Dupin cyclides

Introduction: We will study the problem of finding a Dupin cyclide given three contact conditions. A contact condition is a point m in R3 and an orientation at that point, i.e., a vector with initial point m, this vector can be seen as the normal vector of an oriented plane through m. A Dupin cyclid...

Descripción completa

Detalles Bibliográficos
Autor: Villa Isaza, Alejandro Alberto
Tipo de recurso: tesis de maestría
Estado:Versión aceptada para publicación
Fecha de publicación:2014
País:Colombia
Institución:Universidad Nacional de Colombia
Repositorio:Repositorio UN
Idioma:español
OAI Identifier:oai:repositorio.unal.edu.co:unal/51894
Acceso en línea:https://repositorio.unal.edu.co/handle/unal/51894
http://bdigital.unal.edu.co/46120/
Access Level:acceso abierto
Palabra clave:51 Matemáticas / Mathematics
Dupin cyclides
Surfaces
Descripción
Sumario:Introduction: We will study the problem of finding a Dupin cyclide given three contact conditions. A contact condition is a point m in R3 and an orientation at that point, i.e., a vector with initial point m, this vector can be seen as the normal vector of an oriented plane through m. A Dupin cyclide that, historically, is defined as the envelope of a family of spheres which are simultaneously tangent to three given spheres, can be defined in the context of the projective five-dimensional space as 2-plane section of a quadric in this projective space. The points of this quadric correspond to oriented spheres in 3D.