Interpolatory, solid subdivision of unstructured hexahedral meshes

Authors:
Kevin T. McDonnell;Yu-Sung Chang;Hong Qin
Affiliations:
State University of New York at Stony Brook, Department of Computer Science, 11794–4400, Stony Brook, NY, USA;State University of New York at Stony Brook, Department of Computer Science, 11794–4400, Stony Brook, NY, USA;State University of New York at Stony Brook, Department of Computer Science, 11794–4400, Stony Brook, NY, USA
Venue:
The Visual Computer: International Journal of Computer Graphics - Special section on implicit surfaces
Year:
2004

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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.