Multisidet

Multisidet is a term used to describe a hypothetical geometric construct representing a polygonal outline whose number of sides can vary under certain operations. In this sense, it generalizes the concept of a polygon by treating S, the count of boundary segments, as a dynamic parameter. The term is not standard in formal geometry but appears in informal discussions of adaptive boundaries in computer graphics, computational geometry, and modeling.

Definition and representation: A multisidet is defined by an ordered sequence of vertices V = (v1, v2, ..., vS), with edges connecting consecutive vertices and, for closed forms, the last vertex back to the first. The parameter S may change via topological operations such as edge subdivision (increasing S by 1) or edge collapse (decreasing S by 1). The geometry can be constrained to a plane or generalized to higher-dimensional surfaces, depending on the context.

Variants and properties: Closed multisidet forms a loop, producing a polygonal boundary, while open multisidet represents an open polyline. The vertex positions determine convexity, concavity, or self-intersections. Because S is variable, properties that depend on the number of sides (such as edge count) are context-dependent and can change during modeling or processing.

Applications and relationship: In computer graphics and CAD, multisidet helps model adaptive silhouettes, evolving boundaries, or meshes with variable resolution. It relates to polygons, polygonal chains, and polygon meshes but emphasizes the ability to alter boundary length and structure during a workflow.

See also: polygon, polyline, polygonal chain, mesh, adaptive refinement.