Adaptive Caustic Maps Using Deferred Shading

Caustic maps provide an interactive image-space method to render caustics, the focusing of light via reflection and refraction. Unfortunately, caustic mapping suffers problems similar to shadow mapping: aliasing from poor sampling and map projection as well as temporal incoherency from frame-to-frame sampling variations. To reduce these problems, researchers have suggested methods ranging from caustic blurring to building a multiresolution caustic map. Yet these all require a fixed photon sampling, precluding the use of importance-based photon densities. This paper introduces adaptive caustic maps. Instead of densely sampling photons via a rasterization pass, we adaptively emit photons using a deferred shading pass. We describe deferred rendering for refractive surfaces, which speeds rendering of refractive geometry up to 25% and with adaptive sampling speeds caustic rendering up to 200%. These benefits are particularly noticable for complex geometry or using millions of photons. While developed for a GPU rasterizer, adaptive caustic map creation can be performed by any renderer that individually traces photons, e.g., a GPU ray tracer.     

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.     

Multi‐layer Depth Peeling by Single‐Pass Rasterisation for Faster Isosurface Raytracing on GPUs

Empty‐space skipping is an essential acceleration technique for volume rendering. Image‐order empty‐space skipping is not well suited to GPU implementation, since it must perform checks on, essentially, a per‐sample basis, as in kd‐tree traversal, which can lead to a great deal of divergent branching at runtime, which is very expensive in a modern GPU pipeline. In contrast, object‐order empty‐space skipping is extremely fast on a GPU and has negligible overheads compared with approaches without empty‐space skipping, since it employs the hardware unit for rasterisation. However, previous object‐order algorithms have been able to skip only exterior empty space and not the interior empty space that lies inside or between volume objects. In this paper, we address these issues by proposing a multi‐layer depth‐peeling approach that can obtain all of the depth layers of the tight‐fitting bounding geometry of the isosurface by a single rasterising pass. The maximum count of layers peeled by our approach can be up to thousands, while maintaining 32‐bit float‐point accuracy, which was not possible previously. By raytracing only the valid ray segments between each consecutive pair of depth layers, we can skip both the interior and exterior empty space efficiently. In comparisons with 3 state‐of‐the‐art GPU isosurface rendering algorithms, this technique achieved much faster rendering across a variety of data sets.     

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.     

GPU Ray Tracing using Irregular Grids

We present a spatial index structure to accelerate ray tracing on GPUs. It is a flat, non‐hierarchical spatial subdivision of the scene into axis aligned cells of varying size. In order to construct it, we first nest an octree into each cell of a uniform grid. We then apply two optimization passes to increase ray traversal performance: First, we reduce the expected cost for ray traversal by merging cells together. This adapts the structure to complex primitive distributions, solving the “teapot in a stadium” problem. Second, we decouple the cell boundaries used during traversal for rays entering and exiting a given cell. This allows us to extend the exiting boundaries over adjacent cells that are either empty or do not contain additional primitives. Now, exiting rays can skip empty space and avoid repeating intersection tests. Finally, we demonstrate that in addition to the fast ray traversal performance, the structure can be rebuilt efficiently in parallel, allowing for ray tracing dynamic scenes.     

Crack‐free rendering of dynamically tesselated B‐rep models

We propose a versatile pipeline to render B‐Rep models interactively, precisely and without rendering‐related artifacts such as cracks. Our rendering method is based on dynamic surface evaluation using both tesselation and ray‐casting, and direct GPU surface trimming. An initial rendering of the scene is performed using dynamic tesselation. The algorithm we propose reliably detects then fills up cracks in the rendered image. Crack detection works in image space, using depth information, while crack‐filling is either achieved in image space using a simple classification process, or performed in object space through selective ray‐casting. The crack filling method can be dynamically changed at runtime. Our image space crack filling approach has a limited runtime cost and enables high quality, real‐time navigation. Our higher quality, object space approach results in a rendering of similar quality than full‐scene ray‐casting, but is 2 to 6 times faster, can be used during navigation and provides accurate, reliable rendering. Integration of our work with existing tesselation‐based rendering engines is straightforward.     

Memory‐Efficient Interactive Online Reconstruction From Depth Image Streams

We describe how the pipeline for 3D online reconstruction using commodity depth and image scanning hardware can be made scalable for large spatial extents and high scanning resolutions. Our modified pipeline requires less than 10% of the memory that is required by previous approaches at similar speed and resolution. To achieve this, we avoid storing a 3D distance field and weight map during online scene reconstruction. Instead, surface samples are binned into a high‐resolution binary voxel grid. This grid is used in combination with caching and deferred processing of depth images to reconstruct the scene geometry. For pose estimation, GPU ray‐casting is performed on the binary voxel grid. A one‐to‐one comparison to level‐set ray‐casting in a distance volume indicates slightly lower pose accuracy. To enable unlimited spatial extents and store acquired samples at the appropriate level of detail, we combine a hash map with a hierarchical tree representation.     

Geometry Presorting for Implicit Object Space Partitioning

We present a new data structure for object space partitioning that can be represented completely implicitly. The bounds of each node in the tree structure are recreated at run‐time from the scene objects contained therein. By applying a presorting procedure to the geometry, only a known fraction of the geometry is needed to locate the bounding planes of any node. We evaluate the impact of the implicit bounding plane representation and compare our algorithm to a classic bounding volume hierarchy. Though the representation is completely implicit, we still achieve interactive frame rates on commodity hardware.     

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.     

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.     

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.     

Probabilistic visibility evaluation using geometry proxies

Evaluating the visibility between two points is a fundamental problem for ray‐tracing and path‐tracing algorithms. Ideally, visibility computations are organized such that a minimum number of geometric primitives need to be checked for each ray. Replacing complex geometric shapes by a simpler set of primitives is one strategy to control the amount of intersection calculations. However, approximating the original geometry introduces inaccuracies in e.g. shadow regions when shadow rays are intersected with the approximate geometry. This paper presents a theoretical framework for probabilistic visibility evaluation. When intersecting a shadow ray with the scene, we randomly select the original geometry, the approximated geometry, or one of several correction terms, to be tested. Not all shadow rays will therefore intersect the original geometry, but our method is able to produce unbiased images that converge to the correct solution. Although probabilistic visibility evaluation is an experimental idea, we show several example scenes that highlight the potential for future improvements.     

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.     

Decoupled Opacity Optimization for Points,Lines and Surfaces

Displaying geometry inflow visualization is often accompanied by occlusion problems, making it difficult to perceive information that is relevant in the respective application. In a recent technique, named opacity optimization, the balance of occlusion avoidance and the selection of meaningful geometry was recognized to be a view‐dependent, global optimization problem. The method solves a bounded‐variable least‐squares problem, which minimizes energy terms for the reduction of occlusion, background clutter, adding smoothness and regularization. The original technique operates on an object‐space discretization and was shown for line and surface geometry. Recently, it has been extended to volumes, where it was solved locally per ray by dropping the smoothness energy term and replacing it by pre‐filtering the importance measure. In this paper, we pick up the idea of splitting the opacity optimization problem into two smaller problems. The first problem is a minimization with analytic solution, and the second problem is a smoothing of the obtained minimizer in object‐space. Thereby, the minimization problem can be solved locally per pixel, making it possible to combine all geometry types (points, lines and surfaces) consistently in a single optimization framework. We call this decoupled opacity optimization and apply it to a number of steady 3D vector fields.     

Decoupled Space and Time Sampling of Motion and Defocus Blur for Unified Rendering of Transparent and Opaque Objects

We propose a unified rendering approach that jointly handles motion and defocus blur for transparent and opaque objects at interactive frame rates. Our key idea is to create a sampled representation of all parts of the scene geometry that are potentially visible at any point in time for the duration of a frame in an initial rasterization step. We store the resulting temporally‐varying fragments (t‐fragments) in a bounding volume hierarchy which is rebuild every frame using a fast spatial median construction algorithm. This makes our approach suitable for interactive applications with dynamic scenes and animations. Next, we perform spatial sampling to determine all t‐fragments that intersect with a specific viewing ray at any point in time. Viewing rays are sampled according to the lens uv‐sampling for depth‐of‐field effects. In a final temporal sampling step, we evaluate the predetermined viewing ray/t‐fragment intersections for one or multiple points in time. This allows us to incorporate all standard shading effects including transparency. We describe the overall framework, present our GPU implementation, and evaluate our rendering approach with respect to scalability, quality, and performance.     

Hybrid Data Visualization Based on Depth Complexity Histogram Analysis

In many cases, only the combination of geometric and volumetric data sets is able to describe a single phenomenon under observation when visualizing large and complex data. When semi‐transparent geometry is present, correct rendering results require sorting of transparent structures. Additional complexity is introduced as the contributions from volumetric data have to be partitioned according to the geometric objects in the scene. The A‐buffer, an enhanced framebuffer with additional per‐pixel information, has previously been introduced to deal with the complexity caused by transparent objects. In this paper, we present an optimized rendering algorithm for hybrid volume‐geometry data based on the A‐buffer concept. We propose two novel components for modern GPUs that tailor memory utilization to the depth complexity of individual pixels. The proposed components are compatible with modern A‐buffer implementations and yield performance gains of up to eight times compared to existing approaches through reduced allocation and reuse of fast cache memory. We demonstrate the applicability of our approach and its performance with several examples from molecular biology, space weather and medical visualization containing both, volumetric data and geometric structures.     

3D Video Billboard Clouds

3D video billboard clouds reconstruct and represent a dynamic three-dimensional scene using displacement-mapped billboards. They consist of geometric proxy planes augmented with detailed displacement maps and combine the generality of geometry-based 3D video with the regularization properties of image-based 3D video. 3D video billboards are an image-based representation placed in the disparity space of the acquisition cameras and thus provide a regular sampling of the scene with a uniform error model. We propose a general geometry filtering framework which generates time-coherent models and removes reconstruction and quantization noise as well as calibration errors. This replaces the complex and time-consuming sub-pixel matching process in stereo reconstruction with a bilateral filter. Rendering is performed using a GPU-accelerated algorithm which generates consistent view-dependent geometry and textures for each individual frame. In addition, we present a semi-automatic approach for modeling dynamic three-dimensional scenes with a set of multiple 3D video billboards clouds.     

Improved Half Vector Space Light Transport

In this paper, we present improvements to half vector space light transport (HSLT) [ KHD14 ], which make this approach more practical, robust for difficult input geometry, and faster. Our first contribution is the computation of half vector space ray differentials in a different domain than the original work. This enables a more uniform stratification over the image plane during Markov chain exploration. Furthermore, we introduce a new multi chain perturbation in half vector space, which, if combined appropriately with half vector perturbation, makes the mutation strategy both more robust to geometric configurations with fine displacements and faster due to reduced number of ray casts. We provide and analyze the results of improved HSLT and discuss possible applications of our new half vector ray differentials.     

Occlusion-Driven Scene Sorting for Efficient Culling

Image space occlusion culling is a powerful approach to reduce the rendering load of large polygonal models. However, occlusion culling is not for free; it trades overhead costs with the rendering costs of the possibly occluded geometry. Meanwhile, occlusion queries based on image space occlusion culling are supported on modern graphics hardware. However, a significant consumption of fillrate bandwidth and latency costs are associated with these queries. In this paper, we propose new techniques to reduce redundant occlusion queries. Our approach uses several "Occupancy Maps" to organize scene traversal. The respective information is accumulated efficiently by hardware‐supported asynchronous occlusion queries. To avoid redundant requests, we arrange these multiple occlusion queries according to the information of the Occupancy Maps. Our presented technique is conservative and benefits from a partial depth order of the geometry.