are often used as the mesh (in this case, a triangle mesh) underlying a computation. In this case, the triangles must form a subdivision of the domain to be simulated, but instead of restricting the vertices to input points, it is allowed to add additional Steiner points as vertices. In order to be suitable as finite element meshes, a triangulation must have well-shaped triangles, according to criteria that depend on the details of the finite element simulation (see mesh quality); for instance, some methods require that all triangles be right or acute, forming nonobtuse meshes. Many meshing techniques are known, including Delaunay refinement algorithms such as Chew's second algorithm and Ruppert's algorithm. In more general topological spaces, triangulations of a space generally refer to simplicial complexes that are homeomorphic to the space. Generalization The concept of a triangulation may also be generalized somewhat to subdivisions into shapes related to triangles. In particular, a pseudotriangulation of a point set is a partition of the convex hull of the points into pseudotriangles -- polygons that, like triangles, have exactly three convex vertices. As in point set triangulations, pseudotriangulations are required to have their vertices at the given input points. External links