{"_id":"5799","doi":"10.1016/j.dam.2015.11.017","author":[{"last_name":"Biswas","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","full_name":"Biswas, Ranita","first_name":"Ranita","orcid":"0000-0002-5372-7890"},{"last_name":"Bhowmick","first_name":"Partha","full_name":"Bhowmick, Partha"},{"last_name":"Brimkov","first_name":"Valentin E.","full_name":"Brimkov, Valentin E."}],"quality_controlled":"1","title":"On the polyhedra of graceful spheres and circular geodesics","publication":"Discrete Applied Mathematics","publication_status":"published","oa_version":"None","abstract":[{"lang":"eng","text":"We construct a polyhedral surface called a graceful surface, which provides best possible approximation to a given sphere regarding certain criteria. In digital geometry terms, the graceful surface is uniquely characterized by its minimality while guaranteeing the connectivity of certain discrete (polyhedral) curves defined on it. The notion of “gracefulness” was first proposed in Brimkov and Barneva (1999) and shown to be useful for triangular mesh discretization through graceful planes and graceful lines. In this paper we extend the considerations to a nonlinear object such as a sphere. In particular, we investigate the properties of a discrete geodesic path between two voxels and show that discrete 3D circles, circular arcs, and Mobius triangles are all constructible on a graceful sphere, with guaranteed minimum thickness and the desired connectivity in the discrete topological space."}],"date_updated":"2021-01-12T08:03:33Z","volume":216,"extern":"1","type":"journal_article","publication_identifier":{"issn":["0166-218X"]},"intvolume":"       216","language":[{"iso":"eng"}],"status":"public","publisher":"Elsevier","year":"2017","page":"362-375","day":"10","date_published":"2017-01-10T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ieee":"R. Biswas, P. Bhowmick, and V. E. Brimkov, “On the polyhedra of graceful spheres and circular geodesics,” <i>Discrete Applied Mathematics</i>, vol. 216. Elsevier, pp. 362–375, 2017.","ama":"Biswas R, Bhowmick P, Brimkov VE. On the polyhedra of graceful spheres and circular geodesics. <i>Discrete Applied Mathematics</i>. 2017;216:362-375. doi:<a href=\"https://doi.org/10.1016/j.dam.2015.11.017\">10.1016/j.dam.2015.11.017</a>","mla":"Biswas, Ranita, et al. “On the Polyhedra of Graceful Spheres and Circular Geodesics.” <i>Discrete Applied Mathematics</i>, vol. 216, Elsevier, 2017, pp. 362–75, doi:<a href=\"https://doi.org/10.1016/j.dam.2015.11.017\">10.1016/j.dam.2015.11.017</a>.","short":"R. Biswas, P. Bhowmick, V.E. Brimkov, Discrete Applied Mathematics 216 (2017) 362–375.","apa":"Biswas, R., Bhowmick, P., &#38; Brimkov, V. E. (2017). On the polyhedra of graceful spheres and circular geodesics. <i>Discrete Applied Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.dam.2015.11.017\">https://doi.org/10.1016/j.dam.2015.11.017</a>","chicago":"Biswas, Ranita, Partha Bhowmick, and Valentin E. Brimkov. “On the Polyhedra of Graceful Spheres and Circular Geodesics.” <i>Discrete Applied Mathematics</i>. Elsevier, 2017. <a href=\"https://doi.org/10.1016/j.dam.2015.11.017\">https://doi.org/10.1016/j.dam.2015.11.017</a>.","ista":"Biswas R, Bhowmick P, Brimkov VE. 2017. On the polyhedra of graceful spheres and circular geodesics. Discrete Applied Mathematics. 216, 362–375."},"month":"01","date_created":"2019-01-08T20:41:12Z"}