Geodesic
Ortho-Circles of Dupin Cyclides
Journal for geometry and graphics, Tome 10 (2006) no. 1, pp. 73-98 Cet article a éte moissonné depuis la source Heldermann Verlag

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We study the set of circles which intersect a Dupin cyclide in at least two different points orthogonally. Dupin cyclides can be obtained by inverting a cylinder, or cone of revolution, or by inverting a torus. Since orthogonal intersection is invariant under M�bius transformations we first study the ortho-circles of cylinder/cone of revolution and tori and transfer the results afterwards.
Classification : 53A05, 51N20, 51N35
Mots-clés : Ortho-circle, double normal, Dupin cyclide, torus, inversion 
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     author = {M. Schrott and B. Odehnal },
     title = {Ortho-Circles of {Dupin} {Cyclides}},
     journal = {Journal for geometry and graphics},
     pages = {73--98},
     year = {2006},
     volume = {10},
     number = {1},
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}
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M. Schrott; B. Odehnal . Ortho-Circles of Dupin Cyclides. Journal for geometry and graphics, Tome 10 (2006) no. 1, pp. 73-98. http://geodesic.mathdoc.fr/item/JGG_2006_10_1_JGG_2006_10_1_a5/