meshes

A mesh is a collection of vertices connected by edges to form a discrete representation of a geometric surface or region. Faces, typically polygons, join edges to enclose areas; the simplest mesh is a wireframe, while polygonal meshes with triangles or quadrilaterals are used to approximate smooth shapes. Meshes enable finite representation in computer graphics, modeling, and numerical simulation.

In computer graphics and geometric modeling, triangular meshes are widely used for robustness and simplicity; quad meshes are preferred for subdivision surfaces and animation. Topology, including manifoldness and watertightness, affects rendering and manipulation. Common operations include subdivision (refining faces), decimation (simplification), smoothing, and remeshing. Standard formats such as OBJ, STL, and PLY store mesh geometry and, sometimes, color or texture data. Algorithms include Delaunay triangulation, marching cubes for isosurface extraction, and Catmull-Clark subdivision.

In numerical simulation, especially finite element analysis, meshes discretize a domain into elements to solve partial differential equations. Element types include triangles, quadrilaterals, tetrahedra, and hexahedra. Mesh quality metrics—minimum angle, aspect ratio, skewness—impact accuracy and convergence. Mesh refinement, coarsening, and adaptive meshing based on error estimates improve efficiency and fidelity.

In networking, a mesh topology connects nodes so that data can traverse multiple paths. Wireless mesh networks use multi-hop routing and redundancy to improve reliability and coverage in dynamic environments. Meshes can self-heal as nodes join or fail, at the cost of greater routing complexity and overhead.