On Ellipse Intersections by Means of Distance Geometry

The problem of intersecting two ellipses arises as a frequent subproblem in computational kinematics and geometry. In this paper, an efficient solution method to this problem is presented using the concept of the power of a point with respect to an ellipse. The point-ellipse power appears in Distanc...

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Detalles Bibliográficos
Autores: Bongardt, Bertold, Thomas, Federico
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2023
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/355057
Acceso en línea:http://hdl.handle.net/10261/355057
https://api.elsevier.com/content/abstract/scopus_id/85177061103
Access Level:acceso abierto
Palabra clave:Computational kinematics
Distance geometry
Ellipse constellations
Power of a point with respect to an ellipse
Squared distances
Descripción
Sumario:The problem of intersecting two ellipses arises as a frequent subproblem in computational kinematics and geometry. In this paper, an efficient solution method to this problem is presented using the concept of the power of a point with respect to an ellipse. The point-ellipse power appears in Distance Geometry as a generalization to the squared distance between two points. For establishing the intersection method, several algebraic forms of ellipses are reviewed and the interoperability of distinct definitions for the power of points and ellipses is outlined.