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 Scatter Data 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 Delauney criterion. The Delauney 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 Delauney Criterion.

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

Triangulate

The vertices associated with the active scatter set can be triangulated
using the Triangulate command
from the Triangles menu in the
Scatter Data module. To mesh nodes
(either the selected nodes, or all nodes) can be triangulated using the
Triangulate command from the Elements menu in the 2D
Mesh module.