A “rooted” plane triangulation is a plane triangulation with one designated vertex on the outer face. A simple algorithm to generate all triconnected rooted plane triangulations with at most n vertices is presented. The algorithm uses O(n) 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 all triconnected rooted plane triangulations having exactly n vertices including exactly r vertices on the outer face in O(r) time per triangulation can be generated without duplicates, while the previous best algorithm generates such triangulations in O(n²) time per triangulation. All triconnected (non-rooted) plane triangulations having exactly n vertices including exactly r vertices on the outer face can also be generated without duplicates in O(r²n) time per triangulation, and all maximal planar graphs can be generated in O(n³) time per graph.