Applications of Gröbner Bases in Non-Linear Computational Geometry

  • Bruno Buchberger
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 14)


Gröbner bases are certain finite sets of multivariate polynomials. Many problems in polynomial ideal theory (algebraic geometry, non-linear computational geometry) can be solved by easy algorithms after transforming the polynomial sets involved in the specification of the problems into Gröbner basis form. In this paper we give some examples of applying the Gröbner bases method to problems in non-linear computational geometry (inverse kinematics in robot programming, collision detection for superellipsoids, implicitization of parametric representations of curves and surfaces, inversion problem for parametric representations, automated geometrical theorem proving, primary decomposition of implicitly defined geometrical objects). The paper starts with a brief summary of the Gröbner bases method.


Prime Ideal Parametric Representation Common Zero Implicit Equation Primary Decomposition 
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Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • Bruno Buchberger
    • 1
  1. 1.RISC-LINZ (Research Institute for Symbolic Computation)Johannes Kepler UniversityLinzAustria

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