CTRIA

CTRIA is an open-source software library for two-dimensional constrained triangulation and mesh generation. It focuses on constructing triangle meshes that respect a given set of geometric constraints, such as polygon boundaries, holes, and fixed edges, while striving for favorable element quality. The input is a planar straight-line graph; the output is a triangle mesh suitable for numerical simulation or visual rendering.

Key features include support for multiple components, constraint handling by introducing Steiner points as necessary, a combination of incremental insertion with edge-flipping to enforce constrained Delaunay criteria, mesh quality controls such as minimum angle constraints and adaptive sizing fields, export of standard mesh formats, and interoperability with other geometry libraries.

Approach and algorithms: CTRIA typically uses an incremental refinement strategy that inserts points to satisfy constraints and improve element quality, together with local reconnection to maintain near-Delaunay properties under constraints. The approach balances boundary fidelity, mesh simplicity, and computational efficiency, and can be extended with custom sizing functions for adaptive meshing.

Applications: used in finite element analysis, computer graphics, geographic information systems, and physical simulations where accurate boundary representation and mesh quality are important.

See also: Delaunay triangulation; constrained triangulation; mesh generation; triangulation algorithms; CGAL.