CLC number: TV5
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2018-03-20
Cited: 0
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Yu-fei Wu, Liang He, Zhi-dong Li. Curve smoothing using a continuous function[J]. Journal of Zhejiang University Science A, 2018, 19(4): 304-314.
@article{title="Curve smoothing using a continuous function",
author="Yu-fei Wu, Liang He, Zhi-dong Li",
journal="Journal of Zhejiang University Science A",
volume="19",
number="4",
pages="304-314",
year="2018",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A1700502"
}
%0 Journal Article
%T Curve smoothing using a continuous function
%A Yu-fei Wu
%A Liang He
%A Zhi-dong Li
%J Journal of Zhejiang University SCIENCE A
%V 19
%N 4
%P 304-314
%@ 1673-565X
%D 2018
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1700502
TY - JOUR
T1 - Curve smoothing using a continuous function
A1 - Yu-fei Wu
A1 - Liang He
A1 - Zhi-dong Li
J0 - Journal of Zhejiang University Science A
VL - 19
IS - 4
SP - 304
EP - 314
%@ 1673-565X
Y1 - 2018
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A1700502
Abstract: Current curve smoothing technologies provide a smoothed curve by joining together separate curves that have certain degrees of continuity at junctions. These technologies have found many applications in science and engineering. However, none of them can provide a smoothed curve using a single continuous function for arbitrary segmental curves. This paper reports a new approach that can be used to construct a single continuous function that joins an arbitrary number of different segmental curves, with the required degree of continuity at all junctions. The smoothness of transition at different junctions can be controlled by separate parameters to suit different needs. The combined continuous function can approach the original segmental functions asymptotically or match the original segmental functions “exactly” inside each segment by adjusting the smoothness parameter. This new approach may also find application outside the scope of curve smoothing/curving fitting in the future.
This work developed a new curve smoothing technology using a single continuous function for arbitrary segmental curves. The single continuous function has required degree of continuity at all junctions, which can be controlled by separate parameters for different demands. This new approach is significantly important in the field of the constitutive relations of materials in civil engineering, since the constitutive relations of materials always consist of segmental curves. The smoothness of the single continuous function at all junctions for the constitutive relation is also significant for numerical application.
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