Subdivises

Subdivises is a term used in mathematics and related disciplines to describe processes that subdivide a geometric object into smaller components. The standard English verb is subdivide, but subdivises appears in some texts as a plural noun or as a label for subdivision procedures, especially in translations or field slang.

A subdivise operation takes a domain—such as a polygonal region, a mesh, or a surface patch—and partitions it into smaller, non-overlapping elements that together reproduce the original object. The subdivision is often organized as a hierarchy or levels of detail, with level 0 corresponding to the initial object and higher levels representing progressively finer representations.

Subdivision strategies can be uniform or adaptive. Uniform subdivision applies the same refinement rule across all elements, creating regular grids or meshes. Adaptive subdivision refines only where needed, according to error estimates, feature size, or curvature, yielding efficient representations for rendering or analysis.

In graphics and geometry, subdivision methods include triangulation and quadrangulation, as well as subdivision surfaces such as Catmull-Clark and Loop schemes, which produce smooth surfaces in the limit. In numerical analysis, subdivises enable mesh refinement for finite element methods, improving accuracy where solution features are localized.

Applications span computer graphics, CAD/CAM, finite element analysis, and geographic information systems. See also mesh refinement, subdivision surface, and multiresolution modeling.