Data point selection for piecewise linear curve approximation

“…liquid level and surrounding RI), piecewise linear approximation is applied to linearize K n,m in various ranges of the surrounding RI using optimized data points obtained following the published procedure [32].…”

Section: Sensitivity To Surrounding Refractive Indexmentioning

confidence: 99%

Simultaneous detection of liquid level and refractive index with a long-period fiber grating based sensor device

Huang

Chen

et al. 2013

Meas. Sci. Technol.

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In this study, a long-period fiber grating (LPFG) based optical fiber sensor device is proposed for simultaneous detection of liquid level and refractive index. When part of the grating was submerged in an unknown liquid, the resonant wavelength of each cladding mode of the LPFG sensor varied linearly with the submerged length and nonlinearly with the refractive index of the liquid. By retaining the first-order (sensitivity) and second-order (cross sensitivity) terms of a Taylor expansion of the nonlinear relation, the changes in submerged length (or liquid level) and refractive index can be simultaneously evaluated from the changes in resonant wavelength of two cladding modes. The sensitivity coefficients to liquid level, refractive index, their cross effect, and environmental effects were studied both analytically and experimentally. The maximum prediction error by the proposed evaluation algorithm was found to be 1 mm for liquid level and 0.005 for refractive index.

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“…Unlike the problem of piecewise linear curve approximation to freeform curves discussed in [3] and [5], the feature points, such as curvature extrema and inflection points, are critical to retrieve the underlying curves of the data points. These kinds of points play a basic role in constraining the overall shape of the reconstructed curves.…”

Section: The Algorithmmentioning

confidence: 98%

“…Hamann and Chen [3] presented a more complex scheme to estimate the discrete curvature by computing a locally interpolating quadratic polynomial. However, due to the noise in the measured data points, the frequently.…”

Section: Discrete Curvature Of Data Pointsmentioning

confidence: 99%

A Heuristic Knot Placement Algorithm for B-Spline Curve Approximation

Li¹,

Xu²,

Zhao³

et al. 2004

Computer-Aided Design and Applications

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A new knot placement algorithm for B-spline curve approximating to dense and noisy data points is presented in this paper. In this algorithm, the discrete curvature of the points, in contrast to the points themselves as in the traditional approaches, is smoothed to expose the curvature characteristics of the underlying curve of the data. With respect to the smoothed curvature, knots are placed to satisfy a heuristic rule. Experimental results are included to demonstrate the validity of this algorithm.

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Data point selection for piecewise linear curve approximation

Cited by 78 publications

References 8 publications

Adaptive Triangulation of Evolving, Closed, or Open Surfaces by the Advancing-Front Method

Adaptive Triangulation of Evolving, Closed, or Open Surfaces by the Advancing-Front Method

Simultaneous detection of liquid level and refractive index with a long-period fiber grating based sensor device

A Heuristic Knot Placement Algorithm for B-Spline Curve Approximation

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