Trends in Computer Algebra pp 52-80 | Cite as

# Applications of Gröbner bases in non-linear computational geometry

## Abstract

*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.

## Keywords

Prime Ideal Parametric Representation Common Zero Implicit Equation Primary Decomposition## Preview

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