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Smoothness of Subdivision Surfaces with Boundary

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Abstract

Subdivision rules for meshes with boundary are essential for practical applications of subdivision surfaces. These rules have to result in piecewise \(C^{\ell }\)-continuous boundary limit curves and ensure \(C^{\ell }\)-continuity of the surface itself. Extending the theory of Zorin (Constr Approx 16(3):359–397, 2000), we present in this paper general necessary and sufficient conditions for \(C^{\ell }\)-continuity of subdivision schemes for surfaces with boundary, and specialize these to practically applicable sufficient conditions for \(C^1\)-continuity. We use these conditions to show that certain boundary rules for Loop and Catmull–Clark are in fact \(C^1\) continuous.

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Correspondence to Sara Grundel.

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Communicated by Wolfgang Dahmen.

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Biermann, H., Grundel, S. & Zorin, D. Smoothness of Subdivision Surfaces with Boundary. Constr Approx 42, 1–29 (2015). https://doi.org/10.1007/s00365-015-9292-4

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  • DOI: https://doi.org/10.1007/s00365-015-9292-4

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