Implicit equations of non-degenerate rational Bezier quadric triangles

Cantón Pire, Alicia and Fernández Jambrina, Leonardo and Rosado María, María Eugenia and Vázquez Gallo, María Jesús (2015). Implicit equations of non-degenerate rational Bezier quadric triangles. "Lecture Notes in Computer Science", v. 9213 ; pp. 70-79. ISSN 0302-9743. https://doi.org/10.1007/978-3-319-22804-4_6.

Description

Title: Implicit equations of non-degenerate rational Bezier quadric triangles
Author/s:
  • Cantón Pire, Alicia
  • Fernández Jambrina, Leonardo
  • Rosado María, María Eugenia
  • Vázquez Gallo, María Jesús
Item Type: Article
Título de Revista/Publicación: Lecture Notes in Computer Science
Date: August 2015
ISSN: 0302-9743
Volume: 9213
Subjects:
Freetext Keywords: Quadric, Steiner surfaces, Rational Bézier triangles
Faculty: E.T.S.I. Navales (UPM)
Department: Matemática e Informática Aplicadas a la Ingenierías Civil y Naval
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

In this paper we review the derivation of implicit equations for non-degenerate quadric patches in rational Bézier triangular form. These are the case of Steiner surfaces of degree two. We derive the bilinear forms for such quadrics in a coordinate-free fashion in terms of their control net and their list of weights in a suitable form. Our construction relies on projective geometry and is grounded on the pencil of quadrics circumscribed to a tetrahedron formed by vertices of the control net and an additional point which is required for the Steiner surface to be a non-degenerate quadric.

More information

Item ID: 44513
DC Identifier: http://oa.upm.es/44513/
OAI Identifier: oai:oa.upm.es:44513
DOI: 10.1007/978-3-319-22804-4_6
Official URL: https://link.springer.com/chapter/10.1007/978-3-319-22804-4_6
Deposited by: Memoria Investigacion
Deposited on: 27 Jun 2017 07:42
Last Modified: 27 Jun 2017 07:42
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