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Displacement mapping is an effective technique for encoding the high levels of detail of surface models using coarse triangle meshes and displacement maps. These maps are 2D representations containing the distances between the coarse mesh and the surface to represent. Displacement maps have been used in many applications such as ray tracing, image warping, and volume rendering. In this article, we propose modifications to our previous grouping strategy, a new subdivision strategy based on the Modified Butterfly algorithm and new heuristics for the adaptive subdivision procedure, and, finally, the corresponding modifications on our hardware proposal. A meshing scheme and an adaptive subdivision strategy based on displacement mapping reduce the bottleneck between the CPU and graphics pipeline common in high-performance graphics systems.