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...
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| 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 |
| 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. |
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