[{"issue":"2-3","language":[{"iso":"eng"}],"quality_controlled":"1","doi":"10.1016/S0925-7721(01)00021-9","publication_identifier":{"issn":["0925-7721"]},"article_type":"original","article_processing_charge":"No","scopus_import":"1","publication":"Computational Geometry: Theory and Applications","publisher":"Elsevier","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publist_id":"2123","title":"Shape space from deformation","day":"01","author":[{"last_name":"Cheng","first_name":"Ho","full_name":"Cheng, Ho"},{"orcid":"0000-0002-9823-6833","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert","first_name":"Herbert","last_name":"Edelsbrunner"},{"first_name":"Ping","last_name":"Fu","full_name":"Fu, Ping"}],"citation":{"ama":"Cheng H, Edelsbrunner H, Fu P. Shape space from deformation. <i>Computational Geometry: Theory and Applications</i>. 2001;19(2-3):191-204. doi:<a href=\"https://doi.org/10.1016/S0925-7721(01)00021-9\">10.1016/S0925-7721(01)00021-9</a>","apa":"Cheng, H., Edelsbrunner, H., &#38; Fu, P. (2001). Shape space from deformation. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/S0925-7721(01)00021-9\">https://doi.org/10.1016/S0925-7721(01)00021-9</a>","mla":"Cheng, Ho, et al. “Shape Space from Deformation.” <i>Computational Geometry: Theory and Applications</i>, vol. 19, no. 2–3, Elsevier, 2001, pp. 191–204, doi:<a href=\"https://doi.org/10.1016/S0925-7721(01)00021-9\">10.1016/S0925-7721(01)00021-9</a>.","ista":"Cheng H, Edelsbrunner H, Fu P. 2001. Shape space from deformation. Computational Geometry: Theory and Applications. 19(2–3), 191–204.","chicago":"Cheng, Ho, Herbert Edelsbrunner, and Ping Fu. “Shape Space from Deformation.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2001. <a href=\"https://doi.org/10.1016/S0925-7721(01)00021-9\">https://doi.org/10.1016/S0925-7721(01)00021-9</a>.","ieee":"H. Cheng, H. Edelsbrunner, and P. Fu, “Shape space from deformation,” <i>Computational Geometry: Theory and Applications</i>, vol. 19, no. 2–3. Elsevier, pp. 191–204, 2001.","short":"H. Cheng, H. Edelsbrunner, P. Fu, Computational Geometry: Theory and Applications 19 (2001) 191–204."},"intvolume":"        19","extern":"1","status":"public","date_published":"2001-07-01T00:00:00Z","publication_status":"published","_id":"4001","year":"2001","acknowledgement":"National Science Foundation under grants CCR-96-19542 and CCR-97-12088, and by the Army Research Office under grant DAAG55-98-1-0177.","date_created":"2018-12-11T12:06:22Z","volume":19,"type":"journal_article","oa_version":"None","month":"07","abstract":[{"text":"The construction of shape spaces is studied from a mathematical and a computational viewpoint. A program is outlined reducing the problem to four tasks: the representation of geometry, the canonical deformation of geometry, the measuring of distance in shape space, and the selection of base shapes. The technical part of this paper focuses on the second task: the specification of a deformation mixing two or more shapes in continuously changing proportions. (C) 2001 Elsevier Science B.V All rights reserved.","lang":"eng"}],"date_updated":"2023-05-10T12:57:14Z","page":"191 - 204"},{"publication_status":"published","date_published":"2001-07-01T00:00:00Z","status":"public","citation":{"chicago":"Cheng, Siu, Herbert Edelsbrunner, Ping Fu, and Ka Lam. “Design and Analysis of Planar Shape Deformation.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2001. <a href=\"https://doi.org/10.1016/S0925-7721(01)00020-7\">https://doi.org/10.1016/S0925-7721(01)00020-7</a>.","ieee":"S. Cheng, H. Edelsbrunner, P. Fu, and K. Lam, “Design and analysis of planar shape deformation,” <i>Computational Geometry: Theory and Applications</i>, vol. 19, no. 2–3. Elsevier, pp. 205–218, 2001.","short":"S. Cheng, H. Edelsbrunner, P. Fu, K. Lam, Computational Geometry: Theory and Applications 19 (2001) 205–218.","ama":"Cheng S, Edelsbrunner H, Fu P, Lam K. Design and analysis of planar shape deformation. <i>Computational Geometry: Theory and Applications</i>. 2001;19(2-3):205-218. doi:<a href=\"https://doi.org/10.1016/S0925-7721(01)00020-7\">10.1016/S0925-7721(01)00020-7</a>","apa":"Cheng, S., Edelsbrunner, H., Fu, P., &#38; Lam, K. (2001). Design and analysis of planar shape deformation. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/S0925-7721(01)00020-7\">https://doi.org/10.1016/S0925-7721(01)00020-7</a>","ista":"Cheng S, Edelsbrunner H, Fu P, Lam K. 2001. Design and analysis of planar shape deformation. Computational Geometry: Theory and Applications. 19(2–3), 205–218.","mla":"Cheng, Siu, et al. “Design and Analysis of Planar Shape Deformation.” <i>Computational Geometry: Theory and Applications</i>, vol. 19, no. 2–3, Elsevier, 2001, pp. 205–18, doi:<a href=\"https://doi.org/10.1016/S0925-7721(01)00020-7\">10.1016/S0925-7721(01)00020-7</a>."},"extern":"1","intvolume":"        19","abstract":[{"text":"Shape deformation refers to the continuous change of one geometric object to another. We develop a software tool for planning, analyzing and visualizing deformations between two shapes in R-2. The deformation is generated automatically without any user intervention or specification of feature correspondences. A unique property of the tool is the explicit availability of a two-dimensional shape space, which can be used for designing the deformation either automatically by following constraints and objectives or manually by drawing deformation paths.","lang":"eng"}],"date_updated":"2023-05-10T14:21:31Z","oa_version":"None","month":"07","type":"journal_article","page":"205 - 218","date_created":"2018-12-11T12:06:22Z","volume":19,"year":"2001","acknowledgement":"NSF under grants CCR-96-19542 and CCR-97-12088.","_id":"4002","publication_identifier":{"issn":["0925-7721"]},"quality_controlled":"1","doi":"10.1016/S0925-7721(01)00020-7","language":[{"iso":"eng"}],"issue":"2-3","day":"01","author":[{"full_name":"Cheng, Siu","last_name":"Cheng","first_name":"Siu"},{"last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"last_name":"Fu","first_name":"Ping","full_name":"Fu, Ping"},{"last_name":"Lam","first_name":"Ka","full_name":"Lam, Ka"}],"publist_id":"2124","title":"Design and analysis of planar shape deformation","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publisher":"Elsevier","article_processing_charge":"No","scopus_import":"1","article_type":"original","publication":"Computational Geometry: Theory and Applications"},{"status":"public","extern":"1","intvolume":"         7","citation":{"apa":"Edelsbrunner, H., &#38; Shah, N. (1997). Triangulating topological spaces. <i>International Journal of Computational Geometry &#38; Applications</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0218195997000223\">https://doi.org/10.1142/S0218195997000223</a>","ista":"Edelsbrunner H, Shah N. 1997. Triangulating topological spaces. International Journal of Computational Geometry &#38; Applications. 7(4), 365–378.","mla":"Edelsbrunner, Herbert, and Nimish Shah. “Triangulating Topological Spaces.” <i>International Journal of Computational Geometry &#38; Applications</i>, vol. 7, no. 4, World Scientific Publishing, 1997, pp. 365–78, doi:<a href=\"https://doi.org/10.1142/S0218195997000223\">10.1142/S0218195997000223</a>.","ama":"Edelsbrunner H, Shah N. Triangulating topological spaces. <i>International Journal of Computational Geometry &#38; Applications</i>. 1997;7(4):365-378. doi:<a href=\"https://doi.org/10.1142/S0218195997000223\">10.1142/S0218195997000223</a>","short":"H. Edelsbrunner, N. Shah, International Journal of Computational Geometry &#38; Applications 7 (1997) 365–378.","chicago":"Edelsbrunner, Herbert, and Nimish Shah. “Triangulating Topological Spaces.” <i>International Journal of Computational Geometry &#38; Applications</i>. World Scientific Publishing, 1997. <a href=\"https://doi.org/10.1142/S0218195997000223\">https://doi.org/10.1142/S0218195997000223</a>.","ieee":"H. Edelsbrunner and N. Shah, “Triangulating topological spaces,” <i>International Journal of Computational Geometry &#38; Applications</i>, vol. 7, no. 4. World Scientific Publishing, pp. 365–378, 1997."},"publication_status":"published","date_published":"1997-01-01T00:00:00Z","acknowledgement":"Partially supported by the National Science Foundation, under grant ASC-200301 and the Alan T. Waterman award, grant CCR-9118874.","year":"1997","_id":"4018","page":"365 - 378","oa_version":"None","type":"journal_article","month":"01","date_updated":"2022-08-19T08:32:23Z","abstract":[{"text":"Given a subspace X subset of or equal to R-d and a finite set S subset of or equal to R-d, we introduce the Delaunay complex, D-X, restricted by X. Its simplices are spanned by subsets T subset of or equal to S for which the common intersection of Voronoi cells meets X in a non-empty set. By the nerve theorem, boolean OR D-X and X are homotopy equivalent if all such sets are contractible. This paper proves a sufficient condition for boolean OR D-X and X be homeomorphic.","lang":"eng"}],"volume":7,"date_created":"2018-12-11T12:06:28Z","issue":"4","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0925-7721"]},"doi":"10.1142/S0218195997000223","quality_controlled":"1","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publisher":"World Scientific Publishing","publication":"International Journal of Computational Geometry & Applications","article_type":"original","article_processing_charge":"No","scopus_import":"1","author":[{"first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert"},{"last_name":"Shah","first_name":"Nimish","full_name":"Shah, Nimish"}],"day":"01","title":"Triangulating topological spaces","publist_id":"2106"},{"doi":"10.1016/S0925-7721(96)00006-5","publication_identifier":{"issn":["0925-7721"]},"issue":"5-6","language":[{"iso":"eng"}],"publist_id":"2105","popular_science":"1","title":"A combinatorial approach to cartograms","day":"01","author":[{"id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert"},{"last_name":"Waupotitsch","first_name":"Roman","full_name":"Waupotitsch, Roman"}],"article_type":"original","article_processing_charge":"No","publication":"Computational Geometry: Theory and Applications","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publisher":"Elsevier","main_file_link":[{"open_access":"1","url":"https://www.sciencedirect.com/science/article/pii/S0925772196000065"}],"date_published":"1997-04-01T00:00:00Z","oa":1,"publication_status":"published","citation":{"ama":"Edelsbrunner H, Waupotitsch R. A combinatorial approach to cartograms. <i>Computational Geometry: Theory and Applications</i>. 1997;7(5-6):343-360. doi:<a href=\"https://doi.org/10.1016/S0925-7721(96)00006-5\">10.1016/S0925-7721(96)00006-5</a>","apa":"Edelsbrunner, H., &#38; Waupotitsch, R. (1997). A combinatorial approach to cartograms. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/S0925-7721(96)00006-5\">https://doi.org/10.1016/S0925-7721(96)00006-5</a>","ista":"Edelsbrunner H, Waupotitsch R. 1997. A combinatorial approach to cartograms. Computational Geometry: Theory and Applications. 7(5–6), 343–360.","mla":"Edelsbrunner, Herbert, and Roman Waupotitsch. “A Combinatorial Approach to Cartograms.” <i>Computational Geometry: Theory and Applications</i>, vol. 7, no. 5–6, Elsevier, 1997, pp. 343–60, doi:<a href=\"https://doi.org/10.1016/S0925-7721(96)00006-5\">10.1016/S0925-7721(96)00006-5</a>.","chicago":"Edelsbrunner, Herbert, and Roman Waupotitsch. “A Combinatorial Approach to Cartograms.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 1997. <a href=\"https://doi.org/10.1016/S0925-7721(96)00006-5\">https://doi.org/10.1016/S0925-7721(96)00006-5</a>.","ieee":"H. Edelsbrunner and R. Waupotitsch, “A combinatorial approach to cartograms,” <i>Computational Geometry: Theory and Applications</i>, vol. 7, no. 5–6. Elsevier, pp. 343–360, 1997.","short":"H. Edelsbrunner, R. Waupotitsch, Computational Geometry: Theory and Applications 7 (1997) 343–360."},"intvolume":"         7","extern":"1","status":"public","date_created":"2018-12-11T12:06:29Z","volume":7,"type":"journal_article","oa_version":"Published Version","month":"04","abstract":[{"text":"A homeomorphism from R-2 to itself distorts metric quantities, such as distance and area. We describe an algorithm that constructs homeomorphisms with prescribed area distortion. Such homeomorphisms can be used to generate cartograms, which are geographic maps purposely distorted so their area distributions reflects a variable different from area, as for example population density. The algorithm generates the homeomorphism through a sequence of local piecewise linear homeomorphic changes. Sample results produced by the preliminary implementation of the method are included.","lang":"eng"}],"date_updated":"2022-08-19T08:12:03Z","page":"343 - 360","_id":"4021","year":"1997","acknowledgement":"The authors thank Jack Snoeyink for bringing the cartogram problem to their attention, and Michael McAllister for providing pointers to the literature on cartograms. "},{"citation":{"short":"B. Chazelle, H. Edelsbrunner, L. Guibas, R. Pollack, R. Seidel, M. Sharir, J. Snoeyink, Computational Geometry: Theory and Applications 1 (1992) 305–323.","chicago":"Chazelle, Bernard, Herbert Edelsbrunner, Leonidas Guibas, Richard Pollack, Raimund Seidel, Micha Sharir, and Jack Snoeyink. “Counting and Cutting Cycles of Lines and Rods in Space.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 1992. <a href=\"https://doi.org/10.1016/0925-7721(92)90009-H\">https://doi.org/10.1016/0925-7721(92)90009-H</a>.","ieee":"B. Chazelle <i>et al.</i>, “Counting and cutting cycles of lines and rods in space,” <i>Computational Geometry: Theory and Applications</i>, vol. 1, no. 6. Elsevier, pp. 305–323, 1992.","apa":"Chazelle, B., Edelsbrunner, H., Guibas, L., Pollack, R., Seidel, R., Sharir, M., &#38; Snoeyink, J. (1992). Counting and cutting cycles of lines and rods in space. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/0925-7721(92)90009-H\">https://doi.org/10.1016/0925-7721(92)90009-H</a>","mla":"Chazelle, Bernard, et al. “Counting and Cutting Cycles of Lines and Rods in Space.” <i>Computational Geometry: Theory and Applications</i>, vol. 1, no. 6, Elsevier, 1992, pp. 305–23, doi:<a href=\"https://doi.org/10.1016/0925-7721(92)90009-H\">10.1016/0925-7721(92)90009-H</a>.","ista":"Chazelle B, Edelsbrunner H, Guibas L, Pollack R, Seidel R, Sharir M, Snoeyink J. 1992. Counting and cutting cycles of lines and rods in space. Computational Geometry: Theory and Applications. 1(6), 305–323.","ama":"Chazelle B, Edelsbrunner H, Guibas L, et al. Counting and cutting cycles of lines and rods in space. <i>Computational Geometry: Theory and Applications</i>. 1992;1(6):305-323. doi:<a href=\"https://doi.org/10.1016/0925-7721(92)90009-H\">10.1016/0925-7721(92)90009-H</a>"},"intvolume":"         1","extern":"1","status":"public","main_file_link":[{"open_access":"1","url":"https://www.sciencedirect.com/science/article/pii/092577219290009H?via%3Dihub"}],"date_published":"1992-06-01T00:00:00Z","oa":1,"publication_status":"published","_id":"3581","year":"1992","acknowledgement":"* Bernard Chazelle wishes to acknowledge the National Science Foundation for supporting this research in part under Grant CCR-9002352. Herbert Edelsbrunner acknowledges the support of the National Science Foundation under grants CCR-8714565 and CCR-8921421. Richard Pollack was supported in part by NSF grant CCR-8901484, NSA grant MDA904-89-H-2030, and DIMACS, a Science and Technology Center under NSF grant STC88-09648. Raimund Seidel acknowledges support by NSF grant CCR-8809040. Mich Sharir was partially supported by the Office of Naval\r\nResearch under Grant N00014-87-K-0129, by the National Science Foundation under Grant CCR-89-01484, and by grants from the U.S.-Israeli Binational Science Foundation and the Fund for Basic Research administered by the Israeli Academy of Sciences.","date_created":"2018-12-11T12:04:04Z","volume":1,"type":"journal_article","oa_version":"Published Version","month":"06","date_updated":"2022-03-16T10:41:58Z","abstract":[{"text":"A number of rendering algorithms in computer graphics sort three-dimensional objects by depth and assume that there is no cycle that makes the sorting impossible. One way to resolve the problem caused by cycles is to cut the objects into smaller pieces. In this paper we address the problem of estimating how many such cuts arc always sufficient. We also consider a few related algorithmic and combinatorial geometry problems. For example, we demonstrate that n lines in space can be sorted in randomized expected time O(n4’st’), provided that they define no cycle. We also prove an 0(n7’4) upper bound on the number of points in space so that there are n lines with the property that for each point there are at least three noncoplanar lines that contain it. ","lang":"eng"}],"page":"305 - 323","issue":"6","language":[{"iso":"eng"}],"quality_controlled":"1","doi":"10.1016/0925-7721(92)90009-H","publication_identifier":{"issn":["0925-7721"]},"article_type":"original","article_processing_charge":"No","scopus_import":"1","publication":"Computational Geometry: Theory and Applications","publisher":"Elsevier","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publist_id":"2804","title":"Counting and cutting cycles of lines and rods in space","day":"01","author":[{"full_name":"Chazelle, Bernard","last_name":"Chazelle","first_name":"Bernard"},{"full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert"},{"last_name":"Guibas","first_name":"Leonidas","full_name":"Guibas, Leonidas"},{"full_name":"Pollack, Richard","first_name":"Richard","last_name":"Pollack"},{"last_name":"Seidel","first_name":"Raimund","full_name":"Seidel, Raimund"},{"full_name":"Sharir, Micha","last_name":"Sharir","first_name":"Micha"},{"last_name":"Snoeyink","first_name":"Jack","full_name":"Snoeyink, Jack"}]}]