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Oriented bounding box (OBB) hierarchies can be used instead of hierarchies based on axis-aligned bounding boxes (AABB), providing tighter fitting to the underlying geometric structures and resulting in improved interference tests, such as ray-geometry intersections. In this paper, we present a method for the fast, parallel transformation of an existing bounding volume hierarchy (BVH), based on AABBs, into a hierarchy based on oriented bounding boxes. To this end, we parallelise a high-quality OBB extraction algorithm from the literature to operate as a standalone OBB estimator and further extend it to efficiently build an OBB hierarchy in a bottom up manner. This agglomerative approach allows for fast parallel execution and the formation of arbitrary, high-quality OBBs in bounding volume hierarchies. The method is fully implemented on the GPU and extensively evaluated with ray intersections.

The design of plausible and effective street lighting configurations for arbitrary urban sites should attain predetermined illuminance levels and adhere to specific layout intentions and functional requirements. This task can be time consuming, even for automated solutions, since there exists an one-to-many mapping between illumination goals and lighting options. In this work, we propose a generative approach for this task, based on an adversarial optimisation scheme. Our proposed method effectively overcomes these task-specific limitations by providing a range of viable solutions that adhere to the input constraints and can be generated within an interactive design life cycle.

In the ever-evolving context of Computer Graphics, the demand for realistic and real-time virtual environments and interaction with digitised or born-digital content has exponentially grown. Whether in gaming, production rendering, computer-aided design, reverse engineering, geometry processing, and understanding or simulation tasks, the ability to rapidly and accurately perform geometric queries of any type is crucial. The actual form of a geometric query varies depending on the task at hand, application domain, input representation, and adopted methodology. These queries may involve intersection tests as in the case of ray tracing, spatial queries, such as needed for recovering nearest sample neighbours, geometry registration in order to classify polygonal primitive inputs, or even virtual scene understanding in order to suggest and embed configurations as in the case of light optimisation and placement. As the applications of these algorithms and, consequently, their complexity continuously grow, traditional geometric queries fall short, when naïvely adopted and integrated in practical scenarios. Therefore, these methods face limitations in terms of computational efficiency and query bandwidth. This is particularly pronounced in scenarios, where vast amounts of geometric data must be processed in interactive or even real-time rates. More often than not, one has to inspect and understand the internal mechanics and theory of the algorithms invoking these geometric queries. This is particularly useful in order to devise appropriately tailored procedures to the underline task, hence maximise their efficiency, both in terms of performance and output quality. As a result, there is an enormous area of research that explores innovative approaches to geometric query acceleration, addressing the challenges posed. The primary focus of this research was to develop innovative methods for accelerating geometric queries within the domain of Computer Graphics. This entails a comprehensive exploration of algorithmic optimisations that include the development of advanced data structures and neural network architectures, tailored to efficiently handle geometric collections. This research addressed not only the computational complexity of individual queries, but also the adaptability of the proposed solutions to diverse applications and scenarios primary within the realm of Computer Graphics but also intersecting domains. The outcome of this research holds the potential to influence the fields that adopt these geometric query methodologies by addressing the associated computational challenges and unlocking novel directions for real-time rendering, interactive simulation, and immersive virtual experiences. More specifically, the contributions of this thesis are divided into two broad directions for accelerating geometric queries: a) global illumination-related, hardware-accelerated nearestneighbour queries and b) application of deep learning to the definition of novel data structures and geometric query methods. In the first part, we consider the task of real-time global illumination using photon density estimators. In particular we investigate scenarios where complex illumination effects, such as caustics, that can mainly be handled from the illumination theory regarding progressive photon mapping algorithms, require vast amount of rays to be traced from both the eye sensor and the light sources. Photons emanating from lights are cached into the surface geometry or volumetric media and must be gathered at query locations on the paths traced from the camera sensor. To achieve real-time frame rates, gathering, an expensive operation, needs to be efficiently handled. This is accomplished by adapting screen space ray tracing and splatting to the hardware-accelerated rasterisation pipeline. Since the gathering phase is an inherent subcategory of nearest neighbours search, we also propose how to efficiently generalise this concept to any form of task by exploiting existing low-level hardware accelerated ray tracing frameworks. Effectively boosting the inference phase by orders of magnitude compared to the traditional strategies involved. In the second part, we shift our focus to a more generic class of geometric queries. The first work involves accurate and fast shape classification using neural networks architectures. We demonstrate that a hybrid architecture, which processes orientation and a voxel-based representation of the input, is capable of processing hard-to-distinguish solid geometry from the context of building information models. Second, we consider the form of geometric queries in the context of scene understanding. More precisely, optimising the placement and light intensities of luminaries in urban places can be a computationally intricate task especially for large inputs and conflicting constraints. Methodologies employed in the literature usually make assumptions about the input representation to mitigate the intractable nature of this task. In this thesis, we approach this problem with a holistic solution that can produce feasible and diverse proposals in real time by adopting a neural-based generative modelling methodology. Finally, we propose a novel and general approach to solve recursive cost evaluators for the construction of geometric query acceleration data structures. This work establishes a new research direction for the construction of data structures guided by recursive cost functions using neural-based architectures. Our goal is to overcome the exhaustive but intractable evaluation of the cost function, in order to generate a high-quality data structure for spatial queries.

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