Segmentidest

Segmentidest is a theoretical construct in the fields of computational geometry and data segmentation that describes a scheme for naming and tracking line segments within a planar subdivision or mesh. The term denotes a system of segment identifiers (SIDs) intended to provide stable references to geometric segments even as the underlying structure undergoes local changes.

Origin and conceptually related ideas

The term appears in discussions of persistent segment representation, where algorithms require reliable references to segments across dynamic updates. Segmentidest emphasizes stability of identity over purely geometric coordinates, enabling robust indexing, querying, and history tracking in evolving graphs, meshes, or DCEL-based representations.

Definition and core properties

In a segmentidest framework, every non-empty segment is assigned a unique SID. SIDs are designed to be invariant under a restricted set of updates, such as local refinement, edge flips, or small subdivisions adjacent to the segment. Key properties include SID uniqueness, referential stability under allowed transformations, and a defined policy for handling splits or merges, such as reusing the original SID for one resultant piece or issuing new SIDs while maintaining a mapping to preserve referential integrity.

Applications and use cases

Segmentidest supports dynamic algorithms in computational geometry, computer graphics, and geographic information systems, where maintaining consistent references to parts of a mesh or subdivision is essential for incremental processing, undo/redo systems, and backtracking explanations.

Limitations and relation to other concepts

As a theoretical construct, segmentidest requires careful definition of acceptable transformations and recovery rules to avoid ambiguity. It is related to persistent identifiers, DCEL representations, and segment-based querying in dynamic planar graphs.

See also: segment, identifier, planar graph, DCEL, persistent identifier.