64
Views
2
CrossRef citations to date
0
Altmetric
Articles

A closed-form general solution for the distance of point-to-ellipse in two dimensions

Pages 337-351 | Received 01 Sep 2018, Published online: 26 Jun 2019

References

  • Zheng, X., Palffy-Muhoray, P. Distance of closest approach of two arbitrary hard ellipses in two dimensions, Physical review E, 2007, 75(6): 061709. doi: 10.1103/PhysRevE.75.061709
  • Kim, I.S. An algorithm for finding the distance between two ellipses, Communications of the Korean mathematical society, 2006, 21(3): 559–567. doi: 10.4134/CKMS.2006.21.3.559
  • Uteshev, A.Y., Goncharova, M.V. Point-to-ellipse and point-to- ellipsoid distance equation analysis, Journal of computational and applied mathematics, 2018, 328(15): 232–251. doi: 10.1016/j.cam.2017.07.021
  • Dai, Y.H. Fast algorithms for projection on an ellipsoid, SIAM Journal on Optimization, 2006, 16(4): 986–1006. doi: 10.1137/040613305
  • Chernov, N., Wijewickrema, S. Algorithms for projecting points onto conics, Journal of Computational and Applied Mathematics, 2013, 251: 8–21. doi: 10.1016/j.cam.2013.03.031
  • Tamasyan, G. Sh., Chumakov, A.A. Finding the distance between ellipsoids, Journal of Applied and Industrial Mathematics, 2014, 8(3): 400–410. doi: 10.1134/S1990478914030132
  • Sampson, P.D. Fitting conic sections to very scattered data: an iterative refinement of the Bookstein algorithm, Computer Graphics and Image Processing, 1982, 18: 97–108. doi: 10.1016/0146-664X(82)90101-0
  • 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, 1991, 13(11): 1115–1138. doi: 10.1109/34.103273
  • Fitzgibbon, A.W., Pilu, M., Fisher, R.B. Direct least-squares fitting of ellipses, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1999, 21(5): 476–480. doi: 10.1109/34.765658
  • Szpak, Z., Chojnacki, W., van den Hengel, A. Guaranteed ellipse fitting with the Sampson Distance, in: LNCS, vol. 7576, Springer, 2012, pp. 87–100.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.