For example, data structures only need to support operations such as neighbor search in a diagram. Special constraints, such as boundary conditions, can be easily taken into account by locally changing the weights of the subdivision schema.
No global constraint systems are required to ensure smooth operation. The domain of the subdivision is an abstract topological complex. No metrics are required, no global (or even local) parameterization, and no embedding is required. Last but not least, important functionalities such as basics for the tangential spaces to the boundary surface and values of the boundary surface can be calculated exactly.
Since the entire process is based on mesh refinement, the subdivision naturally closes the gap between polygonal mesh representations and higher-level modeling paradigms such as patches. Subdivision provides a basic framework for techniques such as level-of-detail rendering, compression, progressive transmission, adaptive meshing, and many other algorithms based on multiresolution. Together with its deep and rich connections to wavelets, it creates a powerful paradigm for precise representation and efficient numerical computation.
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