The Offset to an Algebraic Curve and an Application to Conics

François Anton 1 Ioannis Z. Emiris 2 Bernard Mourrain 3 Monique Teillaud 3
3 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
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.
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François Anton, Ioannis Z. Emiris, Bernard Mourrain, Monique Teillaud. The Offset to an Algebraic Curve and an Application to Conics. International Conference on Computational Science and its Applications, May 2005, Singapore, Singapore. pp.683-696. ⟨inria-00350878⟩

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