AbstractFully automatic three‐dimensional mesh generation is a fundamental requirement for automating the numerical solution of partial differential equations. Two techniques in particular—the octree and Delaunay approaches—have been used towards this end. A method that combines both approaches to fully automatic mesh generation is presented here. The resulting algorithm provides the linear growth rate and divide‐and‐conquer approach of the octree method with the simplicity and optimal properties of the Delaunay tria