Scalable Height Field Self‐Shadowing

We present a new method suitable for general purpose graphics processing units to render self‐shadows on dynamic height fields under dynamic light environments in real‐time. Visibility for each point in the height field is determined as the exact horizon for a set of azimuthal directions in time linear in height field size and the number of directions. The surface is shaded using the horizon information and a high‐resolution light environment extracted on‐line from a high dynamic range cube map, allowing for detailed extended shadows. The desired accuracy for any geometric content and lighting complexity can be matched by choosing a suitable number of azimuthal directions. Our method is able to represent arbitrary features of both high‐ and low‐frequency, unifying hard and soft shadowing. We achieve 23 fps on 1024×1024 height fields with 64 azimuthal directions under a 256×64 environment lighting on an Nvidia GTX 280 GPU.     

Line‐Sweep Ambient Obscurance

Screen‐space ambient occlusion and obscurance have become established methods for rendering global illumination effects in real‐time applications. While they have seen a steady line of refinements, their computational complexity has remained largely unchanged and either undersampling artefacts or too high render times limit their scalability. In this paper we show how the fundamentally quadratic per‐pixel complexity of previous work can be reduced to a linear complexity. We solve obscurance in discrete azimuthal directions by performing line sweeps across the depth buffer in each direction. Our method builds upon the insight that scene points along each line can be incrementally inserted into a data structure such that querying for the largest occluder among the visited samples along the line can be achieved at an amortized constant cost. The obscurance radius therefore has no impact on the execution time and our method produces accurate results with smooth occlusion gradients in a few milliseconds per frame on commodity hardware.     

Fast Global Illumination on Dynamic Height Fields

We present a real-time method for rendering global illumination effects from large area and environmental lights on dynamic height fields. In contrast to previous work, our method handles inter-reflections (indirect lighting) and non-diffuse surfaces. To reduce sampling, we construct one multi-resolution pyramid for height variation to compute direct shadows, and another pyramid for each indirect bounce of incident radiance to compute inter-reflections. The basic principle is to sample the points blocking direct light, or shedding indirect light, from coarser levels of the pyramid the farther away they are from a given receiver point. We unify the representation of visibility and indirect radiance at discrete azimuthal directions (i.e., as a function of a single elevation angle) using the concept of a "casting set" of visible points along this direction whose contributions are collected in the basis of normalized Legendre polynomials. This analytic representation is compact, requires no precomputation, and allows efficient integration to produce the spherical visibility and indirect radiance signals. Sub-sampling visibility and indirect radiance, while shading with full-resolution surface normals, further increases performance without introducing noticeable artifacts. Our method renders 512×512 height fields (> 500K triangles) at 36Hz.     

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.     

Fast,Sub‐pixel Antialiased Shadow Maps

Solving aliasing artifacts is an essential problem in shadow mapping approaches. Many works have been proposed, however, most of them focused on removing the texel‐level aliasing that results from the limited resolution of shadow maps. Little work has been done to solve the pixel‐level shadow aliasing that is produced by the rasterization on the screen plane. In this paper, we propose a fast, sub‐pixel antialiased shadowing algorithm to solve the pixel aliasing problem. Our work is based on the alias‐free shadow maps, which is capable of computing accurate per‐pixel shadow, and only incurs little cost to extend to sub‐pixel accuracy. Instead of direct supersampling the screen space, we take facets to approximate pixels in shadow testing. The shadowed area of one facet is rapidly evaluated by projecting blocker geometry onto a supersampled 2D occlusion mask with bitmasks fusion. It provides a sub‐pixel occlusion sampling so as to capture fine shadow details and features. Furthermore, we introduce the silhouette mask map that limits visibility evaluation to pixels only on the silhouette, which greatly reduces the computation cost. Our algorithm runs entirely on the GPU, achieving real‐time performance and is an order of magnitude faster than the brute‐force supersampling method to produce comparable 32× antialiased shadows.     

Eye‐Centered Color Adaptation in Global Illumination

Color adaptation is a well known ability of the human visual system (HVS). Colors are perceived as constant even though the illuminant color changes. Indeed, the perceived color of a diffuse white sheet of paper is still white even though it is illuminated by a single orange tungsten light, whereas it is orange from a physical point of view. Unfortunately global illumination algorithms only focus on the physics aspects of light transport. The ouput of a global illuminantion engine is an image which has to undergo chromatic adaptation to recover the color as perceived by the HVS. In this paper, we propose a new color adaptation method well suited to global illumination. This method estimates the adaptation color by averaging the irradiance color arriving at the eye. Unlike other existing methods, our approach is not limited to the view frustrum, as it considers the illumination from all the scene. Experiments have shown that our method outperforms the state of the art methods.     

Pre‐convolved Radiance Caching

The incident indirect light over a range of image pixels is often coherent. Two common approaches to exploit this inter‐pixel coherence to improve rendering performance are Irradiance Caching and Radiance Caching. Both compute incident indirect light only for a small subset of pixels (the cache), and later interpolate between pixels. Irradiance Caching uses scalar values that can be interpolated efficiently, but cannot account for shading variations caused by normal and reflectance variation between cache items. Radiance Caching maintains directional information, e.g., to allow highlights between cache items, but at the cost of storing and evaluating a Spherical Harmonics (SH) function per pixel. The arithmetic and bandwidth cost for this evaluation is linear in the number of coefficients and can be substantial. In this paper, we propose a method to replace it by an efficient per‐cache item pre‐filtering based on MIP maps — such as previously done for environment maps — leading to a single constant‐time lookup per pixel. Additionally, per‐cache item geometry statistics stored in distance‐MIP maps are used to improve the quality of each pixel's lookup. Our approximate interactive global illumination approach is an order of magnitude faster than Radiance Caching with Phong BRDFs and can be combined with Monte Carlo‐raytracing, Point‐based Global Illumination or Instant Radiosity.     

A Layered Particle‐Based Fluid Model for Real‐Time Rendering of Water

We present a physically based real‐time water simulation and rendering method that brings volumetric foam to the real‐time domain, significantly increasing the realism of dynamic fluids. We do this by combining a particle‐based fluid model that is capable of accounting for the formation of foam with a layered rendering approach that is able to account for the volumetric properties of water and foam. Foam formation is simulated through Weber number thresholding. For rendering, we approximate the resulting water and foam volumes by storing their respective boundary surfaces in depth maps. This allows us to calculate the attenuation of light rays that pass through these volumes very efficiently. We also introduce an adaptive curvature flow filter that produces consistent fluid surfaces from particles independent of the viewing distance.     

Patch‐based Texture Interpolation

In this paper, we present a novel exemplar‐based technique for the interpolation between two textures that combines patch‐based and statistical approaches. Motivated by the notion of texture as a largely local phenomenon, we warp and blend small image neighborhoods prior to patch‐based texture synthesis. In addition, interpolating and enforcing characteristic image statistics faithfully handles high frequency detail. We are able to create both intermediate textures as well as continuous transitions. In contrast to previous techniques computing a global morphing transformation on the entire input exemplar images, our localized and patch‐based approach allows us to successfully interpolate between textures with considerable differences in feature topology for which no smooth global warping field exists.     

Interactive Rendering of Non‐Constant,Refractive Media Using the Ray Equations of Gradient‐Index Optics

Existing algorithms can efficiently render refractive objects of constant refractive index. For a medium with a continuously varying index of refraction, most algorithms use the ray equation of geometric optics to compute piecewise‐linear approximations of the non‐linear rays. By assuming a constant refractive index within each tracing step, these methods often need a large number of small steps to generate satisfactory images. In this paper, we present a new approach for tracing non‐constant, refractive media based on the ray equations of gradient‐index optics. We show that in a medium of constant index gradient, the ray equation has a closed‐form solution, and the intersection point between a ray and the medium boundaries can be efficiently computed using the bisection method. For general non‐constant media, we model the refractive index as a piecewise‐linear function and render the refraction by tracing the tetrahedron‐based representation of the media. Our algorithm can be easily combined with existing rendering algorithms such as photon mapping to generate complex refractive caustics at interactive frame rates. We also derive analytic ray formulations for tracing mirages – a special gradient‐index optical phenomenon.     

An Area‐Preserving Parametrization for Spherical Rectangles

We present an area‐preserving parametrization for spherical rectangles which is an analytical function with domain in the unit rectangle [0, 1]² and range in a region included in the unit‐radius sphere. The parametrization preserves areas up to a constant factor and is thus very useful in the context of rendering as it allows to map random sample point sets in [0, 1]² onto the spherical rectangle. This allows for easily incorporating stratified, quasi‐Monte Carlo or other sampling strategies in algorithms that compute scattering from planar rectangular emitters.     

Superresolution Reflectance Fields: Synthesizing images for intermediate light directions

Captured reflectance fields tend to provide a relatively coarse sampling of the incident light directions. As a result, sharp illumination features, such as highlights or shadow boundaries, are poorly reconstructed during relighting; highlights are disconnected, and shadows show banding artefacts. In this paper, we propose a novel interpolation technique for 4D reflectance fields that reconstructs plausible images even for non-observed light directions. Given a sparsely sampled reflectance field, we can effectively synthesize images as they would have been obtained from denser sampling. The processing pipeline consists of three steps: (1) segmentation of regions where intermediate lighting cannot be obtained by blending, (2) appropriate flow algorithms for highlights and shadows, plus (3) a final reconstruction technique that uses image-based priors to faithfully correct errors that might be introduced by the segmentation or flow step. The algorithm reliably reproduces scenes that contain specular highlights, interreflections, shadows or caustics.     

Visibility Editing For All‐Frequency Shadow Design

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 oating 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.     

Textures on Rank‐1 Lattices

Storing textures on orthogonal tensor product lattices is predominant in computer graphics, although it is known that their sampling efficiency is not optimal. In two dimensions, the hexagonal lattice provides the maximum sampling efficiency. However, handling these lattices is difficult, because they are not able to tile an arbitrary rectangular region and have an irrational basis. By storing textures on rank‐1 lattices, we resolve both problems: Rank‐1 lattices can closely approximate hexagonal lattices, while all coordinates of the lattice points remain integer. At identical memory footprint texture quality is improved as compared to traditional orthogonal tensor product lattices due to the higher sampling efficiency. We introduce the basic theory of rank‐1 lattice textures and present an algorithmic framework which easily can be integrated into existing off‐line and real‐time rendering systems.     

An Image‐Based Approach for Stochastic Volumetric and Procedural Details

Noisy volumetric details like clouds, grounds, plaster, bark, roughcast, etc. are frequently encountered in nature and bring an important contribution to the realism of outdoor scenes. We introduce a new interactive approach, easing the creation of procedural representations of “stochastic” volumetric details by using a single example photograph. Instead of attempting to reconstruct an accurate geometric representation from the photograph, we use a stochastic multi‐scale approach that fits parameters of a multi‐layered noise‐based 3D deformation model, using a multi‐resolution filter banks error metric. Once computed, visually similar details can be applied to arbitrary objects with a high degree of visual realism, since lighting and parallax effects are naturally taken into account. Our approach is inspired by image‐based techniques. In practice, the user supplies a photograph of an object covered by noisy details, provides a corresponding coarse approximation of the shape of this object as well as an estimated lighting condition (generally a light source direction). Our system then determines the corresponding noise‐based representation as well as some diffuse, ambient, specular and semi‐transparency reflectance parameters. The resulting details are fully procedural and, as such, have the advantage of extreme compactness, while they can be infinitely extended without repetition in order to cover huge surfaces.     

An Exploratory Technique for Coherent Visualization of Time‐varying Volume Data

The selection of an appropriate global transfer function is essential for visualizing time‐varying simulation data. This is especially challenging when the global data range is not known in advance, as is often the case in remote and in‐situ visualization settings. Since the data range may vary dramatically as the simulation progresses, volume rendering using local transfer functions may not be coherent for all time steps. We present an exploratory technique that enables coherent classification of time‐varying volume data. Unlike previous approaches, which require pre‐processing of all time steps, our approach lets the user explore the transfer function space without accessing the original 3D data. This is useful for interactive visualization, and absolutely essential for in‐situ visualization, where the entire simulation data range is not known in advance. Our approach generates a compact representation of each time step at rendering time in the form of ray attenuation functions, which are used for subsequent operations on the opacity and color mappings. The presented approach offers interactive exploration of time‐varying simulation data that alleviates the cost associated with reloading and caching large data sets.     

Multi‐Image Based Photon Tracing for Interactive Global Illumination of Dynamic Scenes

Image space photon mapping has the advantage of simple implementation on GPU without pre‐computation of complex acceleration structures. However, existing approaches use only a single image for tracing caustic photons, so they are limited to computing only a part of the global illumination effects for very simple scenes. In this paper we fully extend the image space approach by using multiple environment maps for photon mapping computation to achieve interactive global illumination of dynamic complex scenes. The two key problems due to the introduction of multiple images are 1) selecting the images to ensure adequate scene coverage; and 2) reliably computing ray‐geometry intersections with multiple images. We present effective solutions to these problems and show that, with multiple environment maps, the image‐space photon mapping approach can achieve interactive global illumination of dynamic complex scenes. The advantages of the method are demonstrated by comparison with other existing interactive global illumination methods.     

A Closed‐Form Solution to Single Scattering for General Phase Functions and Light Distributions

Due to the intricate nature of the equation governing light transport in participating media, accurately and efficiently simulating radiative energy transfer remains very challenging in spite of its broad range of applications. As an alternative to traditional numerical estimation methods such as ray‐marching and volume‐slicing, a few analytical approaches to solving single scattering have been proposed but current techniques are limited to the assumption of isotropy, rely on simplifying approximations and/or require substantial numerical precomputation and storage. In this paper, we present the very first closed‐form solution to the air‐light integral in homogeneous media for general 1‐D anisotropic phase functions and punctual light sources. By addressing an open problem in the overall light transport literature, this novel theoretical result enables the analytical computation of exact solutions to complex scattering phenomena while achieving semi‐interactive performance on graphics hardware for several common scattering modes.     

Semi‐Stochastic Tilings for Example‐Based Texture Synthesis

We investigate semi‐stochastic tilings based on Wang or corner tiles for the real‐time synthesis of example‐based textures. In particular, we propose two new tiling approaches: (1) to replace stochastic tilings with pseudo‐random tilings based on the Halton low‐discrepancy sequence, and (2) to allow the controllable generation of tilings based on a user‐provided probability distribution. Our first method prevents local repetition of texture content as common with stochastic approaches and yields better results with smaller sets of utilized tiles. Our second method allows to directly influence the synthesis result which—in combination with an enhanced tile construction method that merges multiple source textures—extends synthesis tasks to globally‐varying textures. We show that both methods can be implemented very efficiently in connection with tile‐based texture mapping and also present a general rule that allows to significantly reduce resulting tile sets.