A new approach to characterizing the relative position of two ellipses depending on one parameter

By using several tools coming from Real Algebraic Geometry, Computer Algebra and Projective Geometry (Sturm–Habicht sequences and the classification of pencils of conics in P 2 ( R ) ), a new approach for characterizing the ten relative positions of two ellipses is introduced. Each relative position...

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Bibliographic Details
Published inComputer aided geometric design Vol. 23; no. 4; pp. 324 - 350
Main Authors Etayo, Fernando, Gonzalez-Vega, Laureano, del Rio, Natalia
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.05.2006
Elsevier
Subjects
Applied sciences
Computer aided design
Computer science; control theory; systems
Exact sciences and technology
Mechanical engineering. Machine design
Software
Conics
Classification
Geometrical projection
Computer algebra
Computer aided design
Algebraic geometry
Projective geometry
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Summary:By using several tools coming from Real Algebraic Geometry, Computer Algebra and Projective Geometry (Sturm–Habicht sequences and the classification of pencils of conics in P 2 ( R ) ), a new approach for characterizing the ten relative positions of two ellipses is introduced. Each relative position is exclusively characterized by a set of equalities and inequalities depending only on the matrices defining the two considered ellipses and does not require in advance the computation or knowledge of the intersection points between them. Moreover, this characterization is specially well adapted for computionally treating the case where the considered ellipses depend on one or several parameters.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0167-8396
1879-2332
DOI:10.1016/j.cagd.2006.01.002