Triangulated Irregular Network (TIN)

A Triangulated Irregular Network (TIN) is a digital surface representation built from a set of irregularly distributed elevation points connected by Delaunay triangulationDelaunay TriangulationDelaunay triangulation connects a set of points into a network of non-overlapping triangles such that no point lies i... into a continuous mesh of non-overlapping triangles. Each triangle facet has a defined slope, aspect, and area, and the surface within each triangle is typically modeled as a planar patch interpolated from its three vertices.

TIN construction begins with a set of mass points (elevation samples), breaklines (linear features like ridges and stream channels that represent abrupt changes in slope), and optional exclusion or replacement areas (such as water bodies). The Delaunay triangulationDelaunay TriangulationDelaunay triangulation connects a set of points into a network of non-overlapping triangles such that no point lies i... algorithm connects these input features into a topologically consistent triangular mesh. Breaklines are enforced as triangle edges to preserve important terrain features. The resulting surface is a piecewise linear approximation of the true terrain that adapts its level of detail to the complexity of the landscape.

TINs are widely used in civil engineering for cut-and-fill volume calculations, road and dam design, and site grading. Hydrologists use TINs to model drainage patterns, delineate watersheds, and simulate overland flow. Urban planners create TINs from LiDARLiDARLight Detection and Ranging (LiDAR) is a remote sensing technology that measures distances using laser pulses to crea... data to generate accurate building footprintBuilding FootprintA Building Footprint is the outline of a building as seen from directly above, representing the area of ground it occ... elevations and viewshed models. Geologists use TINs to model subsurface geological layers for mining and resource exploration.

TINs are more storage-efficient than raster DEMs for representing terrain with variable complexity, because they use fewer triangles in flat areas and more in complex terrain. They preserve exact input elevations at sample points and enforce linear features along breaklines. However, TINs are computationally more expensive to query than raster grids, and many spatial analysis operations (such as flow directionFlow DirectionFlow direction analysis determines the downhill direction of water flow from each cell in a digital elevation model, ... and kernel density) are designed for raster surfaces, requiring TIN-to-raster conversion.