MATLAB Implementation of Triangulation

Triangulation is a computational geometry method that partitions convex polygons into triangles, widely applied in computer graphics and scientific computing. This technique serves not only for mesh generation but also plays a crucial role in computer simulations and 3D modeling. In MATLAB, triangulation can be efficiently implemented using the Delaunay function, which employs the Delaunay triangulation algorithm to transform a set of scattered points into an optimal triangular mesh structure. The function generates triangles that maximize minimum angles, ensuring numerical stability for subsequent computations. Key implementation aspects include: using DelaunayTri or delaunayTriangulation classes for 2D/3D point sets, accessing topological relationships through vertex connectivity lists, and applying mesh refinement techniques. When performing triangulation, careful consideration of point distribution and density is essential to achieve optimal segmentation results, as improper point placement may lead to sliver triangles or degenerate mesh elements that compromise computational accuracy.