Classification of pairs of natural quadrics from the point of view of Laguerre geometry |
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Authors: | M Kazakevi?iūt? |
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Institution: | (1) Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania |
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Abstract: | The problem of classification of pairs of natural quadrics (spheres, circular cones and circular cylinders) arises in problems such as the blending of two or more natural quadrics using canal surfaces. In this paper, considering this problem from the point of view of Laguerre geometry, we reduce it to the classification of point/line and line/line pairs in the pseudo-Euclidean space with Lorenz metrics. We establish equations of the surfaces of centers for all canonical positions and their projective equivalence with toric surfaces.__________Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 1, pp. 64–83, January–March, 2005.Translated by M. Kazakeviit |
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Keywords: | Laguerre geometry pseudo-Euclidean space orthogonalization natural quadrics canal blending surface bisector surface toric surface |
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