quadriculadas

Quadriculadas is a term used to describe objects, surfaces, or regions that have been subdivided into quadrilaterals, typically by overlaying a grid of lines or by merging unit squares of a rectangular lattice. In Spanish, quadriculado or quadriculadas refers to a grid-like pattern; in English, the equivalent term is quadriculated or quadrilateralized. The concept is common in geometry, computer graphics, and related disciplines.

Construction and varieties: A basic quadriculation arises when a polygonal region is overlaid with a rectangular grid, producing a tiling whose faces are unit squares. More generally, the grid can be skewed or adapted so that the resulting faces are general quadrilaterals. Quadriculated regions can be regular, with all faces square, or irregular, with quadrilaterals of varying shapes. The boundaries influence the structure and the graph formed by the adjacency of faces, edges, and vertices.

Mathematical and practical aspects: Quadriculations give rise to planar graphs in which each face has four sides. They are central in tiling theory, polyhedral combinatorics, and discrete geometry. In many contexts, the dual graph of a quadriculation represents a domino-tiling problem, since placing dominoes corresponds to certain coverings of the quadriculated region. Quadriculated meshes are also widely used in computer graphics and finite element methods for discretizing geometric domains.

Applications and related concepts: Beyond pure tiling theory, quadriculated patterns appear in architectural drawing, texture mapping, and geographic information systems where grid-based representations simplify computations. Related terms include quadrilateral meshes, quad-edge data structures, and domino tilings of quadriculated regions.