Adaptive subdivision of triangular meshes is highly desirable for surface generation algorithms including adaptive displacement mapping in which a highly detailed model can be constructed from a coarse triangle mesh and a displacement map. The communication requirements between the CPU and the graphics pipeline can be reduced if more detailed and complex surfaces are generated, as in displacement mapping, by an adaptive tessellation unit which is part of the graphics pipeline. Generating subdivision surfaces requires a large amount of memory in whicmultiple arbitrary accesses are required to neighbouring vertices to calculate the new vertices. In this paper we present a meshing scheme and new architecture for the implementation of adaptive subdivision of triangular meshes that allows for quick access using a small memory making it feasible in hardware, while at the same time allowing for new vertices to be adaptively inserted. The architecutre is regular and characterized by an efficient data management that minimizes the data storage and avoids the wait cycles that would be associated with the multiple data accesses required for traditional subdivision. This architecture is presented as an improvement for adaptive displacement mapping algorithms, but could also be used for adaptive subdivision surface generation in hardware.