Rendering Plasma Phenomena: Applications and Challenges

Plasmas are ubiquitous in the Universe. An understanding of plasma phenomena is therefore of importance in almost every area of astrophysics, from stellar atmospheres to star clusters. Plasmas also occur in daily life both in industrial processes and in consumer products. Recent groundbreaking data is making this the golden age of plasma science. Although direct observations and analysis of data provide important physical evidence for plasma phenomena, they do not necessarily explain the phenomena. Hence, recent discoveries in this area might not only arise out of observations, but also from visual simulations of the phenomena supported by advanced rendering technologies. This report describes the state of art of such simulations, and examines practical issues often overlooked in the literature. Educational and public outreach applications are also discussed. Although the emphasis is on the predictive rendering of plasma processes, the simulation guidelines and trade-offs addressed in this report can be extended to other types of natural phenomena. The report closes with a discussion of further avenues of research involving the visual simulation of plasma phenomena.     

Combinatorial Bidirectional Path‐Tracing for Efficient Hybrid CPU/GPU Rendering

This paper presents a reformulation of bidirectional path‐tracing that adequately divides the algorithm into processes efficiently executed in parallel on both the CPU and the GPU. We thus benefit from high‐level optimization techniques such as double buffering, batch processing, and asyncronous execution, as well as from the exploitation of most of the CPU, GPU, and memory bus capabilities. Our approach, while avoiding pure GPU implementation limitations (such as limited complexity of shaders, light or camera models, and processed scene data sets), is more than ten times faster than standard bidirectional path‐tracing implementations, leading to performance suitable for production‐oriented rendering engines.     

Accelerating Ray Tracing using Constrained Tetrahedralizations

In this paper we introduce the constrained tetrahedralization as a new acceleration structure for ray tracing. A constrained tetrahedralization of a scene is a tetrahedralization that respects the faces of the scene geometry. The closest intersection of a ray with a scene is found by traversing this tetrahedralization along the ray, one tetrahedron at a time. We show that constrained tetrahedralizations are a viable alternative to current acceleration structures, and that they have a number of unique properties that set them apart from other acceleration structures: constrained tetrahedralizations are not hierarchical yet adaptive; the complexity of traversing them is a function of local geometric complexity rather than global geometric complexity; constrained tetrahedralizations support deforming geometry without any effort; and they have the potential to unify several data structures currently used in global illumination.     

Tensor Clustering for Rendering Many‐Light Animations

Rendering animations of scenes with deformable objects, camera motion, and complex illumination, including indirect lighting and arbitrary shading, is a long‐standing challenge. Prior work has shown that complex lighting can be accurately approximated by a large collection of point lights. In this formulation, rendering of animation sequences becomes the problem of efficiently shading many surface samples from many lights across several frames. This paper presents a tensor formulation of the animated many‐light problem, where each element of the tensor expresses the contribution of one light to one pixel in one frame. We sparsely sample rows and columns of the tensor, and introduce a clustering algorithm to select a small number of representative lights to efficiently approximate the animation. Our algorithm achieves efficiency by reusing representatives across frames, while minimizing temporal flicker. We demonstrate our algorithm in a variety of scenes that include deformable objects, complex illumination and arbitrary shading and show that a surprisingly small number of representative lights is sufficient for high quality rendering. We believe out algorithm will find practical use in applications that require fast previews of complex animation.     

Robust and Efficient Wave Simulations on Deforming Meshes

The goal of this paper is to enable the interactive simulation of phenomena such as animated fluid characters. While full 3D fluid solvers achieve this with control algorithms, these 3D simulations are usually too costly for real‐time environments. In order to achieve our goal, we reduce the problem from a three‐ to a two‐dimensional one, and make use of the shallow water equations to simulate surface waves that can be solved very efficiently. In addition to a low runtime cost, stability is likewise crucial for interactive applications. Hence, we make use of an implicit time integration scheme to obtain a robust solver. To ensure a low energy dissipation, we apply an Implicit Newmark time integration scheme. We propose a general formulation of the underlying equations that is tailored towards the use with an Implicit Newmark integrator. Furthermore, we gain efficiency by making use of a direct solver. Due to the generality of our formulation, the fluid simulation can be coupled interactively with arbitrary external forces, such as forces caused by inertia or collisions. We will discuss the properties of our algorithm, and demonstrate its robustness with simulations on strongly deforming meshes.     

Perception of Visual Artifacts in Image‐Based Rendering of Façades

Image‐based rendering (IBR) techniques allow users to create interactive 3D visualizations of scenes by taking a few snapshots. However, despite substantial progress in the field, the main barrier to better quality and more efficient IBR visualizations are several types of common, visually objectionable artifacts. These occur when scene geometry is approximate or viewpoints differ from the original shots, leading to parallax distortions, blurring, ghosting and popping errors that detract from the appearance of the scene. We argue that a better understanding of the causes and perceptual impact of these artifacts is the key to improving IBR methods. In this study we present a series of psychophysical experiments in which we systematically map out the perception of artifacts in IBR visualizations of façades as a function of the most common causes. We separate artifacts into different classes and measure how they impact visual appearance as a function of the number of images available, the geometry of the scene and the viewpoint. The results reveal a number of counter‐intuitive effects in the perception of artifacts. We summarize our results in terms of practical guidelines for improving existing and future IBR techniques.     

Gradient‐based Interpolation and Sampling for Real‐time Rendering of Inhomogeneous,Single‐scattering Media

We present a real‐time rendering algorithm for inhomogeneous, single scattering media, where all‐frequency shading effects such as glows, light shafts, and volumetric shadows can all be captured. The algorithm first computes source radiance at a small number of sample points in the medium, then interpolates these values at other points in the volume using a gradient‐based scheme that is efficiently applied by sample splatting. The sample points are dynamically determined based on a recursive sample splitting procedure that adapts the number and locations of sample points for accurate and efficient reproduction of shading variations in the medium. The entire pipeline can be easily implemented on the GPU to achieve real‐time performance for dynamic lighting and scenes. Rendering results of our method are shown to be comparable to those from ray tracing.     

Photon Beam Diffusion: A Hybrid Monte Carlo Method for Subsurface Scattering

We present photon beam diffusion, an efficient numerical method for accurately rendering translucent materials. Our approach interprets incident light as a continuous beam of photons inside the material. Numerically integrating diffusion from such extended sources has long been assumed computationally prohibitive, leading to the ubiquitous single‐depth dipole approximation and the recent analytic sum‐of‐Gaussians approach employed by Quantized Diffusion. In this paper, we show that numerical integration of the extended beam is not only feasible, but provides increased speed, flexibility, numerical stability, and ease of implementation, while retaining the benefits of previous approaches. We leverage the improved diffusion model, but propose an efficient and numerically stable Monte Carlo integration scheme that gives equivalent results using only 3–5 samples instead of 20–60 Gaussians as in previous work. Our method can account for finite and multi‐layer materials, and additionally supports directional incident effects at surfaces. We also propose a novel diffuse exact single‐scattering term which can be integrated in tandem with the multi‐scattering approximation. Our numerical approach furthermore allows us to easily correct inaccuracies of the diffusion model and even combine it with more general Monte Carlo rendering algorithms. We provide practical details necessary for efficient implementation, and demonstrate the versatility of our technique by incorporating it on top of several rendering algorithms in both research and production rendering systems.     

Visual Abstractions of Solvent Pathlines near Protein Cavities

Water is known to play a crucial role in protein structure, flexibility and activity. The use of molecular dynamics simulations allows detailed studies of complex protein‐solvent interactions. Cluster analysis and density‐based approaches have been successfully used for the identification and analysis of conserved water molecules and hydration patterns of proteins. However, appropriate tools for analysing long‐time molecular dynamics simulations with respect to tracking and visualising the paths of solvent molecules are lacking. Our method focuses on visualising the solvent paths entering and leaving cavities of the protein and allows to study the route and dynamics of the exchange of tightly bound internal water molecules with the bulk solvent. The proposed visualisation also represents dynamic properties such as direction and velocity in the solvent. Especially, by clustering similar path‐lines with respect to designated properties the visualisation can be abstracted to represent the principal paths of solvent molecules through the cavities. Its application in the analysis of long‐time scale molecular dynamics simulations not only confirmed conjectures based on previous manual observations made by chance, but also led to novel insights into the dynamical and structural role of water molecules and its interplay with protein structure.     

Progressive Expectation‐Maximization for Hierarchical Volumetric Photon Mapping

State‐of‐the‐art density estimation methods for rendering participating media rely on a dense photon representation of the radiance distribution within a scene. A critical bottleneck of such kernel‐based approaches is the excessive number of photons that are required in practice to resolve fine illumination details, while controlling the amount of noise. In this paper, we propose a parametric density estimation technique that represents radiance using a hierarchical Gaussian mixture. We efficiently obtain the coefficients of this mixture using a progressive and accelerated form of the Expectation‐Maximization algorithm. After this step, we are able to create noise‐free renderings of high‐frequency illumination using only a few thousand Gaussian terms, where millions of photons are traditionally required. Temporal coherence is trivially supported within this framework, and the compact footprint is also useful in the context of real‐time visualization. We demonstrate a hierarchical ray tracing‐based implementation, as well as a fast splatting approach that can interactively render animated volume caustics.     

Progressive Virtual Beam Lights

A recent technique that forms virtual ray lights (VRLs) from path segments in media, reduces the artifacts common to VPL approaches in participating media, however, distracting singularities still remain. We present Virtual Beam Lights (VBLs), a progressive many‐lights algorithm for rendering complex indirect transport paths in, from, and to media. VBLs are efficient and can handle heterogeneous media, anisotropic scattering, and moderately glossy surfaces, while provably converging to ground truth. We inflate ray lights into beam lights with finite thicknesses to eliminate the remaining singularities. Furthermore, we devise several practical schemes for importance sampling the various transport contributions between camera rays, light rays, and surface points. VBLs produce artifact‐free images faster than VRLs, especially when glossy surfaces and/or anisotropic phase functions are present. Lastly, we employ a progressive thickness reduction scheme for VBLs in order to render results that converge to ground truth.     

Modeling Complex Unfoliaged Trees from a Sparse Set of Images

We present a novel image‐based technique for modeling complex unfoliaged trees. Existing tree modeling tools either require capturing a large number of views for dense 3D reconstruction or rely on user inputs and botanic rules to synthesize natural‐looking tree geometry. In this paper, we focus on faithfully recovering real instead of realistically‐looking tree geometry from a sparse set of images. Our solution directly integrates 2D/3D tree topology as shape priors into the modeling process. For each input view, we first estimate a 2D skeleton graph from its matte image and then find a 2D skeleton tree from the graph by imposing tree topology. We develop a simple but effective technique for computing the optimal 3D skeleton tree most consistent with the 2D skeletons. For each edge in the 3D skeleton tree, we further apply volumetric reconstruction to recover its corresponding curved branch. Finally, we use piecewise cylinders to approximate each branch from the volumetric results. We demonstrate our framework on a variety of trees to illustrate the robustness and usefulness of our technique.     

Interactive,Multiresolution Image‐Space Rendering for Dynamic Area Lighting

Area lights add tremendous realism, but rendering them interactively proves challenging. Integrating visibility is costly, even with current shadowing techniques, and existing methods frequently ignore illumination variations at unoccluded points due to changing radiance over the light's surface. We extend recent image‐space work that reduces costs by gathering illumination in a multiresolution fashion, rendering varying frequencies at corresponding resolutions. To compute visibility, we eschew shadow maps and instead rely on a coarse screen‐space voxelization, which effectively provides a cheap layered depth image for binary visibility queries via ray marching. Our technique requires no precomputation and runs at interactive rates, allowing scenes with large area lights, including dynamic content such as video screens.     

Interactive Rendering of Interior Scenes with Dynamic Environment Illumination

A rendering system for interior scenes is proposed in this paper. The light reaches the interior scene, usually through small regions, such as windows or abat‐jours, which we call portals. To provide a solution, suitable for rendering interior scenes with portals, we extend the traditional precomputed radiance transfer approaches. In our approach, a bounding sphere, which we call a shell, of the interior, centered at each portal, is created and the light transferred from the shell towards the interior through the portal is precomputed. Each shell acts as an environment light source and its intensity distribution is determined by rendering images of the scene, viewed from the center of the shell. By updating the intensity distribution of the shell at each frame, we are able to handle dynamic objects outside the shells. The material of the portals can also be modified at run time (e.g. changing from transparent glass to frosted glass). Several applications are shown, including the illumination of a cathedral, lit by skylight at different times of a day, and a car, running in a town, at interactive frame rates, with a dynamic viewpoint.     

Direct Ray Tracing of Phong Tessellation

There are two major ways of calculating ray and parametric surface intersections in rendering. The first is through the use of tessellated triangles, and the second is to use parametric surfaces together with numerical methods such as Newton's method. Both methods are computationally expensive and complicated to implement. In this paper, we focus on Phong Tessellation and introduce a simple direct ray tracing method for Phong Tessellation. Our method enables rendering smooth surfaces in a computationally inexpensive yet robust way.     

Sorted Deferred Shading for Production Path Tracing

Ray‐traced global illumination (GI) is becoming widespread in production rendering but incoherent secondary ray traversal limits practical rendering to scenes that fit in memory. Incoherent shading also leads to intractable performance with production‐scale textures forcing renderers to resort to caching of irradiance, radiosity, and other values to amortize expensive shading. Unfortunately, such caching strategies complicate artist workflow, are difficult to parallelize effectively, and contend for precious memory. Worse, these caches involve approximations that compromise quality. In this paper, we introduce a novel path‐tracing framework that avoids these tradeoffs. We sort large, potentially out‐of‐core ray batches to ensure coherence of ray traversal. We then defer shading of ray hits until we have sorted them, achieving perfectly coherent shading and avoiding the need for shading caches.     

Approximate Bias Compensation for Rendering Scenes with Heterogeneous Participating Media

In this paper we present a novel method for high‐quality rendering of scenes with participating media. Our technique is based on instant radiosity, which is used to approximate indirect illumination between surfaces by gathering light from a set of virtual point lights (VPLs). It has been shown that this principle can be applied to participating media as well, so that the combined single scattering contribution of VPLs within the medium yields full multiple scattering. As in the surface case, VPL methods for participating media are prone to singularities, which appear as bright “splotches” in the image. These artifacts are usually countered by clamping the VPLs' contribution, but this leads to energy loss within the short‐distance light transport. Bias compensation recovers the missing energy, but previous approaches are prohibitively costly. We investigate VPL‐based methods for rendering scenes with participating media, and propose a novel and efficient approximate bias compensation technique. We evaluate our technique using various test scenes, showing it to be visually indistinguishable from ground truth.     

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.     

A Fast Simulation Method Using Overlapping Grids for Interactions between Smoke and Rigid Objects

Recently, many techniques using computational fluid dynamics have been proposed for the simulation of natural phenomena such as smoke and fire. Traditionally, a single grid is used for computing the motion of fluids. When an object interacts with a fluid, the resolution of the grid must be sufficiently high because the shape of the object is represented by a shape sampled at the grid points. This increases the number of grid points that are required, and hence the computational cost is increased. To address this problem, we propose a method using multiple grids that overlap with each other. In addition to a large single grid (a global grid) that covers the whole of the simulation space, separate grids (local grids) are generated that surround each object. The resolution of a local grid is higher than that of the global grid. The local grids move according to the motion of the objects. Therefore, the process of resampling the shape of the object is unnecessary when the object moves. To accelerate the computation, appropriate resolutions are adaptively‐determined for the local grids according to their distance from the viewpoint. Furthermore, since we use regular (orthogonal) lattices for the grids, the method is suitable for GPU implementation. This realizes the real‐time simulation of interactions between objects and smoke.     

Simulation of Tearing Cloth with Frayed Edges

Woven cloth can commonly be seen in daily life and also in animation. Unless prevented in some way, woven cloth usually frays at the edges. However, in computer graphics, woven cloth is typically modeled as a continuum sheet, which is not suitable for representing frays. This paper proposes a model that allows yarn movement and slippage during cloth tearing. Drawing upon techniques from textile and mechanical engineering fields, we model cloth as woven yarn crossings where each yarn can be independently torn when the strain limit is reached. To make the model practical for graphics applications, we simulate only tearing part of cloth with a yarn‐level model using a simple constrained mass‐spring system for computational efficiency. We designed conditions for switching from a standard continuum sheet model to our yarn‐level model, so that frays can be initiated and propagated along the torn lines. Results show that our method can achieve plausible tearing cloth animation with frayed edges.