Hierarchical grid conversion

Mahdavi-Amiri, Ali; Harrison, Erika; Samavati, Faramarz

doi:10.1016/j.cad.2016.04.005

Cited by 20 publications

(12 citation statements)

References 28 publications

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“…The level-of-detail (LOD) techniques, the basics, historical overview, and some new perspectives were described by Danovaro et al [17]. The method of creating muliresolution grid structures (called hierarchical grids) is proposed by Mahdavi-Amiri et al [18] and Weiss and De Floriani [19]. Mahdavi-Amiri et al [20] described the use of these structures for representations of 3D objects (computer graphics).…”

Section: Existing Methodsmentioning

confidence: 99%

A Multiresolution Grid Structure Applied to Seafloor Shape Modeling

Maleika

Koziarski

Forczmański

2018

IJGI

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This paper proposes a method of creating a multiresolution depth grid containing bathymetric data describing a stretch of sea floor. The included literature review presents current solutions in the area of the creation of digital terrain models (DTMs) focusing on methods employing regular grids, with a discussion on the strong and weak points of such an approach. As a basis for the investigations, some important recommendations from the International Hydrographic Organization are provided and are related to the accuracy of created models. The authors propose a novel method of storing DTM data, involving multiresolution depth grids. The paper presents the characteristics of this method, numerical algorithms of a conversion between a regular grid and the multiresolution one, and experiments on typical seafloor surfaces. The results are discussed, focusing on the data reduction rate and the variable resolution of the grid structure. The proposed method can be applied in Geographical Information Systems, especially for the purposes of solving sea survey problems.

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Section: Existing Methodsmentioning

confidence: 99%

A Multiresolution Grid Structure Applied to Seafloor Shape Modeling

Maleika

Koziarski

Forczmański

2018

IJGI

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“…The fractal patterns usually have very complex shapes, and thus, they are not appropriate for point clustering. There are three reasonable variants of multi-resolution hexagonal grids often used in the Discrete Global Grid Systems [21][22][23]41,54]. Generally, the grids of aperture 3 and 4 are preferred (see Figure 6) to avoid the problems with fractal shapes.…”

Section: Hexagonal Curve Selectionmentioning

confidence: 99%

“…Beside traditional PCs produced mostly by 3D scanners [9], a set of points can also represent general spatial information [10] such as location, GPS coordinates on the map [11], swarm particles [12], nodes of graph generated by visualization algorithms [13], etc. We focus on 2D point clouds as they are highly investigated in the areas such as data mining [2,3,10], computer graphics [14,15], image analysis [16][17][18], geographic information systems (GISs) [19][20][21][22][23], sensor networks [24,25], triangulation [26][27][28][29] and data visualization [12]. In the mentioned application fields, the point indexing/clustering algorithms are crucial, e.g., for efficient organization of data in the memory, analyzing their properties, visualization of clusters, computation of forces in particle systems and searching near neighbors.…”

Section: Introductionmentioning

confidence: 99%

“…Those methods serve to decompose and represent images with pixels having positive coordinates, but they do not offer any general method for real points indexing and querying. Several papers discussed the problems of different grid systems and their mutual conversion to combine their best properties [21][22][23], but they all miss the correct hierarchical 1-to-7 refinement in the hexagonal grid ( Figure 2) for a correct hexagonal SFC. During the last years, the hexagons have gained increased interest in scientific areas including geographic information systems [19][20][21][22][23]40,41], data clustering and querying [36,38,39,42,43], data visualization [44,45], computer graphics [46] and computer or sensor networks [24,25].…”

Section: Introductionmentioning

confidence: 99%

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Hierarchical Hexagonal Clustering and Indexing

et al. 2019

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Space-filling curves (SFCs) represent an efficient and straightforward method for sparse-space indexing to transform an n-dimensional space into a one-dimensional representation. This is often applied for multidimensional point indexing which brings a better perspective for data analysis, visualization and queries. SFCs are involved in many areas such as big data analysis and visualization, image decomposition, computer graphics and geographic information systems (GISs). The indexing methods subdivide the space into logic clusters of close points and they differ in various parameters including the cluster order, the distance metrics, and the pattern shape. Beside the simple and highly preferred triangular and square uniform grids, the hexagonal uniform grids have gained high interest especially in areas such as GISs, image processing and data visualization for the uniform distance between cells and high effectiveness of circle coverage. While the linearization of hexagons is an obvious approach for memory representation, it seems there is no hexagonal SFC indexing method generally used in practice. The main limitation of hexagons lies in lacking infinite decomposition into sub-hexagons and similarity of tiles on different levels of hierarchy. Our research aims at defining a fast and robust hexagonal SFC method. The Gosper fractal is utilized to preserve the benefits of hexagonal grids and to efficiently and hierarchically linearize points in a hexagonal grid while solving the non-convex shape and recursive transformation issues of the fractal. A comparison to other SFCs and grids is conducted to verify the robustness and effectiveness of our hexagonal method.

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“…No unified subdivision grid for information exchange and comprehensive application has been developed. A few efforts have been made recently on the hierarchical grid conversion along with the indexing methods [9,14]; however, the subdivision methods do not adapt to the existing geographical data in all types of applications, and the indexing efficiency needs further enhancement. Therefore, a globally consistent spatial information subdivision grid model that is compatible with most of the existing subdivision grid systems is needed.…”

Section: Introductionmentioning

confidence: 99%

A Subdivision Method to Unify the Existing Latitude and Longitude Grids

Cheng

Tong

Chen

et al. 2016

IJGI

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Abstract:As research on large regions of earth progresses, many geographical subdivision grids have been established for various spatial applications by different industries and disciplines. However, there is no clear relationship between the different grids and no consistent spatial reference grid that allows for information exchange and comprehensive application. Sharing and exchange of data across departments and applications are still at a bottleneck. It would represent a significant step forward to build a new grid model that is inclusive of or compatible with most of the existing geodesic grids and that could support consolidation and exchange within existing data services. This study designs a new geographical coordinate global subdividing grid with one dimension integer coding on a 2 n tree (GeoSOT) that has 2 n coordinate subdivision characteristics (global longitude and latitude subdivision) and can form integer hierarchies at degree, minute, and second levels. This grid has the multi-dimensional quadtree hierarchical characteristics of a digital earth grid, but also provides good consistency with applied grids, such as those used in mapping, meteorology, oceanography and national geographical, and three-dimensional digital earth grids. No other existing grid codes possess these characteristics.

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Hierarchical grid conversion

Cited by 20 publications

References 28 publications

A Multiresolution Grid Structure Applied to Seafloor Shape Modeling

A Multiresolution Grid Structure Applied to Seafloor Shape Modeling

Hierarchical Hexagonal Clustering and Indexing

A Subdivision Method to Unify the Existing Latitude and Longitude Grids

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