{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T09:44:15Z","timestamp":1725529455709},"publisher-location":"Berlin, Heidelberg","reference-count":22,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540851257"},{"type":"electronic","value":"9783540851264"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009]]},"DOI":"10.1007\/978-3-540-85126-4_13","type":"book-chapter","created":{"date-parts":[[2009,3,17]],"date-time":"2009-03-17T11:19:32Z","timestamp":1237288772000},"page":"285-299","source":"Crossref","is-referenced-by-count":0,"title":["Robust Point-Location in Generalized Voronoi Diagrams"],"prefix":"10.1007","author":[{"given":"Sergey","family":"Bereg","sequence":"first","affiliation":[]},{"given":"Marina L.","family":"Gavrilova","sequence":"additional","affiliation":[]},{"given":"Yuanyi","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"13_CR1","volume-title":"Complexity and real computation","author":"L. Blum","year":"1997","unstructured":"Blum, L., Cucker, F., Shub, M., Smale, S.: Complexity and real computation. Springer, Heidelberg (1997)"},{"key":"13_CR2","unstructured":"Burnikel, C.: Exact Computation of Voronoi Diagrams and Line Segment Intersections. Ph.D thesis, Universit\u00e4t des Saarlandes (March 1996)"},{"issue":"4","key":"13_CR3","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1016\/j.ipl.2005.10.009","volume":"97","author":"Z. Chen","year":"2006","unstructured":"Chen, Z., Papadopoulou, E., Xu, J.: Robustness of algorithm for k-gon Voronoi diagram construction. Information Processing Letters\u00a097(4), 138\u2013145 (2006)","journal-title":"Information Processing Letters"},{"key":"13_CR4","doi-asserted-by":"crossref","unstructured":"Chew, L.P., Drysdale III, R.L.: Voronoi diagrams based on convex distance functions. In: Proc. 1st Annu. ACM Sympos. Comput. Geom., pp. 235\u2013244 (1985)","DOI":"10.1145\/323233.323264"},{"key":"13_CR5","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1016\/0167-8396(92)90044-P","volume":"9","author":"T.K. Dey","year":"1992","unstructured":"Dey, T.K., Sugihara, K., Bajaj, C.L.: Delaunay triangulations in three dimensions with finite precision arithmetic. Computer Aided Geometric Design\u00a09, 457\u2013470 (1992)","journal-title":"Computer Aided Geometric Design"},{"key":"13_CR6","doi-asserted-by":"crossref","unstructured":"Edelsbrunner, H., M\u00fccke, E.: Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms. In: Proc. 4th Annu. ACM Sympos. Comput. Geom., pp. 118\u2013133 (1988)","DOI":"10.1145\/73393.73406"},{"key":"13_CR7","doi-asserted-by":"crossref","unstructured":"Fortune, S., Wyk, C.: Efficient exact arithmetic for computational geometry. In: Proc. 9th Annu. ACM Sympos. Comput. Geom., pp. 163\u2013172 (1993)","DOI":"10.1145\/160985.161015"},{"key":"13_CR8","unstructured":"Gavrilova, M.: A reliable algorithm for computing the generalized Voronoi diagram for a set of spheres in the Euclidean d-dimensional space. In: Canadian Conference on Computational Geometry, pp. 82\u201387 (2002)"},{"key":"13_CR9","unstructured":"Gavrilova, M., Bespamyatnikh, S.: On exact solution of a point-location problem in a system of d-dimensional hyperbolic surfaces. In: Canadian Conference on Computational Geometry, pp. 136\u2013139 (2003)"},{"issue":"1","key":"13_CR10","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1023\/A:1009934225596","volume":"6","author":"M. Gavrilova","year":"2000","unstructured":"Gavrilova, M., Ratschek, H., Rokne, J.: Exact computation of Voronoi diagram and Delaunay triangulation. Reliable Computing\u00a06(1), 39\u201360 (2000)","journal-title":"Reliable Computing"},{"key":"13_CR11","unstructured":"Gavrilova, M.: Algorithm library development for complex biological and mechanical systems. In: DIMACS Workshop on Implementation of Geometric Algorithms (2002)"},{"key":"13_CR12","doi-asserted-by":"crossref","unstructured":"Hoffmann, C.M., Hopcroft, J.E., Karasik, M.S.: Towards implementing robust geometric computations. In: Proc. 4th Annu. ACM Sympos. Comput. Geom., pp. 106\u2013117 (1988)","DOI":"10.1145\/73393.73405"},{"key":"13_CR13","doi-asserted-by":"crossref","unstructured":"Krishnan, S., Foskey, M., Culver, T., Keyser, J., Manocha, D.: PRECISE: Efficient multiprecision evaluation of algebraic roots and predicates for reliable geometric computations. In: Proc. 17th Annu. ACM Sympos. Comput. Geom., pp. 274\u2013283 (2001)","DOI":"10.1145\/378583.378693"},{"issue":"3","key":"13_CR14","doi-asserted-by":"publisher","first-page":"864","DOI":"10.1137\/S0097539796305365","volume":"28","author":"G. Liotta","year":"1998","unstructured":"Liotta, G., Preparata, F.P., Tamassia, R.: Robust proximity queries: an illustration of degree-driven algorithm design. SIAM J. Comput.\u00a028(3), 864\u2013889 (1998)","journal-title":"SIAM J. Comput."},{"key":"13_CR15","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/BF02716580","volume":"15","author":"M. McAllister","year":"1996","unstructured":"McAllister, M., Kirkpatrick, D., Snoeyink, J.: A compact piecewise-linear Voronoi diagram for convex sites in the plane. Discrete Comput. Geom.\u00a015, 73\u2013105 (1996)","journal-title":"Discrete Comput. Geom."},{"key":"13_CR16","unstructured":"S.\u00a0Naher, The LEDA user manual, Version 3.1 (January 16, 1995), ftp.mpi-sb.mpg.de"},{"key":"13_CR17","unstructured":"Stewart, A.J.: Robust point location in approximate polygons.In: Canadian Conference on Computational Geometry, pp. 179\u2013182 (1991)"},{"issue":"2","key":"13_CR18","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1142\/S0218195994000124","volume":"4","author":"K. Sugihara","year":"1994","unstructured":"Sugihara, K., Iri, M.: A robust topology-oriented incremental algorithm for Voronoi diagrams. International Journal of Computational Geometry and Applications\u00a04(2), 179\u2013228 (1994)","journal-title":"International Journal of Computational Geometry and Applications"},{"key":"13_CR19","doi-asserted-by":"publisher","first-page":"728","DOI":"10.1137\/0216049","volume":"16","author":"P. Widmayer","year":"1987","unstructured":"Widmayer, P., Wu, Y.F., Wong, C.K.: On some distance problems in fixed orientations. SIAM J. Comput.\u00a016, 728\u2013746 (1987)","journal-title":"SIAM J. Comput."},{"key":"13_CR20","volume-title":"Computing in Euclidean Geometry","author":"C. Yap","year":"1995","unstructured":"Yap, C., Dube, T.: The exact computation paradigm. In: Du, D.-Z., Hwang, F.K. (eds.) Computing in Euclidean Geometry, 2nd edn., World Scientific Press, Singapore (1995)","edition":"2"},{"key":"13_CR21","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1016\/S0747-7171(08)80069-7","volume":"10","author":"C.K. Yap","year":"1990","unstructured":"Yap, C.K.: Symbolic treatment of geometric degeneracies. Journal of Symbolic Computation\u00a010, 349\u2013370 (1990)","journal-title":"Journal of Symbolic Computation"},{"key":"13_CR22","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0925-7721(95)00040-2","volume":"7","author":"C.K. Yap","year":"1997","unstructured":"Yap, C.K.: Toward exact geometric computation. Computational Geometry: Theory and Applications\u00a07, 3\u201323 (1997)","journal-title":"Computational Geometry: Theory and Applications"}],"container-title":["Studies in Computational Intelligence","Generalized Voronoi Diagram: A Geometry-Based Approach to Computational Intelligence"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-85126-4_13.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T11:15:37Z","timestamp":1619522137000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-85126-4_13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"ISBN":["9783540851257","9783540851264"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-85126-4_13","relation":{},"ISSN":["1860-949X","1860-9503"],"issn-type":[{"type":"print","value":"1860-949X"},{"type":"electronic","value":"1860-9503"}],"subject":[],"published":{"date-parts":[[2009]]}}}