Implicitization of curves and surfaces using predicted support

Authors:
Ioannis Z. Emiris;Tatjana Kalinka;Christos Konaxis
Affiliations:
University of Athens, Athens, Greece;University of Athens, Athens, Greece;University of Athens, Athens, Greece
Venue:
Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Year:
2012

Citing 6
Cited 3

On the Newton Polytope of the Resultant

Journal of Algebraic Combinatorics: An International Journal
Implicitization of parametric curves and surfaces by using multidimensional Newton formulae

Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Numerical Implicitization of Parametric Hypersurfaces with Linear Algebra

AISC '00 Revised Papers from the International Conference on Artificial Intelligence and Symbolic Computation
Implicitization of rational surfaces by means of polynomial interpolation

Computer Aided Geometric Design
Implicit polynomial support optimized for sparseness

ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
An implicitization challenge for binary factor analysis

Journal of Symbolic Computation

An output-sensitive algorithm for computing projections of resultant polytopes

Proceedings of the twenty-eighth annual symposium on Computational geometry
Sparse implicitization by interpolation: Characterizing non-exactness and an application to computing discriminants

Computer-Aided Design
Implicitization of curves and (hyper)surfaces using predicted support

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

Abstract

We reduce implicitization of rational parametric curves and (hyper)surfaces to linear algebra, by interpolating the coefficients of the implicit equation. For this, we may use any method for predicting the implicit support. We focus on methods that exploit input structure in the sense of sparse (or toric) elimination theory, namely by computing the Newton polytope of the implicit polynomial. We offer a public-domain implementation of our methods, and study their numerical stability and efficiency on several classes of plane curves and surfaces, and discuss how it can be used for approximate implicitization in the setting of sparse elimination.