remeshing

Remeshing is the process of generating a new mesh for a geometric domain, often to replace an existing mesh in order to improve element quality, adapt resolution to features, or better satisfy numerical criteria. It can involve changing topology or simply refining or coarsening elements while preserving the overall shape.

Common in 2D and 3D, remeshing typically operates on triangular or tetrahedral meshes, but quadrilateral and hexahedral meshes may also be produced. The objective is to produce elements of suitable size and shape while maintaining fidelity to the domain boundary.

A primary goal is to improve mesh quality metrics such as minimum angle, aspect ratio, and size variation, which influence numerical stability and accuracy in simulations. Remeshing also supports adaptation to estimated solution error, curvature, or other features, by refining where needed and coarsening elsewhere.

Techniques include isotropic remeshing, which uses uniform element size, and anisotropic or metric-based remeshing, which adapts to a local metric guiding anisotropic element shapes. Algorithms include Delaunay refinement, advancing-front methods, and isotropic or anisotropic metric-driven approaches. Operations such as edge split, edge collapse, vertex relocation, and edge flipping are used to improve quality and to conform to boundaries and features. Feature preservation is often required to maintain sharp edges and corners.

A typical workflow starts with defining a target metric or size field, performing local mesh operations and smoothing, enforcing boundary conformity and geometric features, and finally projecting nodes onto the original surface and verifying quality criteria.

Applications include finite element analysis, computational fluid dynamics, computer graphics, and geological modeling. Remeshing is a key step in simulation pipelines to ensure stable, accurate results while controlling computational cost.