D. Vignesh This email address is being protected from spambots. You need JavaScript enabled to view it.1 and T. Palanisamy1

1Department of Mathematics, Amrita school of Engineering Coimbatore, Amrita Vishwa Vidyapeetham, India


Received: April 1, 2022
Accepted: July 6, 2022
Publication Date: August 23, 2022

 Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202305_26(5).0014  


The relationship between a curve and scaled, rotated and translated version is often not evident in terms of their sample points. However it is significant to note that the research fraternity working on linkage mechanism found this relationship useful for their study which they captured through Fourier and wavelet transforms. This has been accomplished by using wavelet transform of a piecewise linear approximations of the given curve in an earlier work. In our proposed work it is interesting to note that the desired relationship is found to be present in a specific ratio of atypical wavelet detailed coefficients of sample points themselves. In fact, we employ a novel technique of wavelet transform using different wavelets unlike the previous attempt which is possible only by Haar wavelet. The results of this mathematical analysis are also supported by illustrated examples of continuous curves. Further the application of the proposed work to a real time image is found to suggest an useful feature which is invariant under certain transformations.

Keywords: Planar curves; Sample points; Atypical wavelet transform; Invariant feature vector


  1. [1] F. Freudenstein, (1999) “Harmonic analysis of crankand-rocker mechanisms with application" Journal of Applied Mechanics 26: 673–675.
  2. [2] J. McGarva and G. Mullineux, (1992) “A new methodology for rapid synthesis of function generators" Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 206: 391–398. DOI: 10.1243/PIME_PROC_1992_206_146_02.
  3. [3] J. McGarva and G. Mullineux, (1993) “Harmonic representation of closed curves" Applied Mathematical Modelling 17: 213–218. DOI: 10.1016/0307-904x(93)90109-t.
  4. [4] J. R. McGarva, (1994) “Rapid search and selection of path generating mechanisms from a library" Mechanism and machine theory 29: 223–235. DOI: 10.1016/0094-114x(94)90032-9.
  5. [5] G. Mullineux, (2011) “Atlas of spherical four-bar mechanisms" Mechanism and machine theory 46: 1811–1823. DOI: 10.1016/j.mechmachtheory.2011.06.001.
  6. [6] S. Jianwei, C. Jinkui, and S. Baoyu, (2012) “A unified model of harmonic characteristic parameter method for dimensional synthesis of linkage mechanism" Applied Mathematical Modelling 36: 6001–6010. DOI: 10.1016/j.apm.2012.01.052.
  7. [7] J.Wu, Q. Ge, and F. Gao, (2009) “An efficient method for synthesizing crank-rocker mechanisms for generating low harmonic curves" International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 49040: 531–538. DOI: 10.1115/DETC2009-87140.
  8. [8] C. Yue, H.-J. Su, and Q. J. Ge, (2012) “A hybrid computer-aided linkage design system for tracing open and closed planar curves" Computer-Aided Design 44: 1141–1150. DOI: 10.1016/j.cad.2012.06.004.
  9. [9] Y. Uesaka, (1984) “A new Fourier descriptor applicable to open curves" Electronics and Communications in Japan (Part I: Communications) 67: 1–10. DOI: 10.1002/ecja.4400670802.
  10. [10] W. Liu, J. Sun, B. Zhang, and J. Chu, (2018) “Wavelet feature parameters representations of open planar curves" Applied Mathematical Modelling 57: 614–624. DOI: 10.1016/j.apm.2017.05.035.
  11. [11] S. Anusha, A. Sriram, and T. Palanisamy, (2016) “A Comparative Study on Decomposition of Test Signals Using Variational Mode Decomposition and Wavelets" International Journal on Electrical Engineering and Informatics 8: 886. DOI: 10.15676/ijeei.2016.8.4.13.
  12. [12] S. Ganga, M. K. Panthangi, and T. Palanisamy, (2020) “Numerical solution of Blasius viscous flow problem using wavelet Galerkin method" International Journal for Computational Methods in Engineering Science and Mechanics: 1–7. DOI: 10.1080/15502287.2020.1772903.
  13. [13] M.W. Frazier. An introduction to wavelets through linear algebra. Springer Science & Business Media, 2006.
  14. [14] T. Palanisamy and J. Ravichandran, (2015) “A waveletbased hybrid approach to estimate variance function in heteroscedastic regression models" Statistical Papers 56: 911–932. DOI: 10.1007/s00362-014-0614-6.
  15. [15] I. Daubechies, (2001) “Ten lectures on wavelets. Philadelphia: SIAM; 1992" Google Scholar Google Scholar Digital Library Digital Library: DOI: 10.1137/1.9781611970104.
  16. [16] T. Palanisamy and J. Ravichandran, (2014) “Estimation of variance function in heteroscedastic regression models by generalized coiflets" Communications in Statistics-Simulation and Computation: 2213–2224. DOI: 10.1080/03610918.2012.749283.


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