Abstract
Classes of curves like par-regularity, \(\mu \)-reach, locally turn boundedness, quasi-regularity (and their generalizations) have been defined so as to guarantee geometrical or topological properties under discretization. An overview of their inter-relations is given. A focus is made on the Locally Turn Bounded (LTB) curves, a class having good discretization properties. It has already been shown that being LTB implies quasi-regularity. In this paper, it is shown that the LTB curves have a positive \(\mu \)-reach. Moreover, we show that a LTB curve having a Lipschitz turn is par-regular.
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Le Quentrec, É., Baudrier, É., Jacquot, C. (2024). A Survey on 2D Euclidean Curve Classes in Discrete Geometry with New Results. In: Brunetti, S., Frosini, A., Rinaldi, S. (eds) Discrete Geometry and Mathematical Morphology. DGMM 2024. Lecture Notes in Computer Science, vol 14605. Springer, Cham. https://doi.org/10.1007/978-3-031-57793-2_31
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DOI: https://doi.org/10.1007/978-3-031-57793-2_31
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