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Implicitization and Offsetting via Regular Systems

Identifieur interne : 003912 ( Crin/Curation ); précédent : 003911; suivant : 003913

Implicitization and Offsetting via Regular Systems

Auteurs : Dongming Wang

Source :

RBID : CRIN:wang03e

English descriptors

Abstract

Given a geometric object defined by rational parametric equations, we show how to compute a disjunction of implicit equations and inequations that define exactly the same object by means of regular systems. The same technique is applied to the computation of quasi-offsets to algebraic curves and surfaces. Regular systems possess the projection property, are relatively easy to compute, and often have a compact form. Several examples are given to illustrate our approach based on the decomposition of polynomial systems into regular systems. A heuristic method is presented to simplify the output disjunction of polynomial equations and inequations.

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Le document en format XML

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<front>
<div type="abstract" xml:lang="en" wicri:score="1555">Given a geometric object defined by rational parametric equations, we show how to compute a disjunction of implicit equations and inequations that define exactly the same object by means of regular systems. The same technique is applied to the computation of quasi-offsets to algebraic curves and surfaces. Regular systems possess the projection property, are relatively easy to compute, and often have a compact form. Several examples are given to illustrate our approach based on the decomposition of polynomial systems into regular systems. A heuristic method is presented to simplify the output disjunction of polynomial equations and inequations.</div>
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</TEI>
<BibTex type="incollection">
<ref>wang03e</ref>
<crinnumber>A03-R-177</crinnumber>
<category>11</category>
<equipe>SPACES</equipe>
<author>
<e>Wang, Dongming</e>
</author>
<title>Implicitization and Offsetting via Regular Systems</title>
<booktitle>{Geometric Computation}</booktitle>
<publisher>World Scientific, Singapore New Jersey</publisher>
<year>2003</year>
<editor>Chen, Falai and Wang, Dongming</editor>
<chapter>5</chapter>
<pages>156-176</pages>
<month>Dec</month>
<keywords>
<e>regular system</e>
<e>implicitization</e>
<e>offsetting</e>
</keywords>
<abstract>Given a geometric object defined by rational parametric equations, we show how to compute a disjunction of implicit equations and inequations that define exactly the same object by means of regular systems. The same technique is applied to the computation of quasi-offsets to algebraic curves and surfaces. Regular systems possess the projection property, are relatively easy to compute, and often have a compact form. Several examples are given to illustrate our approach based on the decomposition of polynomial systems into regular systems. A heuristic method is presented to simplify the output disjunction of polynomial equations and inequations.</abstract>
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