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Interpolatory, solid subdivision of unstructured hexahedral meshes

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Abstract

This paper presents a new, volumetric subdivision scheme for interpolation of arbitrary hexahedral meshes. To date, nearly every existing volumetric subdivision scheme is approximating, i.e., with each application of the subdivision algorithm, the geometry shrinks away from its control mesh. Often, an approximating algorithm is undesirable and inappropriate, producing unsatisfactory results for certain applications in solid modeling and engineering design (e.g., finite element meshing). We address this lack of smooth, interpolatory subdivision algorithms by devising a new scheme founded upon the concept of tri-cubic Lagrange interpolating polynomials. We show that our algorithm is a natural generalization of the butterfly subdivision surface scheme to a tri-variate, volumetric setting.

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Authors and Affiliations

  1. Department of Computer Science, State University of New York at Stony Brook, Stony Brook, NY, 11794–4400, USA

    Kevin T. McDonnell, Yu-Sung Chang & Hong Qin

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  1. Kevin T. McDonnell
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  2. Yu-Sung Chang
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  3. Hong Qin
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Correspondence to Kevin T. McDonnell.

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McDonnell, K., Chang, YS. & Qin, H. Interpolatory, solid subdivision of unstructured hexahedral meshes. Vis Comput 20, 418–436 (2004). https://doi.org/10.1007/s00371-004-0246-2

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  • DOI: https://doi.org/10.1007/s00371-004-0246-2

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