Abstract: Subdivision surfaces provide a curved surface representation that is useful in a number of applications, including modeling surfaces of arbitrary topological type, fitting scattered data, and geometric compression and automatic level-of-detail generation using wavelets. Subdivision surfaces also provide an attractive representation for fast rendering, since they can directly represent complex surfaces of arbitrary topology. We present a method for subdivision surface triangulation that is fast, uses minimum memory, and is simpler in structure than a naive rendering method based on direct subdivision. These features make the algorithm amenable to implementation on both general purpose CPUs and dedicated geometry engine processors, allowing high rendering performance on appropriately equipped graphics hardware.