The offset to an algebraic curve and an application to conics

François Anton; Ioannis Emiris; Bernard Mourrain; Monique Teillaud

The offset to an algebraic curve and an application to conics

François Anton
, Ioannis Emiris
, Bernard Mourrain
, Monique Teillaud

National and Kapodistrian University of Athens
French National Institute for Computer Science and Applied Mathematics
University of Calgary

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

Abstract

Curve offsets are important objects in computer-aided design. We study the algebraic properties of the offset to an algebraic curve, thus obtaining a general formula for its degree. This is applied to computing the degree of the offset to conics. We also compute an implicit equation of the generalised offset to a conic by using sparse resultants and the knowledge of the degree of the implicit equation.

Original language	English
Title of host publication	Lecture Notes in Computer Science
Volume	3480
Publisher	Springer Berlin / Heidelberg
Publication date	2005
Pages	683-696
Publication status	Published - 2005
Externally published	Yes

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title = "The offset to an algebraic curve and an application to conics",

abstract = "Curve offsets are important objects in computer-aided design. We study the algebraic properties of the offset to an algebraic curve, thus obtaining a general formula for its degree. This is applied to computing the degree of the offset to conics. We also compute an implicit equation of the generalised offset to a conic by using sparse resultants and the knowledge of the degree of the implicit equation.",

author = "Fran{\c c}ois Anton and Ioannis Emiris and Bernard Mourrain and Monique Teillaud",

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AU - Anton, François

AU - Emiris, Ioannis

AU - Mourrain, Bernard

AU - Teillaud, Monique

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N2 - Curve offsets are important objects in computer-aided design. We study the algebraic properties of the offset to an algebraic curve, thus obtaining a general formula for its degree. This is applied to computing the degree of the offset to conics. We also compute an implicit equation of the generalised offset to a conic by using sparse resultants and the knowledge of the degree of the implicit equation.

AB - Curve offsets are important objects in computer-aided design. We study the algebraic properties of the offset to an algebraic curve, thus obtaining a general formula for its degree. This is applied to computing the degree of the offset to conics. We also compute an implicit equation of the generalised offset to a conic by using sparse resultants and the knowledge of the degree of the implicit equation.

M3 - Book chapter

VL - 3480

SP - 683

EP - 696

BT - Lecture Notes in Computer Science

PB - Springer Berlin / Heidelberg

ER -

The offset to an algebraic curve and an application to conics

Abstract

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