Fair interpolation and approximation of B-splines by energy minimization and points insertion

An efficient method for interpolation and approximation of both curve and surface points using B-splines is described. Automatic fairing is presented based on minimizing an energy functional. Additional data points, used as degrees of freedom for the fairing, are inserted only where the curve (the s...

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Bibliographic Details
Published in:Computer aided design 1996-09, Vol.28 (9), p.753-760
Main Author: Vassilev, Tzvetomir Ivanov
Format: Article
Language:English
Subjects:
Applied sciences
Artificial intelligence
B-splines
Computer aided design
Computer science
control theory
systems
Exact sciences and technology
interpolation
Pattern recognition. Digital image processing. Computational geometry
smoothing
Software
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Summary:An efficient method for interpolation and approximation of both curve and surface points using B-splines is described. Automatic fairing is presented based on minimizing an energy functional. Additional data points, used as degrees of freedom for the fairing, are inserted only where the curve (the surface) needs them. This reduces the number of the unknowns to a minimum which makes the algorithm very fast and efficient especially when a huge amount of data is concerned. Results of applying the algorithm for about 15,000 face data points, subject to measurement errors due to the digitization, are presented at the end of the paper.
ISSN:0010-4485
1879-2685
DOI:10.1016/0010-4485(95)00087-9