105
Views
7
CrossRef citations to date
0
Altmetric
Section B

Blending canal surfaces along given circles using Dupin cyclides

, &
Pages 641-660 | Received 31 Oct 2012, Accepted 25 Apr 2013, Published online: 01 Jul 2013

References

  • S. Allen and D. Dutta, Cyclides in pure blending I, Comput. Aided Geom. Design 14 (1997), pp. 51–75. doi: 10.1016/S0167-8396(96)00021-0
  • S. Allen and D. Dutta, Cyclides in pure blending II, Comput. Aided Geom. Design 14 (1997), pp. 77–102. doi: 10.1016/S0167-8396(96)00022-2
  • M. Berger, Géométrie 2, 2nd ed., Vol. 5, Cedic-Nathan, Paris, France, 1978.
  • M. Berger and B. Gostiaux, Géométrie Différentielle: Variétés, Courbes et Surfaces, 2nd ed., PUF, Paris, France, 1992.
  • R.M.G.T.A. Bey, R. Chaine, and S. Akkouche, Reconstruction of consistent 3d cad models from point cloud data using a priori cad models, ISPRS Workchop on Laser Scanning, 2011.
  • R.M.A. Bey, R. Chaine, and G. Thibault, Reconstruction de Modèles CAO de scènes industrielles étant données des connaissances a priori, Actes des journées GTMG, Mars, 2012.
  • W. Boehm, On cyclides in geometric modeling, Comput. Aided Geom. Design 7 (1990), pp. 243–255. doi: 10.1016/0167-8396(90)90034-O
  • A. Cayley, On the cyclide, Q. J. Pure Appl. Math. 12 (1873), pp. 148–165.
  • T. Cecil, Lie Sphere Geometry, Universitext, New York, 1992.
  • G. Darboux, Leçons sur la Théorie Générale des Surfaces, Vol. 1, Gauthier-Villars, Paris, France, 1887.
  • G. Darboux, Principes de Géométrie Analytique, Gauthier-Villars, Paris, France, 1917.
  • L. Druoton, L. Garnier, and R. Langevin, Les cyclides de Dupin et l'espace des sphères, Actes des journées AFIG, Novembre, 2010, pp. 147–155.
  • L. Druoton, L. Garnier, and R. Langevin, Les cyclides de Dupin et l'espace des sphères, Revue Electronique Francophone d'Informatique Graphique 5 (2011), pp. 41–59.
  • C.P. Dupin, Application de Géométrie et de Méchanique à la Marine, aux Ponts et Chaussées, etc., Bachelier, Paris, 1822.
  • D. Dutta, R.R. Martin, and M.J. Pratt, Cyclides in surface and solid modeling, IEEE Comput. Graph. Appl. 13 (1993), pp. 53–59. doi: 10.1109/38.180118
  • A.R. Forsyth, Lecture on Differential Geometry of Curves and Surfaces, Cambridge University Press, Cambridge, 1912.
  • L. Garnier, Mathématiques pour la modélisation géométrique, la représentation 3D et la synthèse d'images, Ellipses, Paris, France, 2007.
  • L. Garnier, S. Foufou, and M. Neveu, Blending of surfaces of revolution and planes by Dupin cyclides, in Geometric Modeling and Computing [Proc. book of the 8th SIAM Conference on Geometric Design and Computing, Seattle, USA,Nov. 2003], Nashboro Press, Nashville, 2004.
  • U. Hertrich-Jeromin, Introduction to Mobius Differential Geometry, London Mat. Soc. Lecture note, Cambridge University Press xii, 2003, p. 300.
  • R. Langevin and J. O'Hara, Conformally invariant energies of knots, J. Inst. Math. Jussieu 4 (2005), pp. 219–280. doi: 10.1017/S1474748005000058
  • R. Langevin and J. O'Hara, Conformal arc-length via osculating circles, Rapport de recherche IMB 531, 2008.
  • R. Langevin and G. Solanes, The geometry of canal surfaces and the length of curves in de sitter space, Adv. Geom. 11 (2011), pp. 585–601. doi: 10.1515/advgeom.2011.026
  • R. Langevin and P. Walczak, Conformal geometry of foliations, Geom. Dedicata 132 (2008), pp. 135–178. doi: 10.1007/s10711-007-9213-1
  • R.R. Martin, Principal patches for computational geometry, Ph.D. thesis, Engineering Department, Cambridge University, 1982.
  • M. Paluszny and W. Boehm, General cyclides, Comput. Aided Geom. Design 15 (1998), pp. 699–710. doi: 10.1016/S0167-8396(98)00011-9
  • M.J. Pratt, Cyclides in computer aided geometric design, Comput. Aided Geom. Design 7 (1990), pp. 221–242. doi: 10.1016/0167-8396(90)90033-N
  • T.J. Sharrock, Biarcs in three dimensions, in Proceedings of the 2nd Conference on the Mathematics of Surfaces, Clarendon Press New York, NY, 1987, pp. 395–411.
  • J. Smutny, Global radii of curvature and the biarc approximation of spaces curves: In pursuit of ideal knot shapes, Ph.D. thesis, EPF Lausanne, 2004.

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.