Tessellation data models

Topics

  • [DM-02-007] The Raster Data Model

    The raster data model is a widely used method of storing geographic data. The model most commonly takes the form of a grid-like structure that holds values at regularly spaced intervals over the extent of the raster. Rasters are especially well suited for storing continuous data such as temperature and elevation values, but can hold discrete and categorical data such as land use as well.  The resolution of a raster is given in linear units (e.g., meters) or angular units (e.g., one arc second) and defines the extent along one side of the grid cell. High (or fine) resolution rasters have comparatively closer spacing and more grid cells than low (or coarse) resolution rasters, and require relatively more memory to store. Active research in the domain is oriented toward improving compression schemes and implementation for alternative cell shapes (such as hexagons), and better supporting multi-resolution raster storage and analysis functions.

  • [DM-02-009] The Hexagonal Model

    Hexagons offer significant advantages in geospatial analysis due to their ability to model relationships efficiently while maintaining isotropy, minimizing edge effects, and improving computational efficiency. While circles are ideal for proximity-based modeling, they do not tessellate. Only three geometric shapes—rectangles, triangles, and hexagons—can fully cover a plane without gaps. Among these, hexagons provide superior data storage, visualization, and analysis benefits. However, hexagons have been underutilized due to historical inertia in geographical information systems (GIS), which favor grid-based Cartesian representations. Additionally, the absence of a standardized global hexagonal framework has hindered data comparison and integration. With increasing computational power and growing global-scale research needs, hexagons are gaining traction in geospatial analysis. Their inherent geometric strengths make them a compelling alternative for modeling spatial relationships, and their adoption is expected to rise significantly within the geospatial community.

  • [DM-02-010] Triangular Irregular Network (TIN) Models

    A Triangular Irregular Network (TIN) is a way of storing continuous surfaces. It is vector based, and works in such a way that it connects known data points with straight lines to create triangles, often called facets. These facets are planes that have the same slope and aspect over the facet. Collectively, these hypothetical lines form a network covering the whole surface. TINs are efficient when storing heterogeneous surfaces, since homogenous areas are stored using few data points, while areas with more variability are stored in detail using a larger number of data points. In other words, a TIN can be more detailed where the surface is complex (high variation) by using smaller facets, and less detailed where the surface is more homogeneous by using larger facets. TINs also have a high modelling potential, e.g. in topography and hydrology. However, the unique way of storing data an a TIN often makes it difficult to combine with other spatial data formats. Instead, the TIN data would usually be converted to other suitable formats.

  • [DM-02-011] Hierarchical Data Models

    As the geographic reality naturally follows hierarchical structures, the hierarchical data models have been widely adopted in multiple approaches of geospatial information science and systems. These approaches include (a) a rigorous conceptual representation of real-world features to explain the human perception of the geographic space; (b) a series of indexing mechanisms for both raster and vector datasets to either accelerate their algorithmic processing, such as their retrieval from big data repositories, or compress their volume and storage requirements; (c) the modelling and retrieval of geospatial content to implement efficient mapping services over the web; and (d) the development of advanced geospatial reference frameworks to effectively support a seamless integration of heterogeneous and multi-resolution geospatial data for the whole planet. This article provides an overview of how hierarchical data models can support these areas through a series of illustrated examples. Specifically, the article explains the principles of the Tomlin’s conceptual representation model, the index structures of quadtrees and R-trees, the tile maps and related conventions of online map providers, and the discrete global grid systems as a partitioning approach to divide the Earth’s surface into a group of uniform cells at various levels of resolutions.