Abstract
Convergence and normal continuity analysis of a bivariate nonstationary (level-dependent) subdivision scheme for 2-manifold meshes with arbitrary topology is still an open issue. Exploiting ideas from the theory of asymptotically equivalent subdivision schemes, in this paper we derive new sufficient conditions for establishing convergence and normal continuity of any rotationally symmetric, nonstationary subdivision scheme near an extraordinary vertex/face.
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Acknowledgements
This research has been accomplished within RITA (Research ITalian network on Approximation). The authors are members of the INdAM Research group GNCS, which has partially supported this work. The authors wish to thank the reviewers for their constructive comments that allowed them to improve the presentation of the results and to clarify all the details of their proofs.
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Communicated by Wolfgang Dahmen.
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Conti, C., Donatelli, M., Romani, L. et al. Convergence and Normal Continuity Analysis of Nonstationary Subdivision Schemes Near Extraordinary Vertices and Faces. Constr Approx 50, 457–496 (2019). https://doi.org/10.1007/s00365-019-09477-y
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DOI: https://doi.org/10.1007/s00365-019-09477-y