surfacesplitting

Surface splitting is the process of partitioning a two-dimensional manifold, such as a surface embedded in three-dimensional space, into multiple pieces called patches. These patches are joined along seams or edges and may be processed independently. The practice is common in geometry processing, computer graphics, and numerical simulation, where working with smaller, simpler pieces can simplify modeling, parameterization, and computation.

Splitting is typically accomplished by defining cut curves or seam networks on the surface. Common approaches include geodesic-based splitting along shortest paths on the surface, curvature-driven methods that follow principal curvature lines, and user-specified seams for control over parameterization. Other techniques use cut graphs or clustering in a surface graph to partition the mesh into patches that balance size, shape, and distortion. The resulting patches often aim to have simple geometry (such as planar or low-degree patches) and boundaries that are suitable for unfolding the surface onto a plane or for parallel processing in simulations.

Applications of surface splitting span texture mapping, where seams enable efficient UV parameterization; remeshing and mesh simplification, which rely on dividing complex geometry into manageable patches; and finite element or isogeometric analysis, where patches provide localized basis functions and easier mesh generation. In topology, splitting can refer to decomposing a surface along a curve to study components or connectivity. Related concepts include surface parameterization, patch-based modeling, and seam optimization.