planarizing

Planarizing is the process of transforming a non-planar object into a planar representation. In graph theory and graph drawing, planarization typically refers to converting a non-planar drawing of a graph into a planar graph by introducing new vertices at edge crossings. This substitution, known as edge subdivision at crossings, replaces each crossing with a vertex and four incident edges, yielding a planar graph that can be embedded in the plane without crossings. Planarization is often used as a preprocessing step to apply planar embedding algorithms or to analyze the structure of a drawing. It is important to note that planarization alters the original graph: it increases the number of vertices and edges and changes adjacency, so results derived from the planarized graph must be interpreted with care.

In practical workflows, planarization may also refer to rerouting or removing edges to reduce or eliminate crossings, or to subdividing edges to facilitate routing in circuit design and PCB layout. In these contexts, the goal is a planarity-friendly representation that supports readable visualization or manufacturability.

Limitations and alternatives: not all objects can be planarized without changing their essential properties; in some cases, one prefers planarity testing to decide if a given representation is already planar, or uses non-planar visualization techniques that preserve original connectivity without subdivision.

See also: planarity, planarity testing, graph embedding, edge subdivision, graph drawing.