A closed–form general solution for the distance of point-to-hyperbola in two dimensions
*Chang-Chien ChouCorresponding authorsamuelchou7@yahoo.com.twDepartment of Information Management Lunghwa University of Science and TechnologyWanshou Rd., Guishan District, Taoyuan City, 33360, Taiwan, R.O.C.View full profile → , Gia-Shie Liuliug@gm.lhu.edu.twDepartment of Information Management Lunghwa University of Science and TechnologyTaiwan, R.O.C.View full profile → , Fang-Ling Linfangling@gm.lhu.edu.twDepartment of Information Management Lunghwa University of Science and TechnologyTaiwan, R.O.C.View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 10 Jan 2023
- Published Online:
- 27 Feb 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1727
- Pages:
- 87–107
Abstract
Keywords
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References
[1] Chou, C.-C. A closed-form general solution for the distance of point-to-ellipse in two dimensions. Journal of Interdisciplinary Mathematics. 22(3), 337–351 (2019).
[2] Chou, C.-C. A closed-form general solution for the distance of point-to-parabola in two dimensions. International Journal of Computing Science and Mathematics. 15(2), 132–141 (2022).
[3] Lei, W.; Hou, F.; Xi, J.; Tan, Q.; Xu, M.; Jiang, X.; Liu G.; Gu, Q. Automatic hyperbola detection and fitting in GPR B-scan image. Automation in Construction. 106, 102839 (2019).
[4] Wang, Y.; Cui, G.; Xu, J. Semi-automatic detection of buried rebar in GPR data using a genetic algorithm. Automation in Construction. 114, 103186 (2020).
[5] Tu, X.; Lei, X.; Ma, W.; Zuo, X.; Man, R. Hyperbola minimum-zone evaluation and fitting based on geometry optimised search algorithm. Measurement, 127, 205–209 (2018).
[6] Dai, Q.; Li, Y.; Jiang, T.; Sun, Q. A New B-Scan Interpretation Model in Complex Environments. IEEE Transactions on Instrumentation and Measurement. 71, 1–15 (2022).
[7] Vesely, J.; Van Doan, S. Analytical method solving system of hyperbolic equations. In Proceedings of the 2015 25th International Conference Radioelektronika. 21-22 April 2015, Pardubice, Czech Republic.
[8] Chan, Y.T.; Ho, K.C. A simple and efficient estimator for hyperbolic location. IEEE Transactions on Image Processing. 42(8), 1905–1915 (1994).
[9] Uteshev, A.Y.; Goncharova, M.V. Point-to-ellipse and point-to-ellipsoid distance equation analysis. Journal of Computational and Applied Mathematics. 328(15), 232–251 (2018).
[10] Dai, Y.H. Fast algorithms for projection on an ellipsoid. SIAM Journal on Optimization. 16(4), 986–1006 (2006).
[11] Chernov, N.; Wijewickrema, S. Algorithms for projecting points onto conics. Journal of Computational and Applied Mathematics. 251, 8–21 (2013).
[12] Tamasyan, G. Sh.; Chumakov, A.A. Finding the distance between ellipsoids. Journal of Applied and Industrial Mathematics. 8(3), 400–410 (2014).
[13] Sampson, P.D. Fitting conic sections to very scattered data: an iterative refinement of the Bookstein algorithm. Computer Graphics and Image Processing. 18, 97–108 (1982).
[14] Taubin, G. Estimation of planar curves, surfaces and nonplanar space curves defined by implicit equations with application to edge and range image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence. 13(11), 1115–1138 (1991).
[15] Fitzgibbon, A.W.; Pilu, M.; Fisher, R.B. Direct least-squares fitting of ellipses. IEEE Transactions on Pattern Analysis and Machine Intelligence. 21(5), 476–480 (1999).
[16] Szpak, Z.; Chojnacki, W.; van den Hengel, A. Guaranteed ellipse fitting with the Sampson Distance. in: LNCS. , 7576, 87–100 (2012).
[17] Ahn, S.J.; Rauh, W.; Warnecke, H.-J. Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola. Pattern Recognition. 34, 2283–2303 (2001).
[18] Smith, D.E. History of Mathematics, New York: Dover Publications, Vol 1, pp. 300 (1958).
[19] Rudnev, M.; Wheeler , J. On incidence bounds with Möbius hyperbolae in positive characteristic. Finite Fields and Their Applications. 78, 101978 (2022).
[20] Mohammadi, A.; Pham, T.; Warren, A. 10. A point-conic incidence bound and applications over Fp. European Journal of Combinatorics. 107, 103596 (2023).
[21] Maalek R.; Lichti, D.D. New confocal hyperbola-based ellipse fitting with applications to estimating parameters of mechanical pipes from point clouds. Pattern Recognition. 116, 107948 (2021).
[22] Dogan, I.; Akpinar, A. On Distance in Some Finite Planes and Graphs Arising from Those Planes. Journal of Mathematics, Article ID 6668682, 17 pages (2021).
