Triangles and triangulations

Abstract

Triangulations are widely used as a basis for representing geometries and other information appearing in a huge variety of applications. In geographical information systems (GIS), triangulations are used to represent terrain surfaces and relations between geographical objects. Systems for modeling geological structures in the oil and gas industry use triangulations for representing surfaces that separate different geological structures, and for representing properties of these structures. Computer aided design (CAD) systems with triangulation features are common in the manufacturing industry and in particular within the automotive industry, which has been a driving force for this research for many decades. We also find applications using triangulations within engineering fields that simulate physical phenomena using finite element methods (FEM). Finally, we will mention the importance of triangulation in visualization and computer graphics.