Fast Soft Self‐Shadowing on Dynamic Height Fields

We present a new, real‐time method for rendering soft shadows from large light sources or lighting environments on dynamic height fields. The method first computes a horizon map for a set of azimuthal directions. To reduce sampling, we compute a multi‐resolution pyramid on the height field. Coarser pyramid levels are indexed as the distance from caster to receiver increases. For every receiver point and every azimuthal direction, a smooth function of blocking angle in terms of log distance is reconstructed from a height difference sample at each pyramid level. This function's maximum approximates the horizon angle. We then sum visibility at each receiver point over wedges determined by successive pairs of horizon angles. Each wedge represents a linear transition in blocking angle over its azimuthal extent. It is precomputed in the order‐4 spherical harmonic (SH) basis, for a canonical azimuthal origin and fixed extent, resulting in a 2D table. The SH triple product of 16D vectors representing lighting, total visibility, and diffuse reflectance then yields the soft‐shadowed result. Two types of light sources are considered; both are distant and low‐frequency. Environmental lights require visibility sampling around the complete 360 ° azimuth, while key lights sample visibility within a partial swath. Restricting the swath concentrates samples where the light comes from (e.g. 3 azimuthal directions vs. 16‐32 for a full swath) and obtains sharper shadows. Our GPU implementation handles height fields up to 1024 × 1024 in real‐time. The computation is simple, local, and parallel, with performance independent of geometric content.     

Bidirectional Importance Sampling for Unstructured Direct Illumination

Recent research in bidirectional importance sampling has focused primarily on structured illumination sources such as distant environment maps, while unstructured illumination has received little attention. In this paper, we present a method for bidirectional importance sampling of unstructured illumination, allowing us to use the same method for sampling both distant as well as local/indirect sources. Building upon recent work in [ WFA*05 ], we model complex illumination as a large set of point lights. The subsequent sampling process draws samples only from this point set. We start by constructing a piecewise constant approximation for the lighting using an illumination cut [ CPWAP08 ]. We show that this cut can be used directly for illumination importance sampling. We then use BRDF importance sampling followed by sample counting to update the cut, resulting in a bidirectional distribution that closely approximates the product of the illumination and BRDF. Drawing visibility samples from this new distribution significantly reduces the sampling variance. As a main advance over previous work, our method allows for unstructured sources, including arbitrary local direct lighting and one-bounce of indirect lighting.     

Sample Based Visibility for Soft Shadows using Alias‐free Shadow Maps

This paper introduces an accurate real‐time soft shadow algorithm that uses sample based visibility. Initially, we present a GPU‐based alias‐free hard shadow map algorithm that typically requires only a single render pass from the light, in contrast to using depth peeling and one pass per layer. For closed objects, we also suppress the need for a bias. The method is extended to soft shadow sampling for an arbitrarily shaped area‐/volumetric light source using 128‐1024 light samples per screen pixel. The alias‐free shadow map guarantees that the visibility is accurately sampled per screen‐space pixel, even for arbitrarily shaped (e.g. non‐planar) surfaces or solid objects. Another contribution is a smooth coherent shading model to avoid common light leakage near shadow borders due to normal interpolation.     

Exploiting Visibility Correlation in Direct Illumination

The visibility function in direct illumination describes the binary visibility over a light source, e.g., an environment map. Intuitively, the visibility is often strongly correlated between nearby locations in time and space, but exploiting this correlation without introducing noticeable errors is a hard problem. In this paper, we first study the statistical characteristics of the visibility function. Then, we propose a robust and unbiased method for using estimated visibility information to improve the quality of Monte Carlo evaluation of direct illumination. Our method is based on the theory of control variates, and it can be used on top of existing state‐of‐the‐art schemes for importance sampling. The visibility estimation is obtained by sparsely sampling and caching the 4D visibility field in a compact bitwise representation. In addition to Monte Carlo rendering, the stored visibility information can be used in a number of other applications, for example, ambient occlusion and lighting design.     

Line Sampling for Direct Illumination

Computing direct illumination efficiently is still a problem of major significance in computer graphics. The evaluation involves an integral over the surface areas of the light sources in the scene. Because this integral typically features many discontinuities, introduced by the visibility term and complex material functions, Monte Carlo integration is one of the only general techniques that can be used to compute the integral. In this paper, we propose to evaluate the direct illumination using line samples instead of point samples. A direct consequence of line sampling is that the two‐dimensional integral over the area of the light source is reduced to a one‐dimensional integral. We exploit this dimensional reduction by relying on the property that commonly used sampling patterns, such as stratified sampling and low‐discrepancy sequences, converge faster when the dimension of the integration domain is reduced. We show that, while line sampling is generally more computationally intensive than point sampling, the variance of a line sample is smaller than that of a point sample, resulting in a higher order of convergence.     

Product Importance Sampling for Light Transport Path Guiding

The efficiency of Monte Carlo algorithms for light transport simulation is directly related to their ability to importance‐sample the product of the illumination and reflectance in the rendering equation. Since the optimal sampling strategy would require knowledge about the transport solution itself, importance sampling most often follows only one of the known factors – BRDF or an approximation of the incident illumination. To address this issue, we propose to represent the illumination and the reflectance factors by the Gaussian mixture model (GMM), which we fit by using a combination of weighted expectation maximization and non‐linear optimization methods. The GMM representation then allows us to obtain the resulting product distribution for importance sampling on‐the‐fly at each scene point. For its efficient evaluation and sampling we preform an up‐front adaptive decimation of both factor mixtures. In comparison to state‐of‐the‐art sampling methods, we show that our product importance sampling can lead to significantly better convergence in scenes with complex illumination and reflectance.     

Interactive cloth rendering of microcylinder appearance model under environment lighting

This paper proposes an interactive rendering method of cloth fabrics under environment lighting. The outgoing radiance from cloth fabrics in the microcylinder model is calculated by integrating the product of the distant environment lighting, the visibility function, the weighting function that includes shadowing/masking effects of threads, and the light scattering function of threads. The radiance calculation at each shading point of the cloth fabrics is simplified to a linear combination of triple product integrals of two circular Gaussians and the visibility function, multiplied by precomputed spherical Gaussian convolutions of the weighting function. We propose an efficient calculation method of the triple product of two circular Gaussians and the visibility function by using the gradient of signed distance function to the visibility boundary where the binary visibility changes in the angular domain of the hemisphere. Our GPU implementation enables interactive rendering of static cloth fabrics with dynamic viewpoints and lighting. In addition, interactive editing of parameters for the scattering function (e.g. thread's albedo) that controls the visual appearances of cloth fabrics can be achieved.     

Visibility Silhouettes for Semi‐Analytic Spherical Integration

At each shade point, the spherical visibility function encodes occlusion from surrounding geometry, in all directions. Computing this function is difficult and point‐sampling approaches, such as ray‐tracing or hardware shadow mapping, are traditionally used to efficiently approximate it. We propose a semi‐analytic solution to the problem where the spherical silhouette of the visibility is computed using a search over a 4D dual mesh of the scene. Once computed, we are able to semi‐analytically integrate visibility‐masked spherical functions along the visibility silhouette, instead of over the entire hemisphere. In this way, we avoid the artefacts that arise from using point‐sampling strategies to integrate visibility, a function with unbounded frequency content. We demonstrate our approach on several applications, including direct illumination from realistic lighting and computation of pre‐computed radiance transfer data. Additionally, we present a new frequency‐space method for exactly computing all‐frequency shadows on diffuse surfaces. Our results match ground truth computed using importance‐sampled stratified Monte Carlo ray‐tracing, with comparable performance on scenes with low‐to‐moderate geometric complexity.     

Real‐time Shading with Filtered Importance Sampling

We propose an analysis of numerical integration based on sampling theory, whereby the integration error caused by aliasing is suppressed by pre‐filtering. We derive a pre‐filter for evaluating the illumination integral yielding filtered importance sampling, a simple GPU‐based rendering algorithm for image‐based lighting. Furthermore, we extend the algorithm with real‐time visibility computation. Free from any pre‐computation, the algorithm supports fully dynamic scenes and, above all, is simple to implement.     

Importance Sampling Techniques for Path Tracing in Participating Media

We introduce a set of robust importance sampling techniques which allow efficient calculation of direct and indirect lighting from arbitrary light sources in both homogeneous and heterogeneous media. We show how to distribute samples along a ray proportionally to the incoming radiance for point and area lights. In heterogeneous media, we decouple ray marching from light calculations by computing a representation of the transmittance function that can be quickly evaluated during sampling, at the cost of a small amount of bias. This representation also allows the calculation of another probability density function which can direct samples to regions most likely to scatter light. These techniques are orthogonal and can be combined via multiple importance sampling to further reduce variance. Our method has very modest per‐ray memory requirements and does not require any preprocessing, making it simple to integrate into production ray tracing based renderers.     

IlluminationCut

We present a novel algorithm, IlluminationCut, for rendering images using the many‐lights framework. It handles any light source that can be approximated with virtual point lights (VPLs) as well as highly glossy materials. The algorithm extends the Multidimensional Lightcuts technique by effectively creating an illumination‐aware clustering of the product‐space of the set of points to be shaded and the set of VPLs. Additionally, the number of visibility queries for each product‐space cluster is reduced by using an adaptive sampling technique. Our framework is flexible and achieves around 3 – 6 times speedup over previous state‐of‐the‐art methods.     

High-Quality Adaptive Soft Shadow Mapping

The recent soft shadow mapping technique [ [GBP06] ] allows the rendering in real-time of convincing soft shadows on complex and dynamic scenes using a single shadow map. While attractive, this method suffers from shadow overestimation and becomes both expensive and approximate when dealing with large penumbrae. This paper proposes new solutions removing these limitations and hence providing an efficient and practical technique for soft shadow generation. First, we propose a new visibility computation procedure based on the detection of occluder contours, that is more accurate and faster while reducing aliasing. Secondly, we present a shadow map multi-resolution strategy keeping the computation complexity almost independent on the light size while maintaining high-quality rendering. Finally, we propose a view-dependent adaptive strategy, that automatically reduces the screen resolution in the region of large penumbrae, thus allowing us to keep very high frame rates in any situation.     

Bitmask Soft Shadows

Recently, several real-time soft shadow algorithms have been introduced which all compute a single shadow map and use its texels to obtain a discrete scene representation. The resulting micropatches are backprojected onto the light source and the light areas occluded by them get accumulated to estimate overall light occlusion. This approach ignores patch overlaps, however, which can lead to objectionable artifacts. In this paper, we propose to determine the visibility of the light source with a bit field where each bit tracks the visibility of a sample point on the light source. This approach not only avoids overlapping-related artifacts but offers a solution to the important occluder fusion problem. Hence, it also becomes possible to correctly incorporate information from multiple depth maps. In addition, a new interpretation of the shadow map data is suggested which often provides superior visual results. Finally, we show how the search area for potential occluders can be reduced substantially.     

Importance Sampling Microfacet‐Based BSDFs using the Distribution of Visible Normals

We present a new approach to microfacet‐based BSDF importance sampling. Previously proposed sampling schemes for popular analytic BSDFs typically begin by choosing a microfacet normal at random in a way that is independent of direction of incident light. To sample the full BSDF using these normals requires arbitrarily large sample weights leading to possible fireflies. Additionally, at grazing angles nearly half of the sampled normals face away from the incident ray and must be rejected, making the sampling scheme inefficient. Instead, we show how to use the distribution of visible normals directly to generate samples, where normals are weighted by their projection factor toward the incident direction. In this way, no backfacing normals are sampled and the sample weights contain only the shadowing factor of outgoing rays (and additionally a Fresnel term for conductors). Arbitrarily large sample weights are avoided and variance is reduced. Since the BSDF depends on the microsurface model, we describe our sampling algorithm for two models: the V‐cavity and the Smith models. We demonstrate results for both isotropic and anisotropic rough conductors and dielectrics with Beckmann and GGX distributions.     

Real‐Time Solar Exposure Simulation in Complex Cities

In urban design, estimating solar exposure on complex city models is crucial but existing solutions typically focus on simplified building models and are too demanding in terms of memory and computational time. In this paper, we propose an interactive technique that estimates solar exposure on detailed urban scenes. Given a directional exposure map computed over a given time period, we estimate the sky visibility factor that serves to evaluate the final exposure at each visible point. This is done using a screen‐space method based on a two‐scale approach, which is geometry independent and has low storage costs. Our method performs at interactive rates and is designer‐oriented. The proposed technique is relevant in architecture and sustainable building design as it provides tools to estimate the energy performance of buildings as well as weathering effects in urban environments.     

Solid Angle Sampling of Disk and Cylinder Lights

A new unbiased sampling approach is presented, which allows the direct illumination from disk and cylinder light sources to be sampled with a uniform probability distribution within their solid angles, as seen from each illuminated point. This approach applies to any form of global illumination path tracing algorithm (forward or bidirectional), where the direct illumination integral from light sources needs to be estimated. We show that taking samples based on the solid angle of these two light sources leads to improved estimates and reduced variance of the Monte Carlo integral for direct illumination. This work follows from previously known unbiased methods for the solid angle sampling of triangular and rectangular light sources and extends the class of lights that can be rendered with these improved sampling algorithms.     

Making Imperfect Shadow Maps View‐Adaptive: High‐Quality Global Illumination in Large Dynamic Scenes

We propose an algorithm to compute interactive indirect illumination in dynamic scenes containing millions of triangles. It makes use of virtual point lights (VPL) to compute bounced illumination and a point‐based scene representation to query indirect visibility, similar to Imperfect Shadow Maps (ISM). To ensure a high fidelity of indirect light and shadows, our solution is made view‐adaptive by means of two orthogonal improvements: First, the VPL distribution is chosen to provide more detail, that is, more dense VPL sampling, where these contribute most to the current view. Second, the scene representation for indirect visibility is adapted to ensure geometric detail where it affects indirect shadows in the current view.     

Importance Sampling Spherical Harmonics

In this paper we present the first practical method for importance sampling functions represented as spherical harmonics (SH). Given a spherical probability density function (PDF) represented as a vector of SH coefficients, our method warps an input point set to match the target PDF using hierarchical sample warping. Our approach is efficient and produces high quality sample distributions. As a by-product of the sampling procedure we produce a multi-resolution representation of the density function as either a spherical mip-map or Haar wavelet. By exploiting this implicit conversion we can extend the method to distribute samples according to the product of an SH function with a spherical mip-map or Haar wavelet. This generalization has immediate applicability in rendering, e.g., importance sampling the product of a BRDF and an environment map where the lighting is stored as a single high-resolution wavelet and the BRDF is represented in spherical harmonics. Since spherical harmonics can be efficiently rotated, this product can be computed on-the-fly even if the BRDF is stored in local-space. Our sampling approach generates over 6 million samples per second while significantly reducing precomputation time and storage requirements compared to previous techniques.     

Practical Path Guiding for Efficient Light‐Transport Simulation

We present a robust, unbiased technique for intelligent light‐path construction in path‐tracing algorithms. Inspired by existing path‐guiding algorithms, our method learns an approximate representation of the scene's spatio‐directional radiance field in an unbiased and iterative manner. To that end, we propose an adaptive spatio‐directional hybrid data structure, referred to as SD‐tree, for storing and sampling incident radiance. The SD‐tree consists of an upper part—a binary tree that partitions the 3D spatial domain of the light field—and a lower part—a quadtree that partitions the 2D directional domain. We further present a principled way to automatically budget training and rendering computations to minimize the variance of the final image. Our method does not require tuning hyperparameters, although we allow limiting the memory footprint of the SD‐tree. The aforementioned properties, its ease of implementation, and its stable performance make our method compatible with production environments. We demonstrate the merits of our method on scenes with difficult visibility, detailed geometry, and complex specular‐glossy light transport, achieving better performance than previous state‐of‐the‐art algorithms.     

Sample‐Based Manifold Filtering for Interactive Global Illumination and Depth of Field

We present a fast reconstruction filtering method for images generated with Monte Carlo–based rendering techniques. Our approach specializes in reducing global illumination noise in the presence of depth‐of‐field effects at very low sampling rates and interactive frame rates. We employ edge‐aware filtering in the sample space to locally improve outgoing radiance of each sample. The improved samples are then distributed in the image plane using a fast, linear manifold‐based approach supporting very large circles of confusion. We evaluate our filter by applying it to several images containing noise caused by Monte Carlo–simulated global illumination, area light sources and depth of field. We show that our filter can efficiently denoise such images at interactive frame rates on current GPUs and with as few as 4–16 samples per pixel. Our method operates only on the colour and geometric sample information output of the initial rendering process. It does not make any assumptions on the underlying rendering technique and sampling strategy and can therefore be implemented completely as a post‐process filter.