Observatorio de I+D+i UPM

Memorias de investigación
Research Publications in journals:
Geometric elements and classification of quadrics in rational Bézier form
Year:2016
Research Areas
  • Mathematics,
  • Mechanical aeronautics and naval engineering,
  • Information technology and adata processing,
  • Civil engineering and architecture
Information
Abstract
In this paper we classify and derive closed formulas for geometric elements of quadrics in rational B\'ezier 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.
International
Si
JCR
Si
Title
Journal of Computational And Applied Mathematics
ISBN
0377-0427
Impact factor JCR
1,077
Impact info
Datos JCR del año 2013
Volume
in press
Journal number
From page
xxx
To page
xxx
Month
SIN MES
Ranking
Q1
Participants
  • Autor: Alicia Canton Pire (UPM)
  • Autor: Leonardo Fernandez Jambrina (UPM)
  • Autor: Maria Eugenia Rosado Maria (UPM)
  • Autor: Maria Jesus Vazquez Gallo (UPM)
Research Group, Departaments and Institutes related
  • Creador: Departamento: Matemática Aplicada
S2i 2019 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)