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Most of the needs that occur in applications using subdivision surfaces are covered by our hierarchical mesh data structure. We tested the proposed data structure in some implementations for adaptive visualizations where a highly efficient data structure is essential. Primarily, this means our mesh must support a fast hierarchical refinement of the object with a fast access to the vertices in the different subdivision levels. Only the parts of the object with a contribution to the light transport are computed and stored up to an adequate subdivision depth. A rapid and stable navigation on the mesh must be possible, and storing of ancillary information is required. The modular concept of our mesh enables us to exchange the rules of the subdivision scheme easily. With our hierarchical mesh, the rules for Catmull-Clark, Loop and ESubs, which is another subdivison scheme, were easy to implement.