Real-Time Path Guiding Using Bounding Voxel Sampling

Geographic information systems (GISs) are widely used for representation, management, and analysis of spatial data in many disciplines. In particular, geoscientists increasingly use these tools for data integration and management purposes in many environmental applications, ranging from water resources management to the study of global warming. Beyond these capabilities, geoscientists need to model and simulate three-dimensional (3D) dynamic fields and readily integrate those results with other relevant spatial information in order to have a better understanding of the environmental problems. However, GISs are very limited for the modeling and simulation of spatial fields, which are mostly 3D and dynamic. These limitations are mainly related to the existing GIS spatial data structures that are static and limited to 2D space. In order to overcome these limitations, we develop and implement a new kinetic 3D spatial data structure based on Delaunay tetrahedralization and a 3D Voronoi diagram to support a 3D dynamic field simulation within GISs. In this article, we describe in detail the different steps from discretization of a 3D continuous field to its numerical integration, based on an event-driven method. For validation of the proposed spatial data structure itself and its potential for the simulation of a dynamic field, two case studies are presented in the article. According to our observations, during the simulation process, the data structure is maintained and the 3D spatial information is managed adequately. Furthermore, the results obtained from both experiments are very satisfactory and are comparable with the results obtained from other existing methods for the simulation of the same dynamic field. To conclude, we discuss the current challenges related to the development of the 3D kinetic data structure itself and its adaptation to 3D dynamic field simulation and suggest some solutions for its improvement.

Spatial data structures form a core ingredient of many geometric algorithms, both in theory and in practice. Many of these data structures, especially the ones used in practice, are based on partitioning the underlying space (examples are binary space partitions and decompositions of polygons) or partitioning the set of objects (examples are bounding-volume hierarchies). The efficiency of such data structures---and, hence, of the algorithms that use them---depends on certain characteristics of the partitioning. For example the performance of many algorithms that use binary space partitions (BSPs) depends on the size of the BSPs. Similarly, the performance of answering range queries using bounding-volume hierarchies (BVHs) depends on the so-called crossing number that can be associated with the partitioning on which the BVH is based. Much research has been done on the problem of computing partitioning whose characteristics are good in the worst case. In this thesis, we studied the problem from a different point of view, namely instance-optimality. In particular, we considered the following question: given a class of geometric partitioning structures---like BSPs, simplicial partitions, polygon triangulations, …---and a cost function---like size or crossing number---can we design an algorithm that computes a structure whose cost is optimal or close to optimal for any input instance (rather than only worst-case optimal). We studied the problem of finding optimal data structures for some of the most important spatial data structures. As an example having a set of n points and an input parameter r, It has been proved that there are input sets for which any simplicial partitions has crossing number ¿(vr). It has also been shown that for any set of n input points and the parameter r one can make a simplicial partition with stabbing number O(vr). However, there are input point sets for which one can make simplicial partition with lower stabbing number. As an example when the points are on a diagonal, one can always make a simplicial partition with stabbing number 1. We started our research by studying BSPs for line segments in the plane, where the cost function is the size of the BSPs. A popular type of BSPs for line segments are the so-called auto-partitions. We proved that finding an optimal auto-partition is NP-hard. In fact, finding out if a set of input segments admits an auto-partition without any cuts is already NP-hard. We also studied the relation between two other types of BSPs, called free and restricted BSPs, and showed that the number of cuts of an optimal restricted BSP for a set of segments in R2 is at most twice the number of cuts of an optimal free BSP for that set. The details are being represented in Chapter 1 of the thesis. Then we turned our attention to so-called rectilinear r-partitions for planar point sets, with the crossing number as cost function. A rectilinear r-partition of a point set P is a partitioning of P into r subsets, each having roughly |P|/r points. The crossing number of the partition is defined using the bounding boxes of the subsets; in particular, it is the maximum number of bounding boxes that can be intersected by any horizontal or vertical line. We performed some theoretical as well as experimental studies on rectilinear r-partitions. On the theoretical side, we proved that computing a rectilinear r-partition with optimal stabbing number for a given set of points and parameter r is NP-hard. We also proposed an exact algorithm for finding optimal rectilinear r-partitions whose running time is polynomial when r is a constant, and a faster 2-approximation algorithm. Our last theoretical result showed that considering only partitions whose bounding boxes are disjoint is not sufficient for finding optimal rectilinear r-partitions. On the experimental side, we performed a comparison between four different heuristics for constructing rectilinear r-partitions. The so-called windmill KD-tree gave the best results. Chapter 2 of the thesis describes all the details of our research on rectilinear r-partitions. We studied another spatial data structure in Chapter 3 of the thesis. Decomposition of the interior of polygons is one of the fundamental problems in computational geometry. In case of a simple polygon one usually wants to make a Steiner triangulation of it, and when we have a rectilinear polygon at hand, one typically wants to make a rectilinear decomposition for it. Due to this reason there are algorithms which make Steiner triangulations and rectangular decompositions with low stabbing number. These algorithms are worst-case optimal. However, similar to the two previous data structures, there are polygons for which one can make decompositions with lower stabbing numbers. In 3 we proposed a 3-approximation for finding an optimal rectangular decomposition of a rectilinear polygon. We also proposed an O(1)-approximation for finding optimal Steiner triangulation of a simple polygon. Finally, in Chapter 4 of the thesis, we considered another optimization problem, namely how to approximate a piecewise-linear function F: R ¿R with another piecewise-linear function with fewer pieces. Here one can distinguish two versions of the problem. The first one is called the min-k problem; the goal is then to approximate the function within a given error e such that the resulting function has the minimum number of links. The second one is called the min-e problem; here the goal is to find an approximation with at most k links (for a given k) such that the error is minimized. These problems have already been studied before. Our contribution is to consider the problem for so-called uncertain functions, where the value of the input function F at its vertices is given as a discrete set of different values, each with an associated probability. We show how to compute an approximation that minimizes the expected error.

Spatial data structures, once considered mere variations of structures designed for conventional (non-spatial) data, increasingly evolve along a different track. The reason for this lies in the rich structure of Euclidean space. Even without the presence of objects, regions of space admit a multitude of operations and relations that are relevant for efficient query processing, such as: distance, containment, intersection, touching, in front of. This fact suggests that the main task of a spatial data structure is to organize the embedding space in a systematic manner, rather than the content, i.e. the transient set of objects present at any moment. This is particularly true when objects move or are subject to other transformations, as is the case in applications such as computer-aided design (CAD). A second difference between spatial and non-spatial data lies in the query population. Rather than retrieving objects based on their inherent characteristics, the majority of spatial queries are based on proximity of the objects to be retrieved to query regions of the most varied shape (rays, boxes, arbitrary polyhedra). This implies that retrieval begins with a coarse filter that retrieves a cluster of neighboring objects, followed by a fine filter that analyzes their geometric properties. Thus, proximity in space should be reflected in contiguous storage to the extent possible. This survey is concerned with spatial data structures suitable for external storage devices. This implies a conceptual and technical simplicity that excludes a few sophisticated list structures designed for central memory. We explain concepts, and their intuitive justification, in the context of their historical development. We emphasize common sense principles more than detailed techniques; and we illustrate basic ideas by presenting a sample of spatial data structures selected by virtue of their conceptual simplicity. Thus, we hope to provide a user’s guide to an applications programmer confronted with a bewildering multitude of structures described in the research literature, many of which differ only in detail: “If you ask the right questions, common sense will provide answers”.

We present a reactive data structure, that is, a spatial data structure with detail levels. The two properties, spatial organization and detail levels, are the basis for a geographic information system (GIS) with a multi-scale database. A reactive data structure is a novel type of data structure catering to multiple detail levels with rapid responses to spatial queries. It is presented here as a modification of the binary space partitioning tree that includes the levels of detail. This tree is one of the few spatial data structures that does not organize space in a rectangular manner. A prototype system has been implemented. An important result of this implementation is that it shows that binary space partitioning trees of real maps have O(n) storage space complexity in contrast to the theoretical worst case O(n2 ), with n the number of line segments in the map.

A data structure is history independent if its internal representation reveals nothing about the history of operations beyond what can be determined from the current contents of the data structure. History independence is typically viewed as a security or privacy guarantee, with the intent being to minimize risks incurred by a security breach or audit. Despite widespread advances in history independence, there is an important data-structural primitive that previous work has been unable to replace with an equivalent history-independent alternative---dynamic partitioning. In dynamic partitioning, we are given a dynamic set S of ordered elements and a size-parameter B, and the objective is to maintain a partition of S into ordered groups, each of size Θ(B). Dynamic partitioning is important throughout computer science, with applications to B-tree rebalancing, write-optimized dictionaries, log-structured merge trees, other external-memory indexes, geometric and spatial data structures, cache-oblivious data structures, and order-maintenance data structures. The lack of a history-independent dynamic-partitioning primitive has meant that designers of history-independent data structures have had to resort to complex alternatives. In this paper, we achieve history-independent dynamic partitioning. Our algorithm runs asymptotically optimally against an oblivious adversary, processing each insert/delete with O(1) operations in expectation and O(B log N/loglog N) with high probability in set size N.

A data structure is history independent if its internal representation reveals nothing about the history of operations beyond what can be determined from the current contents of the data structure. History independence is typically viewed as a security or privacy guarantee, with the intent being to minimize risks incurred by a security breach or audit. Despite widespread advances in history independence, there is an important data-structural primitive that previous work has been unable to replace with an equivalent history-independent alternative—dynamic partitioning. In dynamic partitioning, we are given a dynamic set S of ordered elements and a size-parameter B, and the objective is to maintain a partition of S into ordered groups, each of size θ(B). Dynamic partitioning is important throughout computer science, with applications to B-tree rebalancing, write-optimized dictionaries, log-structured merge trees, other external-memory indexes, geometric and spatial data structures, cache-oblivious data structures, and order-maintenance data structures. The lack of a historyindependent dynamic-partitioning primitive has meant that designers of history-independent data structures have had to resort to complex alternatives. In this paper, we achieve history-independent dynamic partitioning. Our algorithm runs asymptotically optimally against an oblivious adversary, processing each insert/delete with O(1) operations in expectation and O(B logN/ loglogN) with high probability in set size N.

The visualization of massive 3D models is an intensively examined field of research. Due to their rapidly growing complexity of such models, visualisation them in real-time will never be possible through a higher speed of rasterization alone. Instead, a practical solution has to reduce the amount of data to be processed, using a fast visibility determination.In recent years, the combination of Javascript and WebGL raised attention for the possibility of rendering hardware-accelerated 3D graphics directly in the browser. However, when compared to desktop applications, they are still fighting with their disadvantages of a generally slower execution speed, or a downgraded set of functionality.We demonstrate the integration of spatial data structures, computed on the client side, using latest technology trends to mitigate the shortcomings of the 3D Web environment. We employ comparably small bounding volume hierarchies to accelerate our visibility determination, as well as to enable specific culling techniques. This allows for an interactive visualization of such massive 3D data sets. Our in-depth analysis of different data structures and environments shows which combination of data structure and visibility determination techniques are currently the best fit for the Web.

Neighborhood grid: A novel data structure for fluids animation with GPU computing

Terrain is a dynamic component of the landscape, subject to rapid changes, particularly in scenarios such as landslides. This study investigates how the spatial resolution and data structure of digital terrain models (DTMs) influence the estimation of landslide volume changes. We selected a landslide formed by the undercutting action of the Belá River in Slovakia as our research site. Our findings indicate that raster data structures, across various spatial resolutions, generally yield more consistent volume estimates compared to 3D mesh data structures. Nonetheless, at higher spatial resolutions (0.1 m and 0.25 m), the 3D mesh data structure demonstrates superior capability in capturing detailed terrain features, resulting in more precise volume estimations of the landslide.

In order to deal with the problem of massive historical multi-station SCADA data storage in distribution management system, this paper proposes a data compression method for power distribution system based on tensor Tucker decomposition. Firstly, to maintain the high-dimensional spatial structure of multi-station SCADA data of distribution management system in the presentation stage, we establish a third-order tensor representation model of multi-station SCADA data. Then, a historical SCADA data compression method for distribution management system based on tensor tucker decomposition is proposed. This method can compress the data while maintaining the spatial intrinsic structure of multi-station SCADA data. Finally, the effectiveness of the method is verified using real data. And, the results of comparison with singular value decomposition method and principal component analysis method show that the proposed method is superior to the traditional method.

Generative Adversarial Networks (GANs) triggered an increased interest in problem of image generation due to their improved output image quality and versatility for expansion towards new methods. Numerous GAN-based works attempt to improve generation by architectural and loss-based extensions. We argue that one of the crucial points to improve the GAN performance in terms of realism and similarity to the original data distribution is to be able to provide the model with a capability to learn the spatial structure in data. To that end, we propose the DeshuffleGAN to enhance the learning of the discriminator and the generator, via a self-supervision approach. Specifically, we introduce a deshuffling task that solves a puzzle of randomly shuffled image tiles, which in turn helps the DeshuffleGAN learn to increase its expressive capacity for spatial structure and realistic appearance. We provide experimental evidence for the performance improvement in generated images, compared to the baseline methods, which is consistently observed over two different datasets.

In this paper, we motivate four different user defined window query classes and derive a probabilistic model for each of them. For each model, we characterize the efficiency of spatial data structures in terms of the expected number of data bucket accesses needed to perform a window query. Our analytical approach exhibits the performance phenomena independent of data structure and implementation details and whether the objects are points or non-point objects.

In order to establish the city three-dimensional Geographic Information System, combine with the current emerging technologies of three-dimensional Geographic Information System, to explore a new method to open out 3D GIS by integrating Google SketchUp and ArcGIS. The results show that: Google SketchUp combine with ArcGIS can set up the 3D city model quickly, however, the 3D spatial query and analysis functions of GIS is difficult to achieve, can only choose C#.NET as the development platform and ArcGIS Engine as software development kit, to realize some functions such as three-dimensional roaming, integrated query, buffer analysis, underground pipeline explosion analysis, etc.; The results may have some reference value in the three-dimensional spatial data model and data structure, three-dimensional spatial data management and spatial data analysis and visualization of expression.

Geographic space is typically conceptualized either as discrete objects or as continuous fields. Considerable efforts have been carried out for the representation and management of the spatial data, based on the object view of the space. However field-based data models are less developed in GIS especially when it comes to the modeling and representation of dynamic fields. Dynamic phenomena such as urban dynamics, air pollution, fire propagation, etc. are examples of dynamic fields with important spatial and temporal components. These phenomena should be represented in GIS in order to help users and decision makers in different disciplines to better understand and predict their dynamic behaviour. The limitations of GIS for modeling and simulation of those phenomena are mostly related to the 2D and static nature of their spatial data structures. In this paper, we explore the potentials of the Voronoi diagram as an alternative spatial data model that allows realistic representation of the spatial dynamic fields in 2D and 3D spaces. The paper presents how different types of Voronoi diagrams for points in two and three dimensional spaces as well as Voronoi diagrams for line segments and polygons could be effectively used in different contexts to represent and simulate different dynamic spatial fields and processes.

The combination of cognitive and geometric approaches to space provides an integrated framework for a broad range of topics in spatial information theory. This framework, called geocognostics, organises space-time events into two basic representational structures, called views and trajectories. These structures are defined first in cognitive terms, but may be re-interpreted geometrically (in space-time) and hence serve as a common framework for both formal geometric representations of spatial information and formal representations of cognitive processes. Within this framework, views are collections of perceptual experiences recorded by an agent (and may be re-interpreted as collections of discrete space-time events), while trajectories are sequences of perceptual experiences of similar type (and may be re-interpreted as the space-time locus of persistent point entities). By combining these two low level representations into a series of hybrid representational structures, it is possible to deduce a great variety of conditions concerning perceptual experiences and, by extension, spatial data. To date, the new framework appears to have bearing on the theory of spatial and spatio-temporal data structures, the theory of interpolation, error, and spatial statistics, the processes of planning and way-finding, the design of computer interfaces for geometrical/geographical data and the larger question of human-computer interaction, the development of cognitively-based applications such as natural language interfaces, and many other sectors. In this paper, we describe the broad outlines of this framework and elaborate on some of the consequences of adopting the framework.KeywordsMental ModelPerceptual ExperienceHybrid RepresentationRoute DescriptionRepresentational StructureThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.