Higher Performance Traversal and Construction of Tree-Based Raytracing Acceleration Structures

Ray tracing is an important computational primitive used in different algorithms including collision detection, line-of-sight computations, ray tracing-based sound propagation, and most prominently light transport algorithms. It computes the closest intersections for a given set of rays and geometry. The geometry is usually modeled with a set of geometric primitives such as triangles or quadrangles which define a scene. An efficient ray tracing implementation needs to rely on an acceleration structure to decouple ray tracing complexity from scene complexity as far as possible. The most common ray tracing acceleration structures are kd-trees and bounding volume hierarchies (BVHs) which have an O(log n) ray tracing complexity in the number of scene primitives. Both structures offer similar ray tracing performance in practice. This thesis presents theoretical insights and practical approaches for higher quality, improved graphics processing unit (GPU) ray tracing performance, and faster construction of BVHs and kd-trees, where the focus is on BVHs. The chosen construction strategy for BVHs and kd-trees has a significant impact on final ray tracing performance. The most common measure for the quality of BVHs and kd-trees is the surface area metric (SAM). Using assumptions on the distribution of ray origins and directions the SAM gives an approximation for the cost of traversing an acceleration structure without having to trace a single ray. High quality construction algorithms aim at reducing the SAM cost. The most widespread high quality greedy plane-sweep algorithm applies the surface area heuristic (SAH) which is a simplification of the SAM. Advances in research on quality metrics for BVHs have shown that greedy SAH-based plane-sweep builders often construct BVHs with superior traversal performance despite the fact that the resulting SAM costs are higher than those created by more sophisticated builders. Motivated by this observation we examine different construction algorithms that use the SAM cost of temporarily constructed SAH-built BVHs to guide the construction to higher quality BVHs. An extensive evaluation reveals that the resulting BVHs indeed achieve significantly higher trace performance for primary and secondary diffuse rays compared to BVHs constructed with standard plane-sweeping. Compared to the Spatial-BVH, a kd-tree/BVH hybrid, we still achieve an acceptable increase in performance. We show that the proposed algorithm has subquadratic computational complexity in the number of primitives, which renders it usable in practical applications. An alternative construction algorithm to the plane-sweep BVH builder is agglomerative clustering, which constructs BVHs in a bottom-up fashion. It clusters primitives with a SAM-inspired heuristic and gives mixed quality BVHs compared to standard plane-sweeping construction. While related work only focused on the construction speed of this algorithm we examine clustering heuristics, which aim at higher hierarchy quality. We propose a fully SAM-based clustering heuristic which on average produces better performing BVHs compared to original agglomerative clustering. The definitions of SAM and SAH are based on assumptions on the distribution of ray origins and directions to define a conditional geometric probability for intersecting nodes in kd-trees and BVHs. We analyze the probability function definition and show that the assumptions allow for an alternative probability definition. Unlike the conventional probability, our definition accounts for directional variation in the likelihood of intersecting objects from different directions. While the new probability does not result in improved practical tracing performance, we are able to provide an interesting insight on the conventional probability. We show that the conventional probability function is directly linked to our examined probability function and can be interpreted as covertly accounting for directional variation. The path tracing light transport algorithm can require tracing of billions of rays. Thus, it can pay off to construct high quality acceleration structures to reduce the ray tracing cost of each ray. At the same time, the arising number of trace operations offers a tremendous amount of data parallelism. With CPUs moving towards many-core architectures and GPUs becoming more general purpose architectures, path tracing can now be well parallelized on commodity hardware. While parallelization is trivial in theory, properties of real hardware make efficient parallelization difficult, especially when tracing so called incoherent rays. These rays cause execution flow divergence, which reduces efficiency of SIMD-based parallelism and memory read efficiency due to incoherent memory access. We investigate how different BVH and node memory layouts as well as storing the BVH in different memory areas impacts the ray tracing performance of a GPU path tracer. We also optimize the BVH layout using information gathered in a pre-processing pass by applying a number of different BVH reordering techniques. This results in increased ray tracing performance. Our final contribution is in the field of fast high quality BVH and kd-tree construction. Increased quality usually comes at the cost of higher construction time. To reduce construction time several algorithms have been proposed to construct acceleration structures in parallel on GPUs. These are able to perform full rebuilds in realtime for moderate scene sizes if all data completely fits into GPU memory. The sheer amount of data arising from geometric detail used in production rendering makes construction on GPUs, however, infeasible due to GPU memory limitations. Existing out-of-core GPU approaches perform hybrid bottom-up top-down construction which suffers from reduced acceleration structure quality in the critical upper levels of the tree. We present an out-of-core multi-GPU approach for full top-down SAH-based BVH and kd-tree construction, which is designed to work on larger scenes than conventional approaches and yields high quality trees. The algorithm is evaluated for scenes consisting of up to 1 billion triangles and performance scales with an increasing number of GPUs

Hierarchical octree and k-d tree grids for 3D radiative transfer simulations

A crucial ingredient for numerically solving the 3D radiative transfer problem is the choice of the grid that discretizes the transfer medium. Many modern radiative transfer codes, whether using Monte Carlo or ray tracing techniques, are equipped with hierarchical octree-based grids to accommodate a wide dynamic range in densities. We critically investigate two different aspects of octree grids in the framework of Monte Carlo dust radiative transfer. Inspired by their common use in computer graphics applications, we test hierarchical k-d tree grids as an alternative for octree grids. On the other hand, we investigate which node subdivision-stopping criteria are optimal for constructing of hierarchical grids. We implemented a k-d tree grid in the 3D radiative transfer code SKIRT and compared it with the previously implemented octree grid. We also considered three different node subdivision-stopping criteria (based on mass, optical depth, and density gradient thresholds). Based on a small suite of test models, we compared the efficiency and accuracy of the different grids, according to various quality metrics. For a given set of requirements, the k-d tree grids only require half the number of cells of the corresponding octree. Moreover, for the same number of grid cells, the k-d tree is characterized by higher discretization accuracy. Concerning the subdivision stopping criteria, we find that an optical depth criterion is not a useful alternative to the more standard mass threshold, since the resulting grids show a poor accuracy. Both criteria can be combined; however, in the optimal combination, for which we provide a simple approximate recipe, this can lead to a 20% reduction in the number of cells needed to reach a certain grid quality. An additional density gradient threshold criterion can be added that solves the problem of poorly resolving sharp edges and... (abridged).Comment: 10 pages, 6 figures. Accepted for publication in A&

QuickCSG: Fast Arbitrary Boolean Combinations of N Solids

QuickCSG computes the result for general N-polyhedron boolean expressions without an intermediate tree of solids. We propose a vertex-centric view of the problem, which simplifies the identification of final geometric contributions, and facilitates its spatial decomposition. The problem is then cast in a single KD-tree exploration, geared toward the result by early pruning of any region of space not contributing to the final surface. We assume strong regularity properties on the input meshes and that they are in general position. This simplifying assumption, in combination with our vertex-centric approach, improves the speed of the approach. Complemented with a task-stealing parallelization, the algorithm achieves breakthrough performance, one to two orders of magnitude speedups with respect to state-of-the-art CPU algorithms, on boolean operations over two to dozens of polyhedra. The algorithm also outperforms GPU implementations with approximate discretizations, while producing an output without redundant facets. Despite the restrictive assumptions on the input, we show the usefulness of QuickCSG for applications with large CSG problems and strong temporal constraints, e.g. modeling for 3D printers, reconstruction from visual hulls and collision detection

Object partitioning considered harmful : space subdivision for BVHs

A major factor for the efficiency of ray tracing is the use of good acceleration structures. Recently, bounding volume hierarchies (BVHs) have become the preferred acceleration structures, due to their competitive performance and greater flexibility compared to KD trees. In this paper, we present a study on algorithms for the construction of optimal BVHs. Due to the exponential nature of the problem, constructing optimal BVHs for ray tracing remains an open topic. By exploiting the linearity of the surface area heuristic (SAH), we develop an algorithm that can find optimal partitions in polynomial time. We further generalize this algorithm and show that every SAH-based KD tree or BVH construction algorithm is a special case of the generic algorithm. Based on a number of experiments with the generic algorithm, we conclude that the assumption of non-terminating rays in the surface area cost model becomes a major obstacle for using the full potential of BVHs. We also observe that enforcing space subdivision helps to improve BVH performance. Finally, we develop a simple space partitioning algorithm for building efficient BVHs

QuickCSG: Fast Arbitrary Boolean Combinations of N Solids

QuickCSG computes the result for general N-polyhedron boolean expressions without an intermediate tree of solids. We propose a vertex-centric view of the problem, which simplifies the identification of final geometric contributions, and facilitates its spatial decomposition. The problem is then cast in a single KD-tree exploration, geared toward the result by early pruning of any region of space not contributing to the final surface. We assume strong regularity properties on the input meshes and that they are in general position. This simplifying assumption, in combination with our vertex-centric approach, improves the speed of the approach. Complemented with a task-stealing parallelization, the algorithm achieves breakthrough performance, one to two orders of magnitude speedups with respect to state-of-the-art CPU algorithms, on boolean operations over two to dozens of polyhedra. The algorithm also outperforms GPU implementations with approximate discretizations, while producing an output without redundant facets. Despite the restrictive assumptions on the input, we show the usefulness of QuickCSG for applications with large CSG problems and strong temporal constraints, e.g. modeling for 3D printers, reconstruction from visual hulls and collision detection

Faster data structures and graphics hardware techniques for high performance rendering

Computer generated imagery is used in a wide range of disciplines, each with different requirements. As an example, real-time applications such as computer games have completely different restrictions and demands than offline rendering of feature films. A game has to render quickly using only limited resources, yet present visually adequate images. Film and visual effects rendering may not have strict time requirements but are still required to render efficiently utilizing huge render systems with hundreds or even thousands of CPU cores. In real-time rendering, with limited time and hardware resources, it is always important to produce as high rendering quality as possible given the constraints available. The first paper in this thesis presents an analytical hardware model together with a feed-back system that guarantees the highest level of image quality subject to a limited time budget. As graphics processing units grow more powerful, power consumption becomes a critical issue. Smaller handheld devices have only a limited source of energy, their battery, and both small devices and high-end hardware are required to minimize energy consumption not to overheat. The second paper presents experiments and analysis which consider power usage across a range of real-time rendering algorithms and shadow algorithms executed on high-end, integrated and handheld hardware. Computing accurate reflections and refractions effects has long been considered available only in offline rendering where time isn’t a constraint. The third paper presents a hybrid approach, utilizing the speed of real-time rendering algorithms and hardware with the quality of offline methods to render high quality reflections and refractions in real-time. The fourth and fifth paper present improvements in construction time and quality of Bounding Volume Hierarchies (BVH). Building BVHs faster reduces rendering time in offline rendering and brings ray tracing a step closer towards a feasible real-time approach. Bonsai, presented in the fourth paper, constructs BVHs on CPUs faster than contemporary competing algorithms and produces BVHs of a very high quality. Following Bonsai, the fifth paper presents an algorithm that refines BVH construction by allowing triangles to be split. Although splitting triangles increases construction time, it generally allows for higher quality BVHs. The fifth paper introduces a triangle splitting BVH construction approach that builds BVHs with quality on a par with an earlier high quality splitting algorithm. However, the method presented in paper five is several times faster in construction time