are correct is not fully solved yet, and no standardized methodology is available. We give an overview of existing literature, discuss the strengths and weaknesses of the described methods and illustrate the unsolved problems. We also briefly discuss the related issue of image quality metrics.

As a general approach to procedural mesh definition we propose two mechanisms for mesh modification: generalized subdivision and rule based mesh growing. In standard subdivision, a specific subdivision rule is applied to a mesh to get a succession of meshes converging to a limit surface. A generalized approach allows different subdivision rules at each level of the subdivision process. By limiting the variations introduced at each level, convergence can be ensured: however in a number of cases it may be of advantage to exploit the expressivity of different subdivision steps at each level, without imposing any limits. Rule based mesh growing is an extension of L-systems to not only work on symbols, but connected symbols, representing faces in a mesh. This mechanism allows the controlled introduction of more complex geometry in places where it is needed to model fine details. Using both these mechanisms in combination we demonstrate, that a great variety of complex objects can be easily modeled and compactly represented.

We present a method that makes the use of photon tracing methods feasible for complex scenes when a totally accurate solution is not essential. This is accomplished by using orientation lightmaps, which average the illumination of complex objects depending on the surface normal. Through this averaging, they considerably reduce the variance of the stochastic solution. In order to use these specialised lightmaps, which consume comparatively small amounts of memory, no changes have to be made to the basic photon tracing algorithm. Also, they can be freely mixed with normal lightmaps. This gives the user good control over the amount of inaccuracy he introduces by their application. The area computations necessary for their insertion are performed using a stochastic sampling method that performs well for highly complex objects.