Quadtree and octree mesh generation

Alistair Borthwick, Ahmed Saalehi

Research output: Contribution to journalArticlepeer-review


Engineering analysis often involves the accurate numerical solution of boundary value problems in discrete form. Hierarchical quadtree (or octree) grid generation offers an efficient method for the spatial discretisation of arbitrary-shaped two- (or three-) dimensional domains. It consists of recursive algebraic splitting of sub-domains into quadrants (or cubes), leading to an ordered hierarchical data structure with regard to the storage of mesh information. This paper describes quadtree Cartesian grid generation in detail and gives examples of its application to a circular geometry. The method is simple, rapid and does not experience difficulties with convergence (unlike curvilinear boundary-fitted mapping). Furthermore, the mesh may easily be adapted while preserving a well-ordered integer data structure. Extension to three-dimensions using octrees is straightforward.
Original languageEnglish
Pages (from-to)9-18
Number of pages10
JournalInternational Journal of Engineering
Issue number1
Publication statusPublished - 1996


  • Hierarchical meshes, quadtree, octree, integer tree, spatial domain decomposition, grid generation

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