Classesplanar

Classesplanar is not a widely standardized term, but it is occasionally used informally to refer to a classification or collection of planar objects or planar-embeddable structures. In mathematics and computer science, the closest standard notion is a planar class: a class of objects that can be represented or drawn in the plane without crossings.

In graph theory, a planar class typically means a class of graphs that admit a planar embedding. The defining property is planarity: a graph can be drawn in the plane so that its edges intersect only at their endpoints. Planar graph classes are usually closed under certain operations; for example, subgraphs and disjoint unions of planar graphs remain planar, and all minors of a planar graph are planar as well. Kuratowski’s theorem provides a fundamental characterization: a graph is planar if and only if it contains no subdivision of K5 or K3,3. Planar graph classes are often studied for their structural properties and for the efficiency of algorithms that exploit planarity.

Key algorithmic topics associated with planar classes include planarity testing and planar embedding. Linear-time algorithms exist for recognizing planarity and producing a planar embedding, along with related tasks such as triangulation and face enumeration. Planar graph classes also arise in applications like circuit layout, network visualization, and geographic information systems.

In software contexts, a package or module named “classesplanar” would typically implement data structures and operations for planar geometry or planar objects, such as points, lines, polygons, and operations like intersection, union, area calculation, and triangulation. It could serve as a foundation for computational geometry, computer-aided design, or diagrammatic drawing tools.

See also: Planar graph, Outerplanar graph, Graph minor, Kuratowski’s theorem, Planarity testing, Computational geometry.