Context. Collision is a basic necessity in most simulated environments, especially video games, which demand user interaction. Octrees are a way to divide the simulated environments into smaller, more manageable parts,and is a hierarchical tree-structure, where each node has eight children. Octrees and similar tree-structural methods have been used frequently to optimize collision calculations and partition the objects in the 3D space. Objectives. The aim of this thesis is to find a way to further improve upon the octree structure, by using a two-level octree structure, and simplify the collision of objects that do not demand much complexity, due to their size or the geometric simplicity of their 3D models, this is done by calculating how many pixels the objects occupy on the screen, and use that as a factor when deciding the depth of their individual octrees. Methods. Each object in the 3D environment is divided using an octree. These octrees generated for the objects are then placed in a larger octree. This large octree use the smaller ones to check collision between the objects. The pixel area occupied on the screen by the objects’ octrees is used to determine what depth of the octrees will be check for intersection. Two test scenes were set up to test our model. Results. Our implementation could effectively reduce the depth of octrees belonging to objects occupying little space on the screen. The experiments also showed that the reduced depth could be used with only a slight loss in accuracy. The accuracy loss increased when more objects were used. Conclusions. The results gained in the thesis show that the pixel area can be used effectively, and the simplified octrees can still represent the objects adequately, resulting in a cheaper but slightly less accurate collision.

This master's thesis focuses on representation of geometric information about the surrounding environment for robotic systems. Instead of a common point-cloud based representation, an environment model that stores information about objects described by bounding boxes and planes is proposed. These objects can be obtained from trained object detectors, planar surface detectors, etc. processing data from sensors (e.g. RGB-D camera). The information about the objects (position, etc.) stored in the model is constantly changing according to data obtained from detectors. The environment model is implemented as a module for Robot Operating System. To illustrate and visualize features of the model, a demonstration application was also prepared.

<p>Real-time global illumination has been a very important topic and is widely used in game industry. Previous offline rendering requires a large amount of time to converge and reduce the noise generated in Monte Carlo method. Thus, it cannot be easily adapted in real-time rendering. Using voxels in the field of global illumination has become a popular approach. While a naïve voxel grid occupies huge memory in video card, a data structure called <i>sparse voxel octree</i> is often implemented in order to reduce memory cost of voxels and achieve efficient ray casting performance in an interactive frame rate. </p> <p>However, rendering of voxels can cause block effects due to the nature of voxel. One solution is to increase the resolution of voxel so that one voxel is smaller than a pixel on screen. But this is usually not feasible because higher resolution results in higher memory consumption. Thus, most of the global illumination methods of SVO (sparse voxel octree) only use it in visibility test and radiance storage, rather than render it directly. Previous research has tried to incorporate SVO in ray tracing, radiosity methods and voxel cone tracing, and all achieved real-time frame rates in complex scenes. However, most of them only focus on static scenes and does not consider dynamic updates of SVO and the influence of it on performance.</p> <p>In this thesis, we will discuss the tradeoff of multiple classic real-time global illumination methods and their implementations using SVO. We will also propose an efficient approach to dynamic update SVO in animated scenes. The deliverables will be implemented in CUDA 11.0 and OpenGL.</p>

The report describes the thesis project with the aim of fusing an arbitrary sequence of stereo measurements into a global 3D representation in real-time. The proposed method involves an octree-based signed distance function for representing the 3D environment, where the geomtric data is fused together using a cumulative weighted update function, and finally rendered by incremental mesh extraction using the marching cubes algorithm. The result of the project was a prototype system, integrated into a real-time stereo reconstruction system, which was evaluated by benchmark tests as well as qualitative comparisons with an older method of overlapping meshes. / <p>Examensarbetet är utfört vid Institutionen för teknik och naturvetenskap (ITN) vid Tekniska fakulteten, Linköpings universitet</p>

Modern semiconductor manufacturing requires photolithographic printing of subillumination wavelength features in photoresist via electromagnetic energy scattered by complicated photomask designs. This results in aerial images which are subject to constructive and destructive wave interference, as well as electromagnetic resonances in the photomask features. This thesis proposes a 3-D full-wave frequency domain nonconformal Octree mesh based Finite Element Method (OFEM) electromagnetic scattering solver in combination with Fourier Optics to accurately simulate the entire projection photolithography system, from illumination source to final image intensity in the photoresist layer. A rapid 1-irregular octree based geometry model mesher is developed and shown to perform remarkably well compared to a tetrahedral mesher. A special set of nonconformal 1st and 2nd order hierarchal OFEM basis functions is presented, and 1st order numerical results show good performance compared to tetrahedral FEM. Optical and modern photomask phenomenology is examined, including optical proximity correction (OPC) with thick PEC metal layer, and chromeless phase inversion (PI) masks.

Meshless methods have recently received much attention but are yet to reach their full potential as the required problem setup (i.e. collocation point distribution) is still significant and far from automated. The distribution of points still closely resembles the nodes of finite volume-type meshes and the free parameter, c, of the radial-basis expansion functions (RBF) still must be tailored specifically to a problem. The localized meshless collocation method investigated requires a local influence region, or topology, used as the expansion medium to produce the required field derivatives. Tests have shown a regular cartesian point distribution produces optimal results, however, in order to maintain a locally cartesian point distribution a recursive quadtree scheme is herein proposed. The quadtree method allows modeling of irregular geometries and refinement of regions of interest and it lends itself for full automation, thus, reducing problem setup efforts. Furthermore, the construction of the localized expansion regions is closely tied up to the point distribution process and, hence, incorporated into the automated sequence. This also allows for the optimization of the RBF free parameter on a local basis to achieve a desired level of accuracy in the expansion. In addition, an optimized auto-segmentation process is adopted to distribute and balance the problem loads throughout a parallel computational environment while minimizing communication requirements.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

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