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A Method for Constructing Interpolatory Subdivision Schemes and Blending Subdivisions

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Abstract

This paper presents a universal method for constructing interpolatory subdivision schemes from known approximatory subdivisions. The method establishes geometric rules of the associated interpolatory subdivision through addition of further weighted averaging operations to the approximatory subdivision. The paper thus provides a novel approach for designing new interpolatory subdivision schemes. In addition, a family of subdivision surfaces varying from the given approximatory scheme to its associated interpolatory scheme, namely the blending subdivisions, can also be established. Based on the proposed method, variants of several known interpolatory subdivision schemes are constructed. A new interpolatory subdivision scheme is also developed using the same technique. Brief analysis of a family of blending subdivisions associated with the Loop subdivision scheme demonstrates that this particular family of subdivisions are globally C1 continuous while maintaining bounded curvature for regular meshes. As a further extension of the blending subdivisions, a volume-preserving subdivision strategy is also proposed in the paper.
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Keywords: 1.3.5 Computational Geometry and Object Modeling; Curve; G.1.1 Interpolation: Interpolation formulas; G.1.2 Approximation: Approximation of surfaces and contours; approximatory subdivision; blending subdivision; interpolatory subdivision; object representations; solid; subdivision schemes; surface; surface modeling; volume-preserving subdivision

Document Type: Research Article

Affiliations: Department of Manufacturing Engineering & Engineering Management, City University of Hong Kong, Hong Kong, China, Email: [email protected]

Publication date: June 1, 2007

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