The items unique to the Scatter module are listed below. The menu items operate on the active scatter set unless otherwise noted:

## Triangulate

Scatter points or mesh nodes can be triangulated to form piecewise linear surfaces. For scattered data, these surfaces are also referred to as TINs (Triangular Irregular Networks). For mesh nodes, they form a finite element mesh. The points/nodes are connected into surfaces as scatter sets or meshes are created, but at times it may be necessary to reconnect the points (i.e. after deleting individual points/nodes or triangles/elements). New triangles are constructed in mass by triangulating a set of points when the Triangulate command from the Triangles menu is executed. The selected points are connected with a series of triangles. If points are not selected, then all points will be triangulated.

### Delaunay Criterion

The resulting triangulation satisfies the Delaunay criterion. The Delaunay criterion ensures that no vertex lies within the interior of any of the circumcircles of the triangles in the network as shown below:

Two Adjacent Triangles Which (a) Violate and (b) Honor the Delaunay Criterion

The result of enforcing the Delaunay criterion is that long thin triangles are avoided as much as possible.

## Optimize Triangulation

The Delaunay triangulation connects the points in the scatter set (TIN) to form triangles as close to equilateral triangles as possible. This does not mean that the resulting triangulation is the truest representation of the surface the scatter points were taken from. For example, two points on opposite banks of a channel could be close enough together to be connected by the Delaunay criterion, but connecting them creates a barrier in the surface which obstructs flow in the channel. Recognizing that the Delaunay triangulation may not be the most appropriate, SMS allows supports alternate triangulation methods as well as manual mesh editing which result in triangulations that are not Delaunay. Refer to the article on the *Swap Edges Tool and the breakline workflow for information on manual edits to the surface. An alternate triangulation method can be selected in the Scatter Options command.

## Select Thin Triangles

During the process of triangulation, a mesh of triangular elements is created around existing nodes. This usually creates triangular elements outside the desired scatter set boundary. Many of these exterior triangles are very skinny, and some are virtually invisible. The Select Thin Triangles command finds and selects skinny triangular elements which are on the scatter set boundary.

Thin triangles interior to the scatter set will not be selected when this command is performed, since deletion of interior triangles would result in gaps in the mesh. After the thin triangles have been selected, they can be removed by selecting the Delete macro.

## Select/Delete Long Triangles

This option in the Scatter Module, Triangles Menu finds triangles longer than the length specified in the Scatter Options dialog. The Scatter Options also allows selecting the option to delete or select the long triangles. Selecting/deleting long triangles is useful for deleting triangles that span regions where interpolation is not desired, such as over regions of land (see figure below, the selected triangles are over land).

## Process Boundary Triangles

When scatter points are triangulated, the resulting convex hull often contains triangles outside the desired mesh boundary. The Process Boundary Triangles dialog was developed to help remove invalid boundary triangles. To open the Process Boundary Triangles dialog:

OR