Mesh

Mesh refers to a discrete representation of a geometric space, consisting of interconnected elements that approximate the shape of an object or region. In mathematics and computer graphics, a mesh is typically a collection of vertices, edges, and faces that define the surface or volume of a shape. Faces are usually polygons, with triangles and quadrilaterals being most common.

Polygon meshes are widely used in 3D modeling and rendering. A vertex is a point in space; an edge connects two vertices; and a face is a polygon bounded by edges. Triangular meshes are especially common because they are simple to process, while quad meshes support smooth subdivision for production workflows.

Mesh generation and processing aim to create or improve a mesh for accuracy, efficiency, or quality. Algorithms include Delaunay triangulation, Voronoi-based methods, and advancing-front techniques. Subdivision methods such as Catmull-Clark or Loop produce smoother surfaces, and operations like smoothing, refinement, coarsening, and remeshing adjust density and quality.

Quality is assessed by metrics such as element shape quality (aspect ratio, skewness), size variation, and checks that ensure elements are valid (non-inverted). Data structures such as half-edge, winged-edge, and quad-edge encode connectivity and support efficient traversal and editing.

Applications span computer graphics, geometric modeling, finite element analysis, computational fluid dynamics, and scientific visualization. In networking, a mesh describes a mesh network, a topology where nodes forward data for the network, often with self-healing routing and multi-hop paths.