arrangementbased
Arrangementbased (arrangement-based) refers to approaches and analyses that rely on the arrangement of geometric or combinatorial objects to derive results. The term emphasizes that the properties of interest arise from how these objects intersect and partition the ambient space, rather than from intrinsic algebraic or numeric form alone. The concept is widely used in mathematics, computer science, and related disciplines.
In mathematics, arrangement-based methods study structures formed by objects such as lines, planes, or higher-dimensional hyperplanes,
In algorithmic and computational geometry contexts, arrangement-based algorithms operate by constructing and traversing the subdivision of
Applications of arrangement-based methods extend to discrete geometry, optimization, and the analysis of incidence structures in
See also hyperplane arrangement, Orlik–Solomon algebra, arrangement (combinatorics), and computational geometry.