QRB−tree Indexing: Optimized Spatial Index Expanding upon the QR−tree Index

Support for region queries is crucial in geographic information systems, which process exact queries through spatial indexing to filter features and subsequently refine the selection. Although the filtering step has been extensively studied, the refinement step has received little attention. This research builds upon the QR−tree index, which decomposes space into hierarchical grids, registers features to the grids, and builds an R−tree for each grid, to develop a new QRB−tree index with two levels of optimization. In the first level, a bucket is introduced in every grid in the QR−tree index to accelerate the loading and search steps of a query region for the grids within the query region. In the second level, the number of candidate features to be eliminated is reduced by limiting the features to those registered to the grids covering the corners of the query region. Subsequently, an approach for determining the maximal grid level, which significantly affects the performance of the QR−tree index, is proposed. Direct comparisons of time costs with the QR−tree index and geohash index show that the QRB−tree index outperforms the other two approaches for rough queries in large query regions and exact queries in all cases.

The Application of Spatial Approximations to Spatial Query Processing: A Systematic Review of Literature

Spatial approximations simplify the geometric shape of complex spatial objects. Hence, they have been employed to alleviate the evaluation of costly computational geometric algorithms when processing spatial queries. For instance, spatial index structures employ them to organize spatial objects in tree structures (e.g., the R-tree). We report experiments considering two real datasets composed of ∼1.5 million regions and ∼2.7 million lines. The experiments confirm the performance benefits of spatial approximations and spatial index structures. However, we also identify that a second processing step is needed to deliver the final answer and often requires higher processing time than the step that uses index structures only. It leads to the interest in studying how spatial approximations can be efficiently used to improve both steps. This paper presents a systematic review on this topic. As a result, we provide an overview and comparison of existing approaches that propose, evaluate, or make use of spatial approximations to optimize the performance of spatial queries. Further, we characterize them and discuss some future trends.

HiIndex: An Efficient Spatial Index for Rapid Visualization of Large-Scale Geographic Vector Data

In the big data era, rapid visualization of large-scale vector data has become a serious challenge in Geographic Information Science (GIS). To fill the gap, we propose HiIndex, a spatial index that enables real-time and interactive visualization of large-scale vector data. HiIndex improves the state of the art with its low memory requirements, fast construction speed, and high visualization efficiency. In HiIndex, we present a tile-quadtree structure (TQ-tree) which divides the global geographic range based on the quadtree recursion method, and each node in the TQ-tree represents a specific and regular spatial range. In this paper, we propose a quick TQ-tree generation algorithm and an efficient visualization algorithm. Experiments show that the HiIndex is simple in structure, fast in construction, and less in memory occupation, and our approach can support interactive and real-time visualization of billion scale vector data with negligible pre-treatment time.

An Accelerated Slicing Algorithm for Frep Models

Complex 3D objects with microstructures can be modelled using the function representation (FRep) approach and then manufactured. The task of modelling a geometric object with a sophisticated microstructure based on unit cell repetition is often too computationally expensive for CAD systems. FRep provides efficient tools to solve this problem. However, even for FRep the slicing step required for manufacturing can take a significant amount of time. An accelerated slicing algorithm for FRep 3D objects is proposed in this paper. This algorithm allows the preparation of FRep models for 3D printing without surface generation stage. The spatial index is employed to accelerate the slicing process. A novel compound adaptive criterion and a novel acceleration criterion are proposed to speed up the evaluation of the defining function of an FRep object. The use of these criteria is significantly reducing the computational time for contour construction during the slicing process. The k-d tree and R-tree data structures are used as spatial indexes. The performance of the accelerated slicing algorithm was tested. The contouring time was reduced 100-fold due to using the novel compound adaptive criterion with the novel acceleration criterion.