The offset to an algebraic curve and an application to conics

Authors:
François Anton;Ioannis Emiris;Bernard Mourrain;Monique Teillaud
Affiliations:
Department of Computer Science, University of Calgary, Calgary, Alberta, Canada;Department of Informatics and Telecommunications, National Kapodistrian University of Athens, Panepistimiopolis, Greece;INRIA Sophia-Antipolis, Sophia-Antipolis, France;INRIA Sophia-Antipolis, Sophia-Antipolis, France
Venue:
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
Year:
2005

Citing 4
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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.