Abstract
We show that the set of local maxima of the distance function to a set of points P in the plane, given certain density and packing restrictions, is also dense.
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References
A.I. Bobenko, B. Springborn, A discrete Laplace-Beltrami operator for simplicial surfaces. Discret. Comput. Geom. 38(4), 740–756 (2007)
J.-D. Boissonnat, A. Ghosh, Manifold reconstruction using tangential Delaunay complexes. Discret. Comput. Geom. 51(1), 221–267 (2014)
J.-D. Boissonnat, L.J. Guibas, S. Oudot, Manifold reconstruction in arbitrary dimensions using witness complexes. Discret. Comput. Geom. 42(1), 37–70 (2009)
J.-D. Boissonnat, R. Dyer, A. Ghosh, Stability of Delaunay-type structures for manifolds [extended abstract], in Symposuim on Computational Geometry 2012, SoCG ’12, Chapel Hill, 17–20 June 2012 (2012), pp. 229–238
T.K. Dey, J. Giesen, E.A. Ramos, B. Sadri, Critical points of the distance to an epsilon-sampling of a surface and flow-complex-based surface reconstruction, in Proceedings of the 21st ACM Symposium on Computational Geometry, Pisa, 6–8 June 2005 (2005), pp. 218–227
R. Dyer, H. Zhang, T. Möller, Delaunay mesh construction, in Proceedings of the Fifth Eurographics Symposium on Geometry Processing, Barcelona, 4–6 July 2007 (2007), pp. 273–282
R. Dyer, G. Vegter, M. Wintraecken, Riemannian simplices and triangulations, in 31st International Symposium on Computational Geometry, SoCG 2015, Eindhoven, 22–25 June 2015 (2015), pp. 255–269
H. Edelsbrunner, Surface reconstruction by wrapping finite sets in space. Algorithms Comb. 25, 379–404 (2003)
J. Giesen, M. John, The flow complex: a data structure for geometric modeling. Comput. Geom. 39(3), 178–190 (2008)
M. Khoury, J.R. Shewchuk, Fixed points of the restricted Delaunay triangulation operator, in 32nd International Symposium on Computational Geometry, SoCG 2016, Boston, 14–18 June 2016 (2016), pp. 47:1–47:15
S. Oudot, On the topology of the restricted delaunay triangulation and witness complex in higher dimensions. CoRR, abs/0803.1296 (2008)
E.A. Ramos, B. Sadri, Geometric and topological guarantees for the WRAP reconstruction algorithm, in Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007, New Orleans, 7–9 January 2007 (2007), pp. 1086–1095
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Amenta, N., Chambers, E.W., Emerson, T., Glover, R., Turner, K., Yap, S. (2018). Density of Local Maxima of the Distance Function to a Set of Points in the Plane. In: Chambers, E., Fasy, B., Ziegelmeier, L. (eds) Research in Computational Topology. Association for Women in Mathematics Series, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-319-89593-2_7
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DOI: https://doi.org/10.1007/978-3-319-89593-2_7
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