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Implicitization of bihomogeneous parametrizations of algebraic surfaces via linear syzygies

Published: 29 July 2007 Publication History

Abstract

We show that the implicit equation of a surface in 3-dimensional projective space parametrized by bi-homogeneous polynomials of bi-degree (d,d)for a given integer d ≥1 can be represented and computed from the linear syzygies of its parametrization if the base points are isolated and form locally a complete intersection.

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Cited By

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  • (2023)An Algorithm to Compute the $$\mu $$-Bases of Rational Parametric Surfaces with Respect to One VariableCommunications in Mathematics and Statistics10.1007/s40304-022-00300-y12:3(523-541)Online publication date: 13-Feb-2023
  • (2021)A Constructive Approach to Implicitizing Rational Surfaces with LCI Base Points by Moving Planes and Moving QuadricsComputer Aided Geometric Design10.1016/j.cagd.2021.102051(102051)Online publication date: Nov-2021
  • (2020)Fibers of Multi-Graded Rational Maps and Orthogonal Projection onto Rational SurfacesSIAM Journal on Applied Algebra and Geometry10.1137/19M12895224:2(322-353)Online publication date: 8-Jun-2020
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cover image ACM Conferences
ISSAC '07: Proceedings of the 2007 international symposium on Symbolic and algebraic computation
July 2007
406 pages
ISBN:9781595937438
DOI:10.1145/1277548
  • General Chair:
  • Dongming Wang
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 29 July 2007

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Author Tags

  1. approximation complexes
  2. implicitization
  3. linear syzygies

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ISSAC07
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ISSAC07: International Symposium on Symbolic and Algebraic Computation
July 29 - August 1, 2007
Ontario, Waterloo, Canada

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Overall Acceptance Rate 395 of 838 submissions, 47%

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Cited By

View all
  • (2023)An Algorithm to Compute the $$\mu $$-Bases of Rational Parametric Surfaces with Respect to One VariableCommunications in Mathematics and Statistics10.1007/s40304-022-00300-y12:3(523-541)Online publication date: 13-Feb-2023
  • (2021)A Constructive Approach to Implicitizing Rational Surfaces with LCI Base Points by Moving Planes and Moving QuadricsComputer Aided Geometric Design10.1016/j.cagd.2021.102051(102051)Online publication date: Nov-2021
  • (2020)Fibers of Multi-Graded Rational Maps and Orthogonal Projection onto Rational SurfacesSIAM Journal on Applied Algebra and Geometry10.1137/19M12895224:2(322-353)Online publication date: 8-Jun-2020
  • (2019)Implicitization of rational hypersurfaces via linear syzygiesJournal of Symbolic Computation10.1016/j.jsc.2015.09.00174:C(493-512)Online publication date: 3-Jan-2019
  • (2018)Survey on the theory and applications of -bases for rational curves and surfacesJournal of Computational and Applied Mathematics10.1016/j.cam.2017.07.023329:C(2-23)Online publication date: 1-Feb-2018
  • (2018)Matrix representations for toric parametrizationsComputer Aided Geometric Design10.1016/j.cagd.2009.03.00526:7(757-771)Online publication date: 31-Dec-2018
  • (2009)Curve/surface intersection problem by means of matrix representationsProceedings of the 2009 conference on Symbolic numeric computation10.1145/1577190.1577205(71-78)Online publication date: 3-Aug-2009

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