Available with 3D Analyst license.

A triangular irregular network (TIN) layer is commonly an elevation surface that represents height values across an extent. TIN layers are available in both map and scene views in ArcGIS Pro.

## What is a TIN?

TINs are a digital means to represent surface morphology. TINs are a form of vector-based digital geographic data constructed by triangulating a set of vertices (points). The vertices are connected with a series of edges to form a network of triangles. The edges of TINs form contiguous, nonoverlapping triangular facets and can be used to capture the position of linear features that play an important role in a surface, such as a ridge line or stream course. Because nodes can be placed irregularly over a surface, TINs can have a higher resolution in areas where a surface is highly variable and a lower resolution in areas that are less variable.

The input features used to create a TIN remain in the same position as the nodes or edges in the TIN. This allows a TIN to preserve all the precision of the input data while simultaneously modeling the values between known points. You can include precisely located features on a surface—such as mountain peaks, roads, and streams—by using them as input features to the TIN nodes.

There are different methods of interpolation to form these triangles, such as Delaunay triangulation or distance ordering. ArcGIS supports the Delaunay triangulation method. The resulting triangulation satisfies the Delaunay triangle criterion, which ensures that no vertex lies within the interior of any of the circumcircles of the triangles in the network. If the Delaunay criterion is satisfied everywhere on the TIN, the minimum interior angle of all triangles is maximized. The result is that long, thin triangles are avoided as much as possible.

A TIN expects units to be in feet or meters, not decimal degrees. Delaunay triangulations are not valid when constructed using angular coordinates from geographic coordinate systems.

TIN models are less widely available than raster surface models and tend to be more expensive to build and process. The cost of obtaining good source data can be high, and processing TINs tends to be less efficient than processing raster data because of the complex data structure.

The maximum allowable size of a TIN varies relative to free, contiguous memory resources. Ten to fifteen million nodes represents the largest size achievable under normal operating conditions with Win32. Regardless, it's strongly recommended to cap the size at a few million for the sake of usability and performance.

## Constrained Delaunay triangulation

A constrained Delaunay triangulation method follows Delaunay rules everywhere except along breaklines.

Using traditional Delaunay triangulation, breaklines are densified by the software with Steiner points to ensure that the resulting TIN remains conforming Delaunay. Steiner points are additional vertices added to the TIN. Therefore, one input breakline segment can result in multiple triangle edges. Using a constrained Delaunay triangulation, no densification occurs, and each breakline segment is added as a single edge.

Setting the constrained property on a TIN does not alter the existing state of the triangulation. It only controls what happens from that point forward. Therefore, if breaklines are added before setting the constrained triangulation property, those features remain unchanged. Any densification points added to enforce those breaklines are not removed.

Once the constrained property has been set on a TIN, there is no way to unset it. Constrained TINs can't be converted into or saved as conforming Delaunay TINs.

### Delaunay or constrained Delaunay?

Conforming Delaunay triangulations are recommended over constrained triangulations. This is because the resulting TINs are likely to contain fewer long, skinny triangles, which are undesirable for surface analysis. Additionally, natural neighbor interpolation and Thiessen (Voronoi) polygon generation can only be performed on conforming Delaunay triangulations.

A constrained Delaunay triangulation can be considered when you need to explicitly define certain edges that are guaranteed not to be modified (that is, split into multiple edges) by the triangulator.

Constrained Delaunay triangulations are also useful for minimizing the size of a TIN, since they have fewer nodes and triangles where breaklines are not densified.