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A Constructive Algorithm for Transforming Conics in a Circle on Imaginary Laguerre Points

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Bibliographic Details
Title: A Constructive Algorithm for Transforming Conics in a Circle on Imaginary Laguerre Points
Authors: Elena Boyashova, Denis Voloshinov, Tatyana Musaeva
Source: Proceedings of the 31th International Conference on Computer Graphics and Vision. Volume 2. :673-681
Publisher Information: Keldysh Institute of Applied Mathematics, 2021.
Publication Year: 2021
Subject Terms: 0101 mathematics, 01 natural sciences, 0104 chemical sciences
Description: The article is devoted to the consideration of the properties of Laguerre points in their constructive relationship with the solution of the problem of transforming a pair of conical curves into two circles. Geometric schemes are presented that reveal the principle of specifying a collinear transformation that establishes a correspondence between conics and their images in the form of circles, including if the Laguerre points defining this transformation are imaginary. In the solution of the problem, a geometric scheme for the formation of the main conjugations of conics is given, one of which is a circle. The conclusion is substantiated that the radical axis of the bundle of circles is a circle that has split into a pair of straight lines, one of which is infinitely distant. An algorithm for the formation of a series of elliptic curves induced by Laguerre points is presented.
Document Type: Article
DOI: 10.20948/graphicon-2021-3027-673-681
Accession Number: edsair.doi...........2888a6fd3cd2fed9e922f83e23c99b4f
Database: OpenAIRE
Description
Abstract:The article is devoted to the consideration of the properties of Laguerre points in their constructive relationship with the solution of the problem of transforming a pair of conical curves into two circles. Geometric schemes are presented that reveal the principle of specifying a collinear transformation that establishes a correspondence between conics and their images in the form of circles, including if the Laguerre points defining this transformation are imaginary. In the solution of the problem, a geometric scheme for the formation of the main conjugations of conics is given, one of which is a circle. The conclusion is substantiated that the radical axis of the bundle of circles is a circle that has split into a pair of straight lines, one of which is infinitely distant. An algorithm for the formation of a series of elliptic curves induced by Laguerre points is presented.
DOI:10.20948/graphicon-2021-3027-673-681