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.
Geometric primitives are the representations used and computations performed in a GIS that concern the spatial aspects of the data, data objects described by coordinates. In vector geometry, we distinguish in zero-, one-, two-, and three-dimensional objects, better known as points, linear features, areal or planar features, and volumetric features. A GIS stores and performs computations on all of these. Often, planar features form a collective known as a (spatial) subdivision. Computations on geometric objects show up in data simplification, neighborhood analysis, spatial clustering, spatial interpolation, automated text placement, segmentation of trajectories, map matching, and many other tasks. They should be contrasted with computations on attributes or networks.
There are various kinds of vector data models for subdivisions. The classical ones are known as spaghetti and pizza models, but nowadays it is recognized that topological data models are the representation of choice. We overview these models briefly.
Computations range from simple to highly complex: deciding whether a point lies in a rectangle needs four comparisons, whereas performing map overlay on two subdivisions requires advanced knowledge of algorithm design. We introduce map overlay, Voronoi diagrams, and Delaunay triangulations and mention algorithmic approaches to compute them.
Triangulated Irregular Networks (TINs), comprised of vertices, edges, and triangles, are widely used data structures for modeling surface morphology. This article introduces digital terrain model and analysis based on TINs, including the concept of TINs, their compositional forms, the methodologies employed in their construction, and TIN-based terrain factor extractions and applications. The construction of TINs is influenced by various methodologies, leading to the creation of distinct TIN models. Presently, the TIN based on Delaunay triangulation (D-TIN) stands as the most widely adopted model. Built upon D-TIN, a series of terrain derivative calculation methodologies have been proposed, enabling the extraction of slope, aspect, flow direction, and facilitating terrain classification. These enhancements further contribute to the scientific characterization of the morphological features and processes of the Earth's surface topography. Moreover, vectorial calculation methods have been utilized to compute surface terrain derivatives based on TINs, effectively leveraging the attribute of TIN's data structure. Finally, the main application of TIN-based terrain factors has been summarized to provide a beneficial resource for researchers and practitioners in the field.