Bounding Volume Hierarchies for Collision Detection

In virtual environment world, performing collision detection between various 3D objects requires sophisticated steps to be followed in order to properly visualize their effect. It is challenging due to the fact that multiple objects undergo various motion depending on the application’s genre. It is however an essential challenge to be resolved since it’s many use in the computer animation, simulation and robotic industry. Thus, object intersection between rigid bodies has become one of the most important areas in order to bring realism to simulation and animation

Bounding Volume Hierarchies for Collision Detection

In virtual environment world, performing collision detection between various 3D objects requires sophisticated steps to be followed in order to properly visualize their effect. It is challenging due to the fact that multiple objects undergo various motion depending on the application’s genre. It is however an essential challenge to be resolved since it’s many use in the computer animation, simulation and robotic industry. Thus, object intersection between rigid bodies has become one of the most important areas in order to bring realism to simulation and animation

Object Hierarchies for Efficient Rendering

This thesis covers the efficient visualization of complex 3d scenes using various rendering methods such as photo-realistic and real-time rendering. Especially the important role of bounding volume hierarchies is discussed in detail in the context of illumination and visibility algorithms. We present a novel approach for automatic generation of object hierarchies and apply the resulting data structure to several rendering techniques. In the field of ray tracing we describe a novel ray acceleration method that combines objects hierarchies and regular grids. We demonstrate how radiosity computations may benefit from available scene hierarchies to determine the radiant flux between object clusters. Finally, we present an adaptive interactive rendering algorithm that may dramatically reduce the number of visibility tests in an occlusion culling framework for interactive real-time visualization.Diese Dissertation untersucht unterschiedliche Verfahren zur effizienten Visualisierung grosser dreidimensionaler Szenengeometrien, sowohl im Bereich des Photorealismus wie auch bei der Echtzeit-Visualisierung. Hierbei wird insbesondere die Nützlichkeit von Hüllkörperhierarchien bei der Beleuchtungsrechnung und bei der Beantwortung von Sichtbarkeitsfragen herausgearbeitet. Ein neuartiges, kostenbasiertes Verfahren zur automatischen Konstruktion von Objekthierarchien wird präsentiert sowie dessen Anwendung für alle gängigen Darstellungsverfahren. Zusätzlich beschreibt diese Disseration im Bereich Ray Tracing ein neues Verfahren zur Szenenstrukturierung, welches die Vorteile von Hüllkörperhierarchien und regulären Gittern kombiniert. Im Bereich der Radiosity wird gezeigt, wie sich Szenenhierarchien ideal zur Berechnung des Lichtflusses zwischen Objekt-Clustern nutzen lassen und im Bereich Echtzeit-Rendering wird ein adaptives Verfahren vorgestellt, dass die Zahl teurer Sichtbarkeitstests beim Occlusion-Culling deutlich reduziert

Constructive Lattice Geometry

Lattice structures are widespread in product and architectural design. Recent work has demonstrated the printing of nano-scale lattices. However, an anticipated increase in product complexity will require the storage, processing, and design of lattices with orders of magnitude more elements than current Computer-Aided Design (CAD) software can manage. To address this, we propose a class of highly regular lattices called Steady Lattices, which due to their regularity, provide opportunities for highly compressed storage, accelerated processing, and intuitive design. Special cases of steady lattices are also presented, which provide varying degrees of compromise between design freedom and geometric regularity. For example, the commonly used regular lattices, which provide little design freedom but offer maximum regularity, are the least general form of steady lattice. We propose the 2-directional, Bent Corner-Operated Trans-Similar (BeCOTS) lattices as a useful compromise between regular lattices and fully general steady lattices. A BeCOTS lattice may be controlled by four non-coplanar points, which represent four corners of the lattice. The Trans-Similar property ensures that a BeCOTS lattice is composed of groups of beams such that each consecutive pair of groups of beams along a particular direction is related by the same similarity. Trans-Similarity also enables constant-time queries such as surface area calculation, volume calculation, and point-membership classification. We take advantage of the regularity in steady lattices to efficiently produce and query highly complex lattice structures that we call Constructive Lattice Geometry (CLG), where CLG is an extension of traditional Constructive Solid Geometry (CSG). CLG models are periodic CSG models for which regular patterns of primitives are combined into many repeating CSG microstructures that are ultimately combined into one CSG macrostructure. We provide strategies for designing and processing recursively defined CLG models to enable the creation of CLG models composed of smaller CLG models. Parameterized steady lattices and CLG models may be defined by a few lines of code, which facilitates lazy (on-demand) evaluation, massively parallel processing, interactive editing, and algorithmic optimization.Ph.D

Technologies for Biomechanically-Informed Image Guidance of Laparoscopic Liver Surgery

Laparoscopic surgery for liver resection has a number medical advantages over open surgery, but also comes with inherent technical challenges. The surgeon only has a very limited field of view through the imaging modalities routinely employed intra-operatively, laparoscopic video and ultrasound, and the pneumoperitoneum required to create the operating space and gaining access to the organ can significantly deform and displace the liver from its pre-operative configuration. This can make relating what is visible intra-operatively to the pre-operative plan and inferring the location of sub-surface anatomy a very challenging task. Image guidance systems can help overcome these challenges by updating the pre-operative plan to the situation in theatre and visualising it in relation to the position of surgical instruments. In this thesis, I present a series of contributions to a biomechanically-informed image-guidance system made during my PhD. The most recent one is work on a pipeline for the estimation of the post-insufflation configuration of the liver by means of an algorithm that uses a database of segmented training images of patient abdomens where the post-insufflation configuration of the liver is known. The pipeline comprises an algorithm for inter and intra-subject registration of liver meshes by means of non-rigid spectral point-correspondence finding. My other contributions are more fundamental and less application specific, and are all contained and made available to the public in the NiftySim open-source finite element modelling package. Two of my contributions to NiftySim are of particular interest with regards to image guidance of laparoscopic liver surgery: 1) a novel general purpose contact modelling algorithm that can be used to simulate contact interactions between, e.g., the liver and surrounding anatomy; 2) membrane and shell elements that can be used to, e.g., simulate the Glisson capsule that has been shown to significantly influence the organ’s measured stiffness

Ray Tracing Complex Scenes on a Multiple-instruction Steam Multiple-Data Stream Concurrent Computer

The Ray Tracing technique generates perhaps the most realistic looking computergenerated images. It does so at the cost of a great deal of computer time. Many algorithms have been developed to speed up the ray tracing procedure, but it still remains the most CPU-intensive realistic image synthesis method. To date, ray tracing has remained largely in the realm of serial computers. The research in this thesis takes ray tracing strongly into the parallel computing domain and deals effectively with all of the central issuessurrounding the parallelization of this procedure. Results from the "Hypercube Ray Tracer" are collected and compared against other ray tracing systems. A new technique for ray tracing Constructive Solid Geometry objects is also developed and implemented.Electrical Engineerin

New Applications of the Nearest-Neighbor Chain Algorithm

The nearest-neighbor chain algorithm was proposed in the eighties as a way to speed up certain hierarchical clustering algorithms. In the first part of the dissertation, we show that its application is not limited to clustering. We apply it to a variety of geometric and combinatorial problems. In each case, we show that the nearest-neighbor chain algorithm finds the same solution as a preexistent greedy algorithm, but often with an improved runtime. We obtain speedups over greedy algorithms for Euclidean TSP, Steiner TSP in planar graphs, straight skeletons, a geometric coverage problem, and three stable matching models. In the second part, we study the stable-matching Voronoi diagram, a type of plane partition which combines properties of stable matchings and Voronoi diagrams. We propose political redistricting as an application. We also show that it is impossible to compute this diagram in an algebraic model of computation, and give three algorithmic approaches to overcome this obstacle. One of them is based on the nearest-neighbor chain algorithm, linking the two parts together

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

Contribution to structural parameters computation: volume models and methods

Bio-CAD and in-silico experimentation are getting a growing interest in biomedical applications where scientific data coming from real samples are used to compute structural parameters that allow to evaluate physical properties. Non-invasive imaging acquisition technologies such as CT, mCT or MRI, plus the constant growth of computer capabilities, allow the acquisition, processing and visualization of scientific data with increasing degree of complexity. Structural parameters computation is based on the existence of two phases (or spaces) in the sample: the solid, which may correspond to the bone or material, and the empty or porous phase and, therefore, they are represented as binary volumes. The most common representation model for these datasets is the voxel model, which is the natural extension to 3D of 2D bitmaps. In this thesis, the Extreme Vertices Model (EVM) and a new proposed model, the Compact Union of Disjoint Boxes (CUDB), are used to represent binary volumes in a much more compact way. EVM stores only a sorted subset of vertices of the object¿s boundary whereas CUDB keeps a compact list of boxes. In this thesis, methods to compute the next structural parameters are proposed: pore-size distribution, connectivity, orientation, sphericity and roundness. The pore-size distribution helps to interpret the characteristics of porous samples by allowing users to observe most common pore diameter ranges as peaks in a graph. Connectivity is a topological property related to the genus of the solid space, measures the level of interconnectivity among elements, and is an indicator of the biomechanical characteristics of bone or other materials. The orientation of a shape can be defined by rotation angles around a set of orthogonal axes. Sphericity is a measure of how spherical is a particle, whereas roundness is the measure of the sharpness of a particle's edges and corners. The study of these parameters requires dealing with real samples scanned at high resolution, which usually generate huge datasets that require a lot of memory and large processing time to analyze them. For this reason, a new method to simplify binary volumes in a progressive and lossless way is presented. This method generates a level-of-detail sequence of objects, where each object is a bounding volume of the previous objects. Besides being used as support in the structural parameter computation, this method can be practical for task such as progressive transmission, collision detection and volume of interest computation. As part of multidisciplinary research, two practical applications have been developed to compute structural parameters of real samples. A software for automatic detection of characteristic viscosity points of basalt rocks and glasses samples, and another to compute sphericity and roundness of complex forms in a silica dataset.El Bio-Diseño Asistido por Computadora (Bio-CAD), y la experimentacion in-silico est an teniendo un creciente interes en aplicaciones biomedicas, en donde se utilizan datos cientificos provenientes de muestras reales para calcular par ametros estructurales que permiten evaluar propiedades físicas. Las tecnologías de adquisicion de imagen no invasivas como la TC, TC o IRM, y el crecimiento constante de las prestaciones de las computadoras, permiten la adquisicion, procesamiento y visualizacion de datos científicos con creciente grado de complejidad. El calculo de parametros estructurales esta basado en la existencia de dos fases (o espacios) en la muestra: la solida, que puede corresponder al hueso o material, y la fase porosa o vacía, por tanto, tales muestras son representadas como volumenes binarios. El modelo de representacion mas comun para estos conjuntos de datos es el modelo de voxeles, el cual es una extension natural a 3D de los mapas de bits 2D. En esta tesis se utilizan el modelo Extreme Verrtices Model (EVM) y un nuevo modelo propuesto, the Compact Union of Disjoint Boxes (CUDB), para representar los volumenes binarios en una forma mucho mas compacta. El modelo EVM almacena solo un subconjunto ordenado de vertices de la frontera del objeto mientras que el modelo CUDB mantiene una lista compacta de cajas. En esta tesis se proponen metodos para calcular los siguientes parametros estructurales: distribucion del tamaño de los poros, conectividad, orientacion, esfericidad y redondez. La distribucion del tamaño de los poros ayuda a interpretar las características de las muestras porosas permitiendo a los usuarios observar los rangos de diametro mas comunes de los poros mediante picos en un grafica. La conectividad es una propiedad topologica relacionada con el genero del espacio solido, mide el nivel de interconectividad entre los elementos, y es un indicador de las características biomecanicas del hueso o de otros materiales. La orientacion de un objeto puede ser definida por medio de angulos de rotacion alrededor de un conjunto de ejes ortogonales. La esfericidad es una medida de que tan esferica es una partícula, mientras que la redondez es la medida de la nitidez de sus aristas y esquinas. En el estudio de estos parametros se trabaja con muestras reales escaneadas a alta resolucion que suelen generar conjuntos de datos enormes, los cuales requieren una gran cantidad de memoria y mucho tiempo de procesamiento para ser analizados. Por esta razon, se presenta un nuevo metodo para simpli car vol umenes binarios de una manera progresiva y sin perdidas. Este metodo genera una secuencia de niveles de detalle de los objetos, en donde cada objeto es un volumen englobante de los objetos previos. Ademas de ser utilizado como apoyo en el calculo de parametros estructurales, este metodo puede ser de utilizado en otras tareas como transmision progresiva, deteccion de colisiones y calculo de volumen de interes. Como parte de una investigacion multidisciplinaria, se han desarrollado dos aplicaciones practicas para calcular parametros estructurales de muestras reales. Un software para la deteccion automatica de puntos de viscosidad característicos en muestras de rocas de basalto y vidrios, y una aplicacion para calcular la esfericidad y redondez de formas complejas en un conjunto de datos de sílice