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A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting
- Source :
- PLoS ONE, PLoS ONE, Vol 12, Iss 3, p e0173857 (2017)
- Publication Year :
- 2017
- Publisher :
- Public Library of Science, 2017.
-
Abstract
- B-spline functions are widely used in many industrial applications such as computer graphic representations, computer aided design, computer aided manufacturing, computer numerical control, etc. Recently, there exist some demands, e.g. in reverse engineering (RE) area, to employ B-spline curves for non-trivial cases that include curves with discontinuous points, cusps or turning points from the sampled data. The most challenging task in these cases is in the identification of the number of knots and their respective locations in non-uniform space in the most efficient computational cost. This paper presents a new strategy for fitting any forms of curve by B-spline functions via local algorithm. A new two-step method for fast knot calculation is proposed. In the first step, the data is split using a bisecting method with predetermined allowable error to obtain coarse knots. Secondly, the knots are optimized, for both locations and continuity levels, by employing a non-linear least squares technique. The B-spline function is, therefore, obtained by solving the ordinary least squares problem. The performance of the proposed method is validated by using various numerical experimental data, with and without simulated noise, which were generated by a B-spline function and deterministic parametric functions. This paper also discusses the benchmarking of the proposed method to the existing methods in literature. The proposed method is shown to be able to reconstruct B-spline functions from sampled data within acceptable tolerance. It is also shown that, the proposed method can be applied for fitting any types of curves ranging from smooth ones to discontinuous ones. In addition, the method does not require excessive computational cost, which allows it to be used in automatic reverse engineering applications. ispartof: PLOS ONE vol:12 issue:3 ispartof: location:United States status: published
- Subjects :
- Polynomial
Computer science
Statistics as Topic
lcsh:Medicine
02 engineering and technology
Least squares
Polynomials
Computer Applications
Mathematical and Statistical Techniques
0202 electrical engineering, electronic engineering, information engineering
Medicine and Health Sciences
Parametric equation
lcsh:Science
Immune Response
Multidisciplinary
Direct method
Applied Mathematics
Simulation and Modeling
Curve Fitting
Multidisciplinary Sciences
Ordinary least squares
Physical Sciences
Curve fitting
Science & Technology - Other Topics
Computer-Aided Design
020201 artificial intelligence & image processing
Algorithm
Algorithms
Research Article
Optimization
Computer and Information Sciences
Immunology
Clonal Selection
Research and Analysis Methods
Knot (unit)
OPTIMIZATION APPROACH
Computer Graphics
Computer Simulation
ALGORITHM
Science & Technology
B-spline
lcsh:R
Biology and Life Sciences
020207 software engineering
Computing Methods
Algebra
Family of curves
lcsh:Q
POINTS
Nonlinear Least Squares Method
Mathematical Functions
Mathematics
APPROXIMATION
Subjects
Details
- Language :
- English
- ISSN :
- 19326203
- Volume :
- 12
- Issue :
- 3
- Database :
- OpenAIRE
- Journal :
- PLoS ONE
- Accession number :
- edsair.doi.dedup.....891a0e5b5a5fe81f369b6359afa985a7