Atlas of connectivity maps

• Set up the first resolution connectivity.
• Treat each patch as a 2D lattice.
• Have efficient and general operations for all types of refinement, subdivision, and multiresolution.

Semiregular models are now ubiquitous in computer graphics. These models are constructed by refining a model with an arbitrary initial connectivity. Due to the regularity enforced by the refinement, the vertices of semiregular models are mostly regular. To benefit from this regularity, it is desirable to have a data structure specifically designed for such models. We discuss how to design such a data structure, which we call the atlas of connectivity maps (ACM) for semiregular models. In an ACM, semiregular models are divided into regular patches. The connectivity between patches is captured at the coarsest resolution. In this paper, we discuss how to find these patches in a given semiregular model and how to set up the ACM. We also show some of the benefits of this data structure in applications such as the multiresolution framework. ACM can support a variety of different multiresolution frameworks including compact and smooth reverse subdivision methods. The efficiency of ACM is also compared with a standard implementation of half-edge.

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