A Superellipse with Deformation and Its Application in Describing the Cross-Sectional Shapes of a Square Bamboo
Abstract
:1. Introduction
2. Materials and Methods
2.1. Cross-Section Sampling and Preparation
2.2. Image Processing and Boundary Data Acquisition
2.3. Fitting the Superellipse Equation and the Introduction of a Deformation Parameter
2.4. Analysis of the Fitted Results
3. Results
4. Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A. Proof of the Superellipse Equation with the Deformation Parameter w
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Ring Type | Data Range | Theoretical Intercept 1 | Estimated Intercept | LCI | UCI | RMSE |
---|---|---|---|---|---|---|
Outer | n ≥ 2 | 0.8421 | 0.8246 | 0.8235 | 0.8257 | 0.0134 |
Outer | n < 2 | 0.7282 | 0.7291 | 0.7279 | 0.7303 | 0.0158 |
Inner | n ≥ 2 | 0.8071 | 0.7994 | 0.7986 | 0.8001 | 0.0092 |
Inner | n < 2 | 0.7637 | 0.7600 | 0.7593 | 0.7607 | 0.0087 |
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Huang, W.; Li, Y.; Niklas, K.J.; Gielis, J.; Ding, Y.; Cao, L.; Shi, P. A Superellipse with Deformation and Its Application in Describing the Cross-Sectional Shapes of a Square Bamboo. Symmetry 2020, 12, 2073. https://doi.org/10.3390/sym12122073
Huang W, Li Y, Niklas KJ, Gielis J, Ding Y, Cao L, Shi P. A Superellipse with Deformation and Its Application in Describing the Cross-Sectional Shapes of a Square Bamboo. Symmetry. 2020; 12(12):2073. https://doi.org/10.3390/sym12122073
Chicago/Turabian StyleHuang, Weiwei, Yueyi Li, Karl J. Niklas, Johan Gielis, Yongyan Ding, Li Cao, and Peijian Shi. 2020. "A Superellipse with Deformation and Its Application in Describing the Cross-Sectional Shapes of a Square Bamboo" Symmetry 12, no. 12: 2073. https://doi.org/10.3390/sym12122073