meshers

Meshers are software tools or algorithms that convert a geometric description of a domain into a mesh, a discretized representation consisting of vertices, edges, and faces. Meshes are used to discretize spaces for numerical simulation, such as finite element analysis or computational fluid dynamics, as well as to create rendering-friendly representations in computer graphics and 3D printing. A mesher may operate on 2D domains (producing polygonal meshes) or on 3D volumes (creating tetrahedral or hexahedral meshes). In 2D, triangulation is common; in 3D, tetrahedral or hybrid element types are typical.

Meshers can be classified by the kind of mesh produced: surface meshes that imitate the boundary geometry and volume meshes that fill the interior. They may generate constrained meshes that respect CAD boundaries or implicit surfaces, and may support anisotropic sizing where element size varies with direction and location to capture features.

Popular generation strategies include Delaunay-based methods, constrained Delaunay triangulation, advancing-front techniques, and voxel- or marching-based approaches. Some meshing pipelines combine surface meshing with volume meshing, where a surface mesh is first produced to approximate the boundary, followed by interior volume generation. Quality criteria such as element shape metrics, minimum angle, and aspect ratio guide refinement and smoothing.

Modern meshers support sizing fields to control density, mesh refinement, and remeshing to improve quality. They may also perform isotropic or anisotropic meshing, smoothing, decimation, or adaptation to local geometric features or solution gradients.

Applications span engineering, physics simulations, geometry processing, and 3D printing. Widely used tools include Gmsh, TetGen, Triangle, Netgen, and CGAL-based meshing libraries, among others. The field has matured since the late 20th century, with ongoing research in adaptive, anisotropic, and parallel meshing algorithms.