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In mathematics, a subpaving is a set of nonoverlapping box of Rn. A subset X of Rn can be approximated by two subpavings X− and X+ such that X− ⊂ X ⊂ X+. The three figures on the right show an approximation of the set X = {(x1, x2) ∈ R2 | x12 + x22 + sin(x1 + x2) ∈ [4,9]} with different accuracies. The set X− corresponds to red boxes and the set X+ contains all red and yellow boxes.
Combined with interval-based methods, subpavings are used to approximate the solution set of non-linear problems such as set inversion problems. Subpavings can also be used to prove that a set defined by nonlinear inequalities is path connected , to provide topological properties of such sets , to solve piano-mover's problems or to implement set computation .