What is a TIN (Triangulated Irregular Network)?

A TIN is a continuous surface made of non-overlapping triangles. Each triangle vertex is a real measured point with its own X, Y and Z, and every point inside a triangle is interpolated across that triangle's plane.

The word irregular is the important one. A raster DEM samples elevation on a fixed grid whether or not the ground has anything to say at that spot. A TIN puts vertices where the measurements are — dense where the ground is complex, sparse where it is flat.

The usual construction is Delaunay triangulation, which connects the points so that no point falls inside the circumcircle of any triangle. In practice that rule avoids long thin slivers and produces triangles as close to equilateral as the point distribution allows — which matters because a sliver triangle interpolates badly.

Constrained triangulation goes one step further: you supply breaklines — a crest, a toe, a road edge, a ditch — and the triangulation is forced to place triangle edges along them. Without that constraint the triangulation may span a triangle straight across a crest, rounding off exactly the feature you surveyed carefully.

Fidelity to features. A TIN can hold a vertical-sided detail because two vertices can share an X,Y with different Z along a breakline. A raster cell has one elevation, so a sharp edge is always smeared across at least one cell.

Storage efficiency. Over a flat area a raster keeps storing cells at full density; a TIN can cover the same flat area with a handful of large triangles. Over complex ground the situation reverses: a TIN needs many small triangles and the vertex list grows quickly.

Computation. Raster grids are simple to compute on — slope, hydrology and map algebra are all cell operations. TIN computation is geometric, which is why analysis workflows usually rasterize a TIN first, and why design surfaces are usually kept as TINs.

Neither is more accurate in the abstract. Accuracy comes from the survey; the representation decides how much of that survey survives.

Design surfaces — a graded platform, a road corridor, a bench template — are naturally TINs. They are defined by edges and breaklines, and the vertices are exactly the design points.

Existing ground from drone photogrammetry or LiDAR is usually delivered as a raster DEM, because the source is a dense point cloud and a regular grid is the compact way to hold it.

Volume between a design and existing ground is where the two meet. Whether the comparison is done TIN-to-TIN, TIN-to-grid or grid-to-grid changes the result slightly, and the honest way to report a volume is to state which surfaces were compared and how.

The most common TIN problem is triangulation across a feature that should have been a breakline. It is easy to miss because the surface still looks smooth and plausible — the crest is simply a little lower and a little rounder than it is on the ground.

The second is extrapolation past the data. A Delaunay triangulation fills the convex hull of the points, which can produce triangles spanning areas nobody surveyed. Those triangles carry a surface, and a volume computed over them is fiction. Clipping the TIN to the surveyed boundary is not optional.