Cyclides and the guiding circle

Authors:
J. Franquiz;M. Paluszny;F. Tovar
Affiliations:
Laboratorio de Computación Gráfica y Geometría Aplicada, Universidad Central de Venezuela, Los Chaguaramos, Caracas, Venezuela;Laboratorio de Computación Gráfica y Geometría Aplicada, Universidad Central de Venezuela, Los Chaguaramos, Caracas, Venezuela;Laboratorio de Computación Gráfica y Geometría Aplicada, Universidad Central de Venezuela, Los Chaguaramos, Caracas, Venezuela
Venue:
Mathematics and Computers in Simulation - Special issue: Applied and computational mathematics - selected papers of the fifth PanAmerican workshop - June 21-25, 2004, Tegucigalpa, Honduras
Year:
2006

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Abstract

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.