Abstract
There are several ways to define a curve in the plane. For example, explicitly parameterized as a continuous function f:[0,1]→ℝ2, or (as in the case of an affine algebraic curve) implicitly as the zero set of a bivariate polynomial. For some technical applications, there are different ways of representing a curve which are more useful in those contexts, for example the representation as a Bézier curve in computer aided design (CAD). A different approach is necessary when we want to represent curves which are the result of a measurement, i.e., when they are only partially known, or the description is not exact.
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Althaus, E., Mehlhorn, K.: Traveling Salesman-based curve reconstruction in polynomial time. SIAM J. Comput. 31(1), 27–66 (2001)
Amenta, N., Bern, M., Eppstein, D.: The crust and the β-skeleton: combinatorial curve reconstruction. Graph. Models Image Process. 60, 125–136 (1998)
Blum, H.: A transformation for extracting new descriptors of shape. In: Whaten-Dunn, W. (ed.) Proc. Symposium on Models for the Perception of Speech and Visual Form, pp. 362–380. MIT Press, Cambridge (1967)
Dey, T.K., Kumar, P.: A simple provable algorithm for curve reconstruction. In: Proc. Symposium on Discrete Algorithms, Baltimore, MD, pp. 893–894 (1999)
Hobby, J.:
. http://cm.bell-labs.com/who/hobby/MetaPost.html
O’Neill, B.: Elementary Differential Geometry, 2nd edn. Elsevier/Academic Press, Amsterdam (2006)
Pressley, A.: Elementary Differential Geometry, 2nd edn. Springer Undergraduate Mathematics Series. Springer, London (2010)
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Joswig, M., Theobald, T. (2013). Reconstruction of Curves. In: Polyhedral and Algebraic Methods in Computational Geometry. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-4817-3_11
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DOI: https://doi.org/10.1007/978-1-4471-4817-3_11
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