Analytic properties of plane offset curves
Computer Aided Geometric Design
Algebraic properties of plane offset curves
Computer Aided Geometric Design
Rational curves and surfaces with rational offsets
Computer Aided Geometric Design
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Local shape of offsets to algebraic curves
Journal of Symbolic Computation
Good global behavior of offsets to plane algebraic curves
Journal of Symbolic Computation
An algebraic analysis of conchoids to algebraic curves
Applicable Algebra in Engineering, Communication and Computing
Rational parametrization of conchoids to algebraic curves
Applicable Algebra in Engineering, Communication and Computing
Conchoidal transform of two plane curves
Applicable Algebra in Engineering, Communication and Computing
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The classical conchoid construction, well-known in Mathematics since its introduction more than 2200 years ago, has been recently revisited in the context of algebraic curves. Partially, the motivation for this has been the analogy, up to a certain extent, between the conchoid and a well-known transformation in CAGD, namely the offset transformation. In this paper, we contribute to this study by addressing properties on the shape of conchoids to plane algebraic curves. For this purpose we introduce the notions of exterior and interior conchoids, and we compare the shapes of these objects with that of the original curve.