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CLC number: TV5

On-line Access: 2018-04-04

Received: 2017-09-16

Revision Accepted: 2018-01-25

Crosschecked: 2018-03-20

Cited: 0

Clicked: 2151

Citations:  Bibtex RefMan EndNote GB/T7714

 ORCID:

Yu-fei Wu

https://orcid.org/0000-0002-3970-3999

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Journal of Zhejiang University SCIENCE A 2018 Vol.19 No.4 P.304-314

http://doi.org/10.1631/jzus.A1700502


Curve smoothing using a continuous function


Author(s):  Yu-fei Wu, Liang He, Zhi-dong Li

Affiliation(s):  School of Engineering, RMIT University, Carlton, Victoria 3053, Australia; more

Corresponding email(s):   yufei.wu@rmit.edu.au

Key Words:  Curve smoothing, Curve fitting, Transition curve, Path planning, Tool path


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.

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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.

连续函数式曲线光滑法

目的:用连续函数实现无限接近原始非连续曲线的光滑.
创新点:首次提出用一个连续函数替代原来由任意多非连续区域函数构成的函数.该方法可视为一种新的函数光滑算法.
方法:1. 通过引入特殊的区域变量,并用该区域变量替代原函数自变量的方法,将区域函数改造成在该区域无限接近原函数而在区域外取值常数的函数. 2. 把所有的区域函数相乘得到一个连续函数的方程.
结论:1. 由任意多非连续区域函数构成的函数可以改造成一个连续函数. 2. 该连续函数在原非连续边界的光滑程度可以由各个边界上独立的参数按需调整. 3. 该方法产生的连续函数没有摆动现象,其形状与原始区域函数无限接近.该方程在数学上是连续的,同时无限接近原始非连续函数,包括原来在边界上函数值的非连续.

关键词:曲线光滑;区域变量;区域函数;连续函数

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