SAH guided spatial split partitioning for fast BVH construction

We present a new SAH guided approach to subdividing triangles as the scene is coarsely partitioned into smaller sets of spatially coherent triangles. Our triangle split approach is integrated into the partitioning stage of a fast BVH construction algorithm, but may as well be used as a stand alone pre‐split pass. Our algorithm significantly reduces the number of split triangles compared to previous methods, while at the same time improving ray tracing performance compared to competing fast BVH construction techniques. We compare performance on Intel's Embree ray tracer and show that BVH construction with our splitting algorithm is always faster than Embree's pre‐split construction algorithm. We also show that our algorithm builds significantly improved quality trees that deliver higher ray tracing performance. Our algorithm is implemented into Embree's open source ray tracing framework, and the source code will be released late 2015.     

T‐SAH: Animation Optimized Bounding Volume Hierarchies

We propose a method for creating a bounding volume hierarchy (BVH) that is optimized for all frames of a given animated scene. The method is based on a novel extension of surface area heuristic to temporal domain (T‐SAH). We perform iterative BVH optimization using T‐SAH and create a single BVH accounting for scene geometry distribution at different frames of the animation. Having a single optimized BVH for the whole animation makes our method extremely easy to integrate to any application using BVHs, limiting the per‐frame overhead only to refitting the bounding volumes. We evaluated the T‐SAH optimized BVHs in the scope of real‐time GPU ray tracing. We demonstrate, that our method can handle even highly complex inputs with large deformations and significant topology changes. The results show, that in a vast majority of tested scenes our method provides significantly better run‐time performance than traditional SAH and also better performance than GPU based per‐frame BVH rebuild.     

The Use of Precomputed Triangle Clusters for Accelerated Ray Tracing in Dynamic Scenes

In this paper we present a hybrid algorithm for building the bounding volume hierarchy (BVH) that is used in accelerating ray tracing of animated models. This algorithm precomputes densely packed clusters of triangles on surfaces. Folowing that, a set of clusters is used to rebuild the BVH in every frame. Our approach utilizes the assumption that groups of connected triangles remain connected throughout the course of the animation. We introduce a novel heuristic to create triangle clusters that are designed for high performance ray tracing. This heuristic combines the density of connectivity, geometric size and the shape of the cluster.
Our approach accelerates the BVH builder by an order of magnitude rebuilding only the set of clusters that is much smaller than the original set of triangles. The speed-up is achieved against a 'brute-force' BVH builder that repartitions all triangles in every frame of animation without using any pre-clustering. The rendering performance is not affected when a cluster contains a few dozen triangles. We demonstrate the real-time/interactive ray tracing performance for highly-dynamic complex models.     

Fast Ray Sorting and Breadth‐First Packet Traversal for GPU Ray Tracing

We present a novel approach to ray tracing execution on commodity graphics hardware using CUDA. We decompose a standard ray tracing algorithm into several data‐parallel stages that are mapped efficiently to the massively parallel architecture of modern GPUs. These stages include: ray sorting into coherent packets, creation of frustums for packets, breadth‐first frustum traversal through a bounding volume hierarchy for the scene, and localized ray‐primitive intersections. We utilize the well known parallel primitives scan and segmented scan in order to process irregular data structures, to remove the need for a stack, and to minimize branch divergence in all stages. Our ray sorting stage is based on applying hash values to individual rays, ray stream compression, sorting and decompression. Our breadth‐first BVH traversal is based on parallel frustum‐bounding box intersection tests and parallel scan per each BVH level. We demonstrate our algorithm with area light sources to get a soft shadow effect and show that our concept is reasonable for GPU implementation. For the same data sets and ray‐primitive intersection routines our pipeline is ～3x faster than an optimized standard depth first ray tracing implemented in one kernel.     

Ray Specialized Contraction on Bounding Volume Hierarchies

In this paper we propose a simple but effective method to modify a BVH based on ray distribution for improved ray tracing performance. Our method starts with an initial BVH generated by any state‐of‐the‐art offline algorithm. Then by traversing a small set of sample rays we collect statistics at each node of the BVH. Finally, a simple but ultra‐fast BVH contraction algorithm modifies the initial binary BVH to a multi‐way BVH. The overall acceleration for ray‐primitive testing is about 25% for incoherent diffuse rays and 30% for shadow rays, which is significant as a data structure optimization. Similar results are also presented for packet ray tracing, and for Quad‐BVHs the improvement is 10% to 15%. The approach has the advantages of being simple, and compatible with almost any existing BVH and ray tracing techniques, and it require very little extra work to generate the modified tree.     

Ray Classification for Accelerated BVH Traversal

For ray tracing based methods, traversing a hierarchical acceleration data structure takes up a substantial portion of the total rendering time. We propose an additional data structure which cuts off large parts of the hierarchical traversal. We use the idea of ray classification combined with the hierarchical scene representation provided by a bounding volume hierarchy. We precompute short arrays of indices to subtrees inside the hierarchy and use them to initiate the traversal for a given ray class. This arrangement is compact enough to be cache‐friendly, preventing the method from negating its traversal gains by excessive memory traffic. The method is easy to use with existing renderers which we demonstrate by integrating it to the PBRT renderer. The proposed technique reduces the number of traversal steps by 42% on average, saving around 15% of time of finding ray‐scene intersection on average.     

Polynomial Optics: A Construction Kit for Efficient Ray‐Tracing of Lens Systems

Simulation of light transport through lens systems plays an important role in graphics. While basic imaging properties can be conveniently derived from linear models (like ABCD matrices), these approximations fail to describe nonlinear effects and aberrations that arise in real optics. Such effects can be computed by proper ray tracing, for which, however, finding suitable sampling and filtering strategies is often not a trivial task. Inspired by aberration theory, which describes the deviation from the linear ray transfer in terms of wavefront distortions, we propose a ray‐space formulation for nonlinear effects. In particular, we approximate the analytical solution to the ray tracing problem by means of a Taylor expansion in the ray parameters. This representation enables a construction‐kit approach to complex optical systems in the spirit of matrix optics. It is also very simple to evaluate, which allows for efficient execution on CPU and GPU alike, including the computation of mixed derivatives of any order. We evaluate fidelity and performance of our polynomial model, and show applications in high‐quality offline rendering and at interactive frame rates.     

Interactive Global Photon Mapping

We present a photon mapping technique capable of computing high quality global illumination at interactive frame rates. By extending the concept of photon differentials to efficiently handle diffuse reflections, we generate footprints at all photon hit points. These enable illumination reconstruction by density estimation with variable kernel bandwidths without having to locate the k nearest photon hits first. Adapting an efficient BVH construction process for ray tracing acceleration, we build photon maps that enable the fast retrieval of all hits relevant to a shading point. We present a heuristic that automatically tunes the BVH build's termination criterion to the scene and illumination conditions. As all stages of the algorithm are highly parallelizable, we demonstrate an implementation using NVidia's CUDA manycore architecture running at interactive rates on a single GPU. Both light source and camera may be freely moved with global illumination fully recalculated in each frame.     

Parallel Reinsertion for Bounding Volume Hierarchy Optimization

We present a novel highly parallel method for optimizing bounding volume hierarchies (BVH) targeting contemporary GPU architectures. The core of our method is based on the insertion‐based BVH optimization that is known to achieve excellent results in terms of the SAH cost. The original algorithm is, however, inherently sequential: no efficient parallel version of the method exists, which limits its practical utility. We reformulate the algorithm while exploiting the observation that there is no need to remove the nodes from the BVH prior to finding their optimized positions in the tree. We can search for the optimized positions for all nodes in parallel while simultaneously tracking the corresponding SAH cost reduction. We update in parallel all nodes for which better position was found while efficiently handling potential conflicts during these updates. We implemented our algorithm in CUDA and evaluated the resulting BVH in the context of the GPU ray tracing. The results indicate that the method is able to achieve the best ray traversal performance among the state of the art GPU‐based BVH construction methods.     

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.     

TSS BVHs: Tetrahedron Swept Sphere BVHs for Ray Tracing Subdivision Surfaces

We present a novel, compact bounding volume hierarchy, TSS BVH, for ray tracing subdivision surfaces computed by the Catmull‐Clark scheme. We use Tetrahedron Swept Sphere (TSS) as a bounding volume to tightly bound limit surfaces of such subdivision surfaces given a user tolerance. Geometric coordinates defining our TSS bounding volumes are implicitly computed from the subdivided mesh via a simple vertex ordering method, and each level of our TSS BVH is associated with a single distance bound, utilizing the Catmull‐Clark scheme. These features result in a linear space complexity as a function of the tree depth, while many prior BVHs have exponential space complexity. We have tested our method against different benchmarks with path tracing and photon mapping. We found that our method achieves up to two orders of magnitude of memory reduction with a high culling ratio over the prior AABB BVH methods, when we represent models with two to four subdivision levels. Overall, our method achieves three times performance improvement thanks to these results. These results are acquired by our theorem that rigorously computes our TSS bounding volumes.     

Improving Memory Space Efficiency of Kd‐tree for Real‐time Ray Tracing

Compared with its competitors such as the bounding volume hierarchy, a drawback of the kd‐tree structure is that a large number of triangles are repeatedly duplicated during its construction, which often leads to inefficient, large and tall binary trees with high triangle redundancy. In this paper, we propose a space‐efficient kd‐tree representation where, unlike commonly used methods, an inner node is allowed to optionally store a reference to a triangle, so highly redundant triangles in a kd‐tree can be culled from the leaf nodes and moved to the inner nodes. To avoid the construction of ineffective kd‐trees entailing computational inefficiencies due to early, possibly unnecessary, ray‐triangle intersection calculations that now have to be performed in the inner nodes during the kd‐tree traversal, we present heuristic measures for determining when and how to choose triangles for inner nodes during kd‐tree construction. Based on these metrics, we describe how the new form of kd‐tree is constructed and stored compactly using a carefully designed data layout. Our experiments with several example scenes showed that our kd‐tree representation technique significantly reduced the memory requirements for storing the kd‐tree structure, while effectively suppressing the unavoidable frame‐rate degradation observed during ray tracing.     

Temporally Coherent Adaptive Sampling for Imperfect Shadow Maps

We propose a new adaptive algorithm for determining virtual point lights (VPL) in the scope of real‐time instant radiosity methods, which use a limited number of VPLs. The proposed method is based on Metropolis‐Hastings sampling and exhibits better temporal coherence of VPLs, which is particularly important for real‐time applications dealing with dynamic scenes. We evaluate the properties of the proposed method in the context of the algorithm based on imperfect shadow maps and compare it with the commonly used inverse transform method. The results indicate that the proposed technique can significantly reduce the temporal flickering artifacts even for scenes with complex materials and textures. Further, we propose a novel splatting scheme for imperfect shadow maps using hardware tessellation. This scheme significantly improves the rendering performance particularly for complex and deformable scenes. We thoroughly analyze the performance of the proposed techniques on test scenes with detailed materials, moving camera, and deforming geometry.     

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.     

Fitted BVH for Fast Raytracing of Metaballs

Raytracing metaballs is a problem that has numerous applications in the rendering of dynamic soft objects such as fluids. However, current techniques are either limited in the visual effects that they can render or their performance drops as the number of metaballs and their density increase. We present a new acceleration structure based on BVH and kd‐tree for efficient raytracing of a large number of metaballs. This structure is built from an adapted SAH using a fast greedy algorithm and allows the visualization of several hundreds of thousands metaballs at interactive‐to‐real‐time framerates. Our method can handle arbitrary rays to simulate any complex secondary effects such as reflections or soft shadows, and is robust with respect to the density of metaballs. We achieve this performance thanks to a balanced CPU‐GPU (using CUDA) implementation of the animation, structure creation, and rendering.     

RBF Volume Ray Casting on Multicore and Manycore CPUs

Modern supercomputers enable increasingly large N‐body simulations using unstructured point data. The structures implied by these points can be reconstructed implicitly. Direct volume rendering of radial basis function (RBF) kernels in domain‐space offers flexible classification and robust feature reconstruction, but achieving performant RBF volume rendering remains a challenge for existing methods on both CPUs and accelerators. In this paper, we present a fast CPU method for direct volume rendering of particle data with RBF kernels. We propose a novel two‐pass algorithm: first sampling the RBF field using coherent bounding hierarchy traversal, then subsequently integrating samples along ray segments. Our approach performs interactively for a range of data sets from molecular dynamics and astrophysics up to 82 million particles. It does not rely on level of detail or subsampling, and offers better reconstruction quality than structured volume rendering of the same data, exhibiting comparable performance and requiring no additional preprocessing or memory footprint other than the BVH. Lastly, our technique enables multi‐field, multi‐material classification of particle data, providing better insight and analysis.     

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.     

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.     

Fast Insertion‐Based Optimization of Bounding Volume Hierarchies

We present an algorithm for fast optimization of bounding volume hierarchies (BVH) for efficient ray tracing. We perform selective updates of the hierarchy driven by the cost model derived from the surface area heuristic. In each step, the algorithm updates a fraction of the hierarchy nodes to minimize the overall hierarchy cost. The updates are realized by simple operations on the tree nodes: removal, search and insertion. Our method can quickly reduce the cost of the hierarchy constructed by the traditional techniques, such as the surface area heuristic. We evaluate the properties of the proposed method on fourteen test scenes of different complexity including individual objects and architectural scenes. The results show that our method can improve a BVH initially constructed with the surface area heuristic by up to 27% and a BVH constructed with the spatial median split by up to 88%.     

Performance Comparison of Bounding Volume Hierarchies and Kd‐Trees for GPU Ray Tracing

We present a performance comparison of bounding volume hierarchies and kd‐trees for ray tracing on many‐core architectures (GPUs). The comparison is focused on rendering times and traversal characteristics on the GPU using data structures that were optimized for very high performance of tracing rays. To achieve low rendering times, we extensively examine the constants used in termination criteria for the two data structures. We show that for a contemporary GPU architecture (NVIDIA Kepler) bounding volume hierarchies have higher ray tracing performance than kd‐trees for simple and moderately complex scenes. On the other hand, kd‐trees have higher performance for complex scenes, in particular for those with high depth complexity. Finally, we analyse the causes of the performance discrepancies using the profiling characteristics of the ray tracing kernels.