Abstract
We introduce a simple algorithm for constructing a spiral serpentine polygonization of a set S of nāā„ā3 points in the plane. Our algorithm simultaneously gives a triangulation of the constructed polygon at no extra cost, runs in O(n logn) time, and uses O(n) space.
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References
Abellanas, M., GarcĆa, J., HernĆ”ndez-PeƱalver, G., Hurtado, F., Serra, O., Urrutia, J.: Onion Polygonizations. Information Processing LettersĀ 57, 165ā173 (1996)
Agarwal, P.K., Hurtado, F., Toussaint, G.T., Trias, J.: On Polyhedra Induced by Point Sets in Space. Discrete Applied MathematicsĀ 156, 42ā54 (2008)
Arkin, E., Fekete, S.P., Hurtado, F., Mitchell, J.S.B., Noy, M., SacristĆ”n, V., Sethia, S.: On the Reflexivity of Point Sets. In: Discrete and Computational Geometry: The Goodman-Pollack Festschrift, Algorithms and Combinatorics, vol.Ā 25, pp. 139ā156 (2003)
Chazelle, B.: On the Convex Layers of a Planar Set. IEEE Transactions on Information TheoryĀ 31, 509ā517 (1985)
Deneen, L., Shute, G.: Polygonizations of Point Sets in the Plane. Discrete and Computational GeometryĀ 3, 77ā87 (1988)
Fekete, S.P.: On Simple Polygonizations with Optimal Area. Discrete and Computational GeometryĀ 23, 73ā110 (2000)
Graham, R.L.: An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set. Information Processing LettersĀ 1, 132ā133 (1972)
GrĆ¼nbaum, B.: Hamiltonian Polygons and Polyhedra. GeombinatoricsĀ 3, 83ā89 (1994)
Hershberger, J., Suri, S.: Applications of a Semi-Dynamic Convex Hull Algorithm. BIT Numerical MathematicsĀ 32, 249ā267 (1992)
Iwerks, J., Mitchell, J. S. B.: Spiral Serpentine Polygonization of a Planar Point Set. In: Proceedings of XIV Spanish Meeting on Computational Geometry, pp. 181ā184 (2011)
Newborn, M., Moser, W.O.J.: Optimal Crossing-Free Hamiltonian Circuit Drawings of K n . Journal of Combinatorial Theory, Series BĀ 29, 13ā26 (1980)
Quintas, L.V., Supnick, F.: On Some Properties of Shortest Hamiltonian Circuits. American Mathematical MonthlyĀ 72, 977ā980 (1965)
Shamos, M.I., Hoey, D.: Closest-Point Problems. In: Proceedings of the Sixteenth IEEE Symposium on Foundations of Computer Science, pp. 151ā162 (1975)
Steinhaus, H.: One Hundred Problems in Elementary Mathematics. Dover Publications, Inc., New York (1964)
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Iwerks, J., Mitchell, J.S.B. (2012). Spiral Serpentine Polygonization of a Planar Point Set. In: MƔrquez, A., Ramos, P., Urrutia, J. (eds) Computational Geometry. EGC 2011. Lecture Notes in Computer Science, vol 7579. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34191-5_14
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DOI: https://doi.org/10.1007/978-3-642-34191-5_14
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