The study of triangulations and their properties has immediate consequences in applied fields. Triangulations are used to model surfaces and produce three-dimensional computer graphics.
Some algorithms used to solve differential equations use finite element methods.
In computational geometry, many algorithms rely upon certain triangulations of a set of points. For example, triangulations are used in point location problems. Suppose we wish to partition a region into school districts. We subdivide the region into districts so that each district contains all residences closest to a certain school. Such a subdivision is called a Voronoi diagram and is associated with a Delaunay triangulation.