Observatorio de I+D+i UPM

Memorias de investigación
Ponencias en congresos:
Bilinear forms for quadrics in rational Bézier triangular representation
Año:2014
Áreas de investigación
  • Matemáticas,
  • Aplicaciones a ingenierías y ciencias de la información
Datos
Descripción
In this paper we classify and derive closed formulas for geometric elements of quadrics in rational Bézier triangular form (such as the center, the conic at infinity, the vertex and the axis of paraboloids and the principal planes), using just the control vertices and the weights for the quadric patch. The results are extended also to quadric tensor product patches. Our results rely on using techniques from projective algebraic geometry to find suitable bilinear forms for the quadric in a coordinate-free fashion, considering a pencil of quadrics that are tangent to the given quadric along a conic. Most of the information about the quadric is encoded in one coefficient, involving the weights of the patch, which allows us to tell apart oval from ruled quadrics. This coefficient is also relevant to determine the affine type of the quadric. Spheres and quadrics of revolution are characterised within this framework.
Internacional
Si
Nombre congreso
Building Mathematics and Mutual Understanding
Tipo de participación
960
Lugar del congreso
Madrid
Revisores
Si
ISBN o ISSN
1072-6691
DOI
Fecha inicio congreso
14/07/2014
Fecha fin congreso
15/07/2014
Desde la página
0
Hasta la página
0
Título de las actas
2014 Madrid Conference on Applied Mathematics in honor of Alfonso Casal, Electron. J. Diff. Eqns., Conference 22 (2015)
Esta actividad pertenece a memorias de investigación
Participantes
  • Autor: Leonardo Fernandez Jambrina (UPM)
Grupos de investigación, Departamentos, Centros e Institutos de I+D+i relacionados
  • Creador: Departamento: Matemática e Informática Aplicadas a la Ingenierías Civil y Naval
S2i 2021 Observatorio de investigación @ UPM con la colaboración del Consejo Social UPM
Cofinanciación del MINECO en el marco del Programa INNCIDE 2011 (OTR-2011-0236)
Cofinanciación del MINECO en el marco del Programa INNPACTO (IPT-020000-2010-22)