positionnot

Positionnot is a term that appears in discussions of grid- or coordinate-based transformations, used to describe the inversion of a position within a bounded space. In many formulations, positionnot acts as a mirror across the center of the domain, producing a counterpart point that occupies the opposite side of the space.

Formally, consider a d-dimensional grid with extents N1, N2, ..., Nd in each dimension, where each coordinate xi satisfies 0 ≤ xi < Ni. The positionnot of a point x = (x1, x2, ..., xd) is the point x' = (x1', x2', ..., xd') defined by xi' = Ni − 1 − xi for every i. This makes positionnot an involutive transformation: applying it twice yields the original position. It is a type of affine transformation equivalent to a central reflection about the center of the domain.

In two dimensions, for a square grid of size N × N, the positionnot of (a, b) is (N − 1 − a, N − 1 − b). In higher dimensions, the same coordinate-wise inversion applies. The operation is distinct from logical negation and from simple coordinate translation; it preserves grid alignment and produces a symmetric counterpart with respect to the space’s midpoint.

Applications of positionnot are mostly conceptual and algorithmic. They appear in symmetry analysis, puzzle design, image and grid transformations, and certain search or optimization problems that rely on mirrored configurations. Terminology varies, and positionnot is not a standardized term in formal literature; it is often described as a center-reflection or coordinate inversion.

See also: reflection transformation, central inversion, coordinate transformation, grid symmetry.