In triangulation, the data points are divided into triangles.  There is a mathematically best way to do make the triangles, which make them as close to equilateral as possible, and avoids long, skinny triangles.  Because of its applicability in many fields, this can be referred to as Delaunay triangulation, Voronoi diagram, Dirichlet tessellationor Thiessen polygons.  The end product can be the triangles, or the areas around each point that are closest to the point.

For interpolation, a triangle defines a plane and provides a unique way to interpolate (in contrast, interpolation within a rectangle can be ambiguous) values or to Reproject an image.

Computer graphics uses triangles, and the speed is the number of triangles that can be drawn per second.  Shading is computed by finding the normal to the triangle, and comparing that vector with the illumination direction.

Triangulation can produce a TIN, an alternative to a grid or DEM, or the triangulation can be used to populate a grid created from randomly spaced points such as a lidar point cloud.

Last revision 3/7/2016