A mesh is a finite collection of simple cells used to discretize a geometric domain or represent a geometric object. In a domain mesh, the cells have disjoint interiors and their union equals the domain. A surface mesh may instead approximate a target surface. Common cells include line segments in one dimension, triangles and quadrilaterals in two dimensions, and tetrahedra and hexahedra in three dimensions (Bern and Plassmann 2000).
The cells of a conforming mesh meet along complete shared faces. When all its cells are simplices, the cells together with all their faces form a geometric simplicial complex. Meshes are used to discretize domains in numerical methods such as the finite element method. Computational geometry and computer graphics commonly use polygon and triangle meshes to represent piecewise-linear surfaces and approximate smooth surfaces (Botsch et al. 2010).
The process of constructing a mesh is called mesh generation. Important attributes include the mesh size, which controls spatial resolution, and cell shape or quality, which can affect the accuracy and stability of numerical methods.
