Interpolatory, solid subdivision of unstructured hexahedral meshes

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,...

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Bibliographic Details
Published in:The Visual computer Vol. 20; no. 6; pp. 418 - 436
Main Authors: McDonnell, Kevin T., Chang, Yu-Sung, Qin, Hong
Format: Journal Article
Language:English
Published: Heidelberg Springer Nature B.V 01.08.2004
Subjects:
Algorithms
Approximation
Design engineering
Finite element method
Interpolation
Polynomials
Solid modelling
ISSN:0178-2789, 1432-2315
Online Access:Get full text
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Summary: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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ISSN:0178-2789
1432-2315
DOI:10.1007/s00371-004-0246-2