Implicitization and Distance Bounds

Ibolya Szilagyi; Martin Aigner; Josef Schicho; Bert Jüttler

Implicitization and Distance Bounds

Ibolya Szilagyi
, Martin Aigner
, Josef Schicho
, Bert Jüttler

Research Institute for Symbolic Computation

Research output: Chapter in Book/Report/Conference proceeding › Conference proceedings › peer-review

Abstract

In this paper, we combine results concerning the numerical stability of the implicitization process for a given planar rational curve, with results on the the stability of the resulting implicit representation. More precisely, it is shown that for any approximate parameterization of the given curve, the curve obtained by an approximate implicitization with a given precision is contained within a certain perturbation region. The results can be generalized to the case of surfaces.

Original language	English
Title of host publication	Mathematic and Visualization
Editors	M. Elkadi
Publisher	Springer
Pages	1-14
Number of pages	14
Publication status	Published - 2005

Publication series

Name	Mathematics and Visualization

Fields of science

101 Mathematics
101001 Algebra
101005 Computer algebra
101009 Geometry
101012 Combinatorics
101013 Mathematical logic
101020 Technical mathematics

Cite this

@inproceedings{5652a4318471488aa314c07a6453c68e,

title = "Implicitization and Distance Bounds",

abstract = "In this paper, we combine results concerning the numerical stability of the implicitization process for a given planar rational curve, with results on the the stability of the resulting implicit representation. More precisely, it is shown that for any approximate parameterization of the given curve, the curve obtained by an approximate implicitization with a given precision is contained within a certain perturbation region. The results can be generalized to the case of surfaces.",

author = "Ibolya Szilagyi and Martin Aigner and Josef Schicho and Bert J{\"u}ttler",

year = "2005",

language = "English",

series = "Mathematics and Visualization",

publisher = "Springer",

pages = "1--14",

editor = "\{M. Elkadi\}",

booktitle = "Mathematic and Visualization",

}

TY - GEN

T1 - Implicitization and Distance Bounds

AU - Szilagyi, Ibolya

AU - Aigner, Martin

AU - Schicho, Josef

AU - Jüttler, Bert

PY - 2005

Y1 - 2005

N2 - In this paper, we combine results concerning the numerical stability of the implicitization process for a given planar rational curve, with results on the the stability of the resulting implicit representation. More precisely, it is shown that for any approximate parameterization of the given curve, the curve obtained by an approximate implicitization with a given precision is contained within a certain perturbation region. The results can be generalized to the case of surfaces.

AB - In this paper, we combine results concerning the numerical stability of the implicitization process for a given planar rational curve, with results on the the stability of the resulting implicit representation. More precisely, it is shown that for any approximate parameterization of the given curve, the curve obtained by an approximate implicitization with a given precision is contained within a certain perturbation region. The results can be generalized to the case of surfaces.

M3 - Conference proceedings

T3 - Mathematics and Visualization

SP - 1

EP - 14

BT - Mathematic and Visualization

A2 - M. Elkadi, null

PB - Springer

ER -