Duplex fitting of zero-level and offset surfaces

Authors:
Shengjun Liu;Charlie C. L. Wang
Affiliations:
Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong and School of Mathematical Science and Computing Technology, Central South University, China;Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong
Venue:
Computer-Aided Design
Year:
2009

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Abstract

Offset surfaces play an important role in various CAD/CAM applications. Given a set of oriented points, we propose a hierarchical method in this paper to fit both the zero-level surface and its offset surface with a single implicit function. The implicit function is formed by compactly supported radial basis functions (CSRBFs). Different from other existing methods in literature, our approach reconstructs an implicit function which interpolates or approximates both the zero-level surface and the offset surface of a given point set, simultaneously. Employing locally supported functions leads to an efficient computational procedure, while the coarse-to-fine hierarchy makes our approach insensitive to the density of scattered data and allows us to reconstruct large parts of missing data. The performance of our method is demonstrated by a number of examples and the application of adaptive slicing hollowed models in rapid prototyping.