A "rooted" plane triangulation is a plane triangulation with one designated vertex r and one designated edge incident to r on the outer face. In this paper we give a simple algorithm to generate all connected rooted plane triangulations with at most m edges. The algorithm uses O(m) space and generates such triangulations in O(1) time per triangulation without duplications. The algorithm does not output entire triangulations but the difference from the previous triangulation. By modifying the algorithm we can generate all connected (non-rooted) plane triangulations with at most m edges in O(m3) time per triangulation.

A plane quadrangulation is a plane graph such that each inner face has exactly four edges on its contour. This is a planar dual of a plane graph such that all inner vertices have degree exactly four. A based plane quadrangulation is a plane quadrangulation with one designated edge on the outer face. In this paper we give a simple algorithm to generate all biconnected based plane quadrangulations with at most f faces. The algorithm uses O(f) space and generates such quadrangulations in O(1) time per quadrangulation without duplications. By modifying the algorithm we can generate all biconnected (non-based) plane quadrangulations with at most f faces in O(f3) time per quadrangulation.