Keywords
implicit modelling
closed surface
algebraic surface
interactive deformation
lemniscata
modelación implícita
superficie cerrada
superficie algebraica
deformación interactiva
How to Cite
Abstract
A 3D lemniscate is a surface consisting of all points whose product of distances to a (finite) set of points or foci is constant. We introduce 3D lemniscates in the context of geometric modelling and consider its deformation, paying attention to disconnectedness issues. We deal mainly with lemniscates of three foci.
References
Catanese, F.; Paluszny, M. (1991) “Polynomial lemniscates trees and braids”, Topology 30: 623–640.
Erdös, P. (1976) “Extremal problems on polynomials”, in: G.Lorentz, C.Chui y L. Schumaker (Eds), Approximation Theory II, Academic Press, New York: 347–355.
Markushevich, A. (1970) Teoŕıa de las Funciones Anaĺıticas. Tomo I. Editorial Mir. Moscú.
Marden, M. (1966) Geometry of Polynomials. Mathematical Surveys, AMS, Providence RI.
Paluszny, M. (1984) “On periodic solutions of polynomial ODE’s in the plane”, J. Differential Equations 53: 24–29.
Yánez, E. (1999) “Deformable orthogonal grids: lemniscates”, J. Computational and Applied Mathematics 104: 41–48.
Walsh, J.L. (1985) Interpolation and Approximation byRational Functions in the Complex Domain. AMS Colloquium Publications, Vol XX, Providence RI.