[{"title":"On the polyhedra of graceful spheres and circular geodesics","doi":"10.1016/j.dam.2015.11.017","quality_controlled":"1","publication_identifier":{"issn":["0166-218X"]},"publication_status":"published","day":"10","publisher":"Elsevier","date_updated":"2021-01-12T08:03:33Z","year":"2017","volume":216,"type":"journal_article","month":"01","author":[{"full_name":"Biswas, Ranita","orcid":"0000-0002-5372-7890","id":"3C2B033E-F248-11E8-B48F-1D18A9856A87","last_name":"Biswas","first_name":"Ranita"},{"last_name":"Bhowmick","first_name":"Partha","full_name":"Bhowmick, Partha"},{"full_name":"Brimkov, Valentin E.","last_name":"Brimkov","first_name":"Valentin E."}],"oa_version":"None","extern":"1","citation":{"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>","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>","ista":"Biswas R, Bhowmick P, Brimkov VE. 2017. On the polyhedra of graceful spheres and circular geodesics. Discrete Applied Mathematics. 216, 362–375.","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.","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>.","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."},"date_created":"2019-01-08T20:41:12Z","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."}],"page":"362-375","date_published":"2017-01-10T00:00:00Z","status":"public","publication":"Discrete Applied Mathematics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"5799","intvolume":"       216","language":[{"iso":"eng"}]},{"article_processing_charge":"No","oa":1,"year":"1998","publication_identifier":{"issn":["0166-218X"]},"day":"09","date_updated":"2022-08-25T15:06:30Z","title":"On the definition and the construction of pockets in macromolecules","doi":"10.1016/S0166-218X(98)00067-5","external_id":{"pmid":["9390238"]},"acknowledgement":"The authors thank Ping Fu and Ernst Miicke for their contributions to the alpha shapes software in which the pockets software is embedded. ","_id":"4013","language":[{"iso":"eng"}],"page":"83 - 102","issue":"1-3","article_type":"original","citation":{"ista":"Edelsbrunner H, Facello M, Liang J. 1998. On the definition and the construction of pockets in macromolecules. Discrete Applied Mathematics. 88(1–3), 83–102.","apa":"Edelsbrunner, H., Facello, M., &#38; Liang, J. (1998). On the definition and the construction of pockets in macromolecules. <i>Discrete Applied Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/S0166-218X(98)00067-5\">https://doi.org/10.1016/S0166-218X(98)00067-5</a>","ama":"Edelsbrunner H, Facello M, Liang J. On the definition and the construction of pockets in macromolecules. <i>Discrete Applied Mathematics</i>. 1998;88(1-3):83-102. doi:<a href=\"https://doi.org/10.1016/S0166-218X(98)00067-5\">10.1016/S0166-218X(98)00067-5</a>","mla":"Edelsbrunner, Herbert, et al. “On the Definition and the Construction of Pockets in Macromolecules.” <i>Discrete Applied Mathematics</i>, vol. 88, no. 1–3, Elsevier, 1998, pp. 83–102, doi:<a href=\"https://doi.org/10.1016/S0166-218X(98)00067-5\">10.1016/S0166-218X(98)00067-5</a>.","short":"H. Edelsbrunner, M. Facello, J. Liang, Discrete Applied Mathematics 88 (1998) 83–102.","chicago":"Edelsbrunner, Herbert, Michael Facello, and Jie Liang. “On the Definition and the Construction of Pockets in Macromolecules.” <i>Discrete Applied Mathematics</i>. Elsevier, 1998. <a href=\"https://doi.org/10.1016/S0166-218X(98)00067-5\">https://doi.org/10.1016/S0166-218X(98)00067-5</a>.","ieee":"H. Edelsbrunner, M. Facello, and J. Liang, “On the definition and the construction of pockets in macromolecules,” <i>Discrete Applied Mathematics</i>, vol. 88, no. 1–3. Elsevier, pp. 83–102, 1998."},"month":"11","author":[{"last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","orcid":"0000-0002-9823-6833"},{"first_name":"Michael","last_name":"Facello","full_name":"Facello, Michael"},{"full_name":"Liang, Jie","first_name":"Jie","last_name":"Liang"}],"volume":88,"type":"journal_article","main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S0166218X98000675?via%3Dihub","open_access":"1"}],"publication_status":"published","publisher":"Elsevier","pmid":1,"quality_controlled":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","intvolume":"        88","abstract":[{"text":"The shape of a protein is important for its functions, This includes the location and size of identifiable regions in its complement space. We formally define pockets as regions in the complement with limited accessibility from the outside. Pockets can be efficiently constructed by an algorithm based on alpha complexes. The algorithm is implemented and applied to proteins with known three-dimensional conformations. 1998 Published by Elsevier Science B.V. All rights reserved.","lang":"eng"}],"date_published":"1998-11-09T00:00:00Z","status":"public","publication":"Discrete Applied Mathematics","publist_id":"2114","extern":"1","scopus_import":"1","date_created":"2018-12-11T12:06:26Z","oa_version":"Published Version"},{"article_processing_charge":"No","oa":1,"year":"1996","day":"05","publication_identifier":{"issn":["0166-218X"]},"date_updated":"2022-08-09T14:06:12Z","doi":"10.1016/S0166-218X(96)00054-6","title":"Triangulating the surface of a molecule","_id":"4025","language":[{"iso":"eng"}],"acknowledgement":"The research of both authors is partially supported by the Office of Naval Research. Herbert Edelsbrunner is also supported through the Alan T. Waterman award, grant CCR-9118874. ","page":"5 - 22","issue":"1-3","article_type":"original","citation":{"ama":"Akkiraju N, Edelsbrunner H. Triangulating the surface of a molecule. <i>Discrete Applied Mathematics</i>. 1996;71(1-3):5-22. doi:<a href=\"https://doi.org/10.1016/S0166-218X(96)00054-6\">10.1016/S0166-218X(96)00054-6</a>","apa":"Akkiraju, N., &#38; Edelsbrunner, H. (1996). Triangulating the surface of a molecule. <i>Discrete Applied Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/S0166-218X(96)00054-6\">https://doi.org/10.1016/S0166-218X(96)00054-6</a>","ista":"Akkiraju N, Edelsbrunner H. 1996. Triangulating the surface of a molecule. Discrete Applied Mathematics. 71(1–3), 5–22.","ieee":"N. Akkiraju and H. Edelsbrunner, “Triangulating the surface of a molecule,” <i>Discrete Applied Mathematics</i>, vol. 71, no. 1–3. Elsevier, pp. 5–22, 1996.","chicago":"Akkiraju, Nataraj, and Herbert Edelsbrunner. “Triangulating the Surface of a Molecule.” <i>Discrete Applied Mathematics</i>. Elsevier, 1996. <a href=\"https://doi.org/10.1016/S0166-218X(96)00054-6\">https://doi.org/10.1016/S0166-218X(96)00054-6</a>.","short":"N. Akkiraju, H. Edelsbrunner, Discrete Applied Mathematics 71 (1996) 5–22.","mla":"Akkiraju, Nataraj, and Herbert Edelsbrunner. “Triangulating the Surface of a Molecule.” <i>Discrete Applied Mathematics</i>, vol. 71, no. 1–3, Elsevier, 1996, pp. 5–22, doi:<a href=\"https://doi.org/10.1016/S0166-218X(96)00054-6\">10.1016/S0166-218X(96)00054-6</a>."},"author":[{"last_name":"Akkiraju","first_name":"Nataraj","full_name":"Akkiraju, Nataraj"},{"orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","first_name":"Herbert","last_name":"Edelsbrunner"}],"month":"12","type":"journal_article","volume":71,"main_file_link":[{"url":"https://www.sciencedirect.com/science/article/pii/S0166218X96000546?via%3Dihub","open_access":"1"}],"publication_status":"published","publisher":"Elsevier","quality_controlled":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","intvolume":"        71","abstract":[{"lang":"eng","text":"Questions of chemical reactivity can often be cast as questions of molecular geometry. Common geometric models for proteins and other molecules are the space-filling diagram, the solvent accessible surface and the molecular surface. In this paper we present a new approach to triangulating the surface of a molecule under the three models, which is fast, robust, and results in topologically correct triangulations. Our computations are based on a simplicial complex dual to the molecule models. All proposed algorithms are parallelizable."}],"publication":"Discrete Applied Mathematics","publist_id":"2102","status":"public","date_published":"1996-12-05T00:00:00Z","extern":"1","scopus_import":"1","date_created":"2018-12-11T12:06:30Z","oa_version":"Published Version"}]