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Cyclides and the guiding circle. (English) Zbl 1103.65020

Summary: Using the fact that spheres of 3D correspond to points in 4-dimensional space which lie outside a certain quadric, we introduce a new shape handle that permits the control of general cyclides: the guiding circle. A general cyclide is the envelope of a quadratic family of spheres which in this context is a conic in 4-dimensional space. The guiding circle is associated to the cyclide via the plane of the conic that corresponds to the cyclide.

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)
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References:

[1] Boehm, W., On cyclides in geometric modeling, Comput. Aided Geom. Des., 7, 243-255 (1995) · Zbl 0712.65009
[2] Dutta, D.; Srinivas, Y., Motion planning in three dimensions using cyclides, Vis. Comput., 781-791 (1992)
[3] Dutta, D.; Srinivas, Y., Rational parametric representation of a parabolic cyclide: formulation and applications, Comput. Aided Geom. Des., 12, 551-566 (1995) · Zbl 0875.68854
[4] J. Franquiz, M. Paluszny, F. Tovar, Cyclides, their tangency and deformation, in: J. Rojo, M.J. Torres, M. Cerrolaza (Eds.), Simulación Numérica y Modelado Computacional, San Cristóbal, Táchira, 2004, pp. TM 41-TM 48.; J. Franquiz, M. Paluszny, F. Tovar, Cyclides, their tangency and deformation, in: J. Rojo, M.J. Torres, M. Cerrolaza (Eds.), Simulación Numérica y Modelado Computacional, San Cristóbal, Táchira, 2004, pp. TM 41-TM 48.
[5] Paluszny, M.; Boehm, W., General cyclides, Comput. Aided Geom. Des., 15, 699-710 (1998) · Zbl 0905.68155
[6] Pratt, M., Cyclides in computer aided geometric design, Comput. Aided Geom. Des., 7, 221-242 (1990) · Zbl 0712.65008
[7] Shene, C., Blending two cones with Dupin cyclides, Comput. Aided Geom. Des., 15, 643-673 (1998) · Zbl 0905.68151
[8] Vilanova, A.; König, A.; Gröller, E., Cylindrical approximation of tubular organs for virtual endoscopy, (Proceedings Computer Graphics and Imaging (CGIM). Proceedings Computer Graphics and Imaging (CGIM), Las Vegas, NV (2000)), 283-289
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