surfacelocal

Surfacelocal is a term used in geometry processing to describe properties and descriptors that pertain to a small region around a point on a surface rather than the surface as a whole. It is used to characterize how the surface behaves locally, to inform analysis, filtering, and reconstruction tasks.

In differential geometry, for a smooth surface S in R^3 and a point p ∈ S, the surfacelocal data typically includes the tangent plane T_pS, the unit normal n(p), and curvature measures such as mean curvature H(p) and Gaussian curvature K(p). The local neighborhood is defined by a radius r or a fixed number of nearby points, allowing the construction of a local coordinate frame.

On discrete meshes, surfacelocal is estimated from adjacent vertices and faces. Common approaches include principal component analysis to estimate the local tangent plane and normal, and local surface fitting, such as quadric or polynomial patches, to infer curvature. The quality of the estimate depends on sampling density, noise, and the chosen neighborhood size.

Applications of surfacelocal concepts include surface denoising, feature detection like edge and corner identification, curvature-based segmentation, local surface reconstruction, and geometric modeling. It also underpins algorithms for normal filtering, smoothing, and mesh parametrization.

Terminology varies; some authors use surfacelocal interchangeably with local surface patch or surface descriptor. When used, it emphasizes locality as a building block for broader surface analysis.