{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T02:26:50Z","timestamp":1761964010308},"reference-count":63,"publisher":"Elsevier BV","issue":"3","license":[{"start":{"date-parts":[[1991,4,1]],"date-time":"1991-04-01T00:00:00Z","timestamp":670464000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computer-Aided Design"],"published-print":{"date-parts":[[1991,4]]},"DOI":"10.1016\/0010-4485(91)90086-c","type":"journal-article","created":{"date-parts":[[2003,3,14]],"date-time":"2003-03-14T09:47:17Z","timestamp":1047635237000},"page":"162-176","source":"Crossref","is-referenced-by-count":3,"title":["Data structures to support B\u00e9zier-based modelling"],"prefix":"10.1016","volume":"23","author":[{"given":"Hanan","family":"Samet","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert E.","family":"Webber","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/0010-4485(91)90086-C_BIB1","series-title":"Computer Aided Geometric Design","article-title":"Mathematical and practical possibilities of UNISURF","author":"B\u00e9zier","year":"1974"},{"key":"10.1016\/0010-4485(91)90086-C_BIB2","series-title":"METAFONTbook","author":"Knuth","year":"1986"},{"key":"10.1016\/0010-4485(91)90086-C_BIB3","series-title":"The Mathematical Basis of the UNISURF CAD System","author":"B\u00e9zier","year":"1986"},{"key":"10.1016\/0010-4485(91)90086-C_BIB4","first-page":"1","article-title":"D\u00e8monstration du th\u00e9r\u00e8me de Weirstrass fonde\u00e9 sur le calcul de probabilit\u00e9","volume":"13","author":"Bernstein","year":"1912","journal-title":"Harkov Soobs. Matem ob-va"},{"key":"10.1016\/0010-4485(91)90086-C_BIB5","series-title":"Curves and Surfaces for Computer Aided Geometric Design","author":"Farin","year":"1988"},{"key":"10.1016\/0010-4485(91)90086-C_BIB6","article-title":"Courbes et surfaces \u00e0 p\u00f4les","author":"de Casteljau","year":"1963"},{"key":"10.1016\/0010-4485(91)90086-C_BIB7","series-title":"Shape Mathematics and CAD","author":"de Casteljau","year":"1986"},{"issue":"No 1","key":"10.1016\/0010-4485(91)90086-C_BIB8","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/0021-9045(84)90132-1","article-title":"The convexity of Bernstein polynomials over triangles","volume":"Vol 40","author":"Chang","year":"1984","journal-title":"J. Approx. Theory"},{"key":"10.1016\/0010-4485(91)90086-C_BIB9","series-title":"Multivariate Approximation Theory III","first-page":"61","article-title":"Convexity and variation diminishing property of Bernstein polynomials over triangles","author":"Chang","year":"1985"},{"issue":"No 2","key":"10.1016\/0010-4485(91)90086-C_BIB10","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/0021-9045(87)90002-5","article-title":"Variation diminishing properties of Bernstein polynomials on triangles","volume":"Vol 50","author":"Goodman","year":"1987","journal-title":"J. Approx. Theory"},{"key":"10.1016\/0010-4485(91)90086-C_BIB11","series-title":"Proc. Conf. Comput. Graph., Pattern Recognition and Data Structure","first-page":"11","article-title":"Computer display of curved surfaces","author":"Catmull","year":"1975"},{"issue":"No 1","key":"10.1016\/0010-4485(91)90086-C_BIB12","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1145\/358808.358815","article-title":"Scan line methods for displaying parametrically defined surfaces","volume":"Vol 23","author":"Lane","year":"1980","journal-title":"Communications of the ACM"},{"key":"10.1016\/0010-4485(91)90086-C_BIB13","article-title":"Geometric modeling for computer vision","author":"Baumgart","year":"1974"},{"key":"10.1016\/0010-4485(91)90086-C_BIB14","series-title":"An Introduction to Solid Modeling","author":"M\u00e4ntyl\u00e4","year":"1987"},{"issue":"No 4","key":"10.1016\/0010-4485(91)90086-C_BIB15","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1145\/356827.356833","article-title":"Representations of rigid solids: theory, methods, and systems","volume":"Vol 12","author":"Requicha","year":"1980","journal-title":"ACM Computing Surveys"},{"issue":"No 7","key":"10.1016\/0010-4485(91)90086-C_BIB16","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1109\/MCG.1982.1674396","article-title":"GWB: A solid modeler with Euler operators","volume":"Vol 2","author":"M\u00e4ntyl\u00e4","year":"1982","journal-title":"IEEE Comput. Graph. Appl."},{"issue":"No 3","key":"10.1016\/0010-4485(91)90086-C_BIB17","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1007\/BF01840397","article-title":"Computational geometry in a curved world","volume":"Vol 5","author":"Dobkin","year":"1990","journal-title":"Algorithmica"},{"issue":"No 3","key":"10.1016\/0010-4485(91)90086-C_BIB18_1","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1145\/964967.801159","article-title":"Localized set operations for solid modeling","volume":"Vol 17","author":"M\u00e4ntyl\u00e4","year":"1983","journal-title":"Computer Graphics"},{"key":"10.1016\/0010-4485(91)90086-C_BIB18_2","series-title":"Proceedings of the SIGGRAPH'83 Conference","author":"M\u00e4ntyl\u00e4","year":"1983"},{"issue":"No 1","key":"10.1016\/0010-4485(91)90086-C_BIB19","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1109\/TPAMI.1980.4766968","article-title":"A theoretical development for the computer generation and display of piecewise polynomial surfaces","volume":"Vol 2","author":"Lane","year":"1980","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"No 4","key":"10.1016\/0010-4485(91)90086-C_BIB20","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1016\/0010-4485(86)90130-2","article-title":"Intersection of parametric surfaces in the Bernstein-B\u00e9zier representation","volume":"Vol 18","author":"Lasser","year":"1986","journal-title":"Comput.-Aided Des."},{"key":"10.1016\/0010-4485(91)90086-C_BIB21","series-title":"The Design and Analysis of Spatial Data Structures","author":"Samet","year":"1990"},{"key":"10.1016\/0010-4485(91)90086-C_BIB22","series-title":"Applications of Spatial Data Structures: Computer Graphics, Image Processing, and GIS","author":"Samet","year":"1990"},{"issue":"No 1\u20132","key":"10.1016\/0010-4485(91)90086-C_BIB23","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/0167-8396(87)90031-8","article-title":"Extended octtree representation of free form surfaces","volume":"Vol 4","author":"Brunet","year":"1987","journal-title":"Comput.-Aided Geom. Des."},{"key":"10.1016\/0010-4485(91)90086-C_BIB24","series-title":"The Design and Analysis of Computer Algorithms","author":"Aho","year":"1974"},{"key":"10.1016\/0010-4485(91)90086-C_BIB25","article-title":"Efficient computation and data structures for graphics","author":"Hunter","year":"1978"},{"issue":"No 3","key":"10.1016\/0010-4485(91)90086-C_BIB26","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/0146-664X(80)90055-6","article-title":"Oct-trees and their use in representing three-dimensional objects","volume":"Vol 14","author":"Jackins","year":"1980","journal-title":"Comput. Graph. and Image Processing"},{"issue":"No 2","key":"10.1016\/0010-4485(91)90086-C_BIB27","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/0146-664X(82)90104-6","article-title":"Geometric modeling using octree encoding","volume":"Vol 19","author":"Meagher","year":"1982","journal-title":"Comput. Graph. and Image Processing"},{"issue":"No 2","key":"10.1016\/0010-4485(91)90086-C_BIB28","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1109\/TPAMI.1979.4766900","article-title":"Operations on images using quad trees","volume":"Vol 1","author":"Hunter","year":"1979","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"10.1016\/0010-4485(91)90086-C_BIB29","series-title":"Electrical and SystemsEngineering Technical Report IPL-TR-80-111","article-title":"Octree encoding: a new technique for the representation, the manipulation, and display of arbitrary 3-D objects by computer","author":"Meagher","year":"1980"},{"issue":"No 1","key":"10.1016\/0010-4485(91)90086-C_BIB30","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1145\/3973.3975","article-title":"Object representation by means of nonminimal division quadtrees and octrees","volume":"Vol 7","author":"Ayala","year":"1985","journal-title":"ACM Trans. Graph."},{"issue":"No 4","key":"10.1016\/0010-4485(91)90086-C_BIB31","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1109\/MCG.1985.276454","article-title":"A hierarchical data structure for representing the spatial decomposition of 3-D objects","volume":"Vol 5","author":"Carlbom","year":"1985","journal-title":"IEEE Comput. Graph. Appl."},{"key":"10.1016\/0010-4485(91)90086-C_BIB32_1","series-title":"Proc. Comput. Graph. '85","first-page":"T1","article-title":"A hierarchical space indexing method","author":"Fujimura","year":"1985"},{"key":"10.1016\/0010-4485(91)90086-C_BIB32_2","series-title":"Proc. Comput. Graph. '85","first-page":"1","article-title":"A hierarchical space indexing method","author":"Fujimura","year":"1985"},{"key":"10.1016\/0010-4485(91)90086-C_BIB33","series-title":"Geometrees for interactive visualization of geology: an evaluation","author":"Hunter","year":"1981"},{"key":"10.1016\/0010-4485(91)90086-C_BIB34","series-title":"Proc. CAD'82 Conference","first-page":"126","article-title":"A spatially-segmented solids database\u2014justification and design","author":"Quinlan","year":"1982"},{"key":"10.1016\/0010-4485(91)90086-C_BIB35","series-title":"Acta Polytechnica Scandinavica","article-title":"The EXCELL method for efficient geometric access to data","author":"Tamminen","year":"1981"},{"key":"10.1016\/0010-4485(91)90086-C_BIB36","series-title":"Research Note","article-title":"Divided leaf octal trees","author":"Vanderschel","year":"1984"},{"key":"10.1016\/0010-4485(91)90086-C_BIB37","article-title":"Contribuci\u00f3 a les t\u00e8cnniques de modelat geom\u00e8tric d' objectes poli\u00e8drics usant la codificaci\u00f3 amb arbres octals","author":"Navazo","year":"1986"},{"issue":"No 4","key":"10.1016\/0010-4485(91)90086-C_BIB38_1","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1145\/15886.15908","article-title":"A consistent hierarchical representation for vector data","volume":"Vol 20","author":"Nelson","year":"1986","journal-title":"Comput. Graph."},{"key":"10.1016\/0010-4485(91)90086-C_BIB38_2","series-title":"Proc. SIGGRAPH'86 Conference","first-page":"270","author":"Nelson","year":"1987"},{"key":"10.1016\/0010-4485(91)90086-C_BIB39","series-title":"Proc. SIGMOD Conference","first-page":"270","article-title":"A population analysis for hierarchical data structures","author":"Nelson","year":"1987"},{"issue":"No 4","key":"10.1016\/0010-4485(91)90086-C_BIB40","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/MCG.1986.276715","article-title":"ARTS: accelerated ray-tracing system","volume":"Vol 6","author":"Fujimoto","year":"1986","journal-title":"IEEE Comput. Graph. Appl."},{"issue":"No 1","key":"10.1016\/0010-4485(91)90086-C_BIB41","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/BF01901265","article-title":"A functional model for constructive solid geometry","volume":"Vol 1","author":"Wyvill","year":"1985","journal-title":"Visual Computer"},{"issue":"No 2","key":"10.1016\/0010-4485(91)90086-C_BIB42","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1111\/j.1467-8659.1986.tb00278.x","article-title":"A geometric modeller based on the exact octree-representation of polyhedra","volume":"Vol 5","author":"Navazo","year":"1986","journal-title":"Comput. Graph. Forum"},{"key":"10.1016\/0010-4485(91)90086-C_BIB43","series-title":"Technical Report LSI-90-14","article-title":"Face octrees: involved algorithms and applications","author":"Brunet","year":"1990"},{"issue":"No 3","key":"10.1016\/0010-4485(91)90086-C_BIB44_1","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1145\/965145.801288","article-title":"An algorithm and data structure for 3D object synthesis using surface patch intersections","volume":"Vol 16","author":"Carlson","year":"1982","journal-title":"Comput. Graph."},{"key":"10.1016\/0010-4485(91)90086-C_BIB44_2","series-title":"Proc. SIGGRAPH'82 Conf.","author":"Carlson","year":"1982"},{"key":"10.1016\/0010-4485(91)90086-C_BIB45","series-title":"Proc. WG'83 (International Workshop on Graphtheoretic Concepts in Comput. Science)","first-page":"100","article-title":"The grid file a data structure designed to support proximity queries on spatial objects","author":"Hinricks","year":"1983"},{"key":"10.1016\/0010-4485(91)90086-C_BIB46","article-title":"The grid file system: implementation and case studies of applications","author":"Hinrichs","year":"1985"},{"issue":"No 1","key":"10.1016\/0010-4485(91)90086-C_BIB47","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1145\/348.318586","article-title":"The grid file: an adaptable, symmetric multikey file structure","volume":"Vol 9","author":"Nievergelt","year":"1984","journal-title":"ACM Trans. Database Systems"},{"issue":"No 4","key":"10.1016\/0010-4485(91)90086-C_BIB48","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/0020-0190(82)90027-8","article-title":"Multidimensional tries used for associative searching","volume":"Vol 14","author":"Orenstein","year":"1982","journal-title":"Inf. Process. Lett."},{"key":"10.1016\/0010-4485(91)90086-C_BIB49","series-title":"Proc. Nineteenth Design Automation Conference","first-page":"352","article-title":"The quad-CIF tree: a data structure for hierarchical on-line algorithms","author":"Kedem","year":"1982"},{"issue":"No 1","key":"10.1016\/0010-4485(91)90086-C_BIB50","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0734-189X(83)90017-8","article-title":"A data structure and algorithm based on a linear key for a rectangle retrieval problem","volume":"Vol 24","author":"Abel","year":"1983","journal-title":"Comput. Vision, Graph. Image Processing"},{"key":"10.1016\/0010-4485(91)90086-C_BIB51","series-title":"Institute for Information Processing Report 47","article-title":"Dynamic rectangle intersection searching","author":"Edelsbrunner","year":"1980"},{"key":"10.1016\/0010-4485(91)90086-C_BIB52","article-title":"Efficient algorithms for enumerating intersecting intervals and rectangles","author":"McCreight","year":"1980","journal-title":"Xerox Palo Alto Research Center Report CSL-80-09"},{"key":"10.1016\/0010-4485(91)90086-C_BIB53","series-title":"Computational Geometry: An Introduction","author":"Preparata","year":"1985"},{"issue":"No 2","key":"10.1016\/0010-4485(91)90086-C_BIB54","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1080\/02693799008941534","article-title":"QUILT: a geographic information system based on quadtrees","volume":"Vol 4","author":"Shaffer","year":"1990","journal-title":"Int. J. Geographical Inf. Systems"},{"key":"10.1016\/0010-4485(91)90086-C_BIB55_1","series-title":"Emploi des Machines \u00e0 Commude Num\u00e9rique","author":"B\u00e9zier","year":"1970"},{"key":"10.1016\/0010-4485(91)90086-C_BIB55_2","series-title":"Numerical Control: Mathematics and Applications","author":"Forrest","year":"1972"},{"key":"10.1016\/0010-4485(91)90086-C_BIB56","series-title":"Proc. National Comput. Conf. 44","first-page":"589","article-title":"A polyhedron representation for computer vision","author":"Baumgart","year":"1975"},{"key":"10.1016\/0010-4485(91)90086-C_BIB57","series-title":"Optimizing Methods in Statistics","first-page":"303","article-title":"Patterns and search statistics","author":"Klinger","year":"1971"},{"key":"10.1016\/0010-4485(91)90086-C_BIB58","series-title":"CMU-CS-78-113 Computer Science Department","article-title":"Representation of three-dimensional objects","author":"Reddy","year":"1978"}],"container-title":["Computer-Aided Design"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:001044859190086C?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:001044859190086C?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,3,26]],"date-time":"2019-03-26T16:20:20Z","timestamp":1553617220000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/001044859190086C"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,4]]},"references-count":63,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1991,4]]}},"alternative-id":["001044859190086C"],"URL":"https:\/\/doi.org\/10.1016\/0010-4485(91)90086-c","relation":{},"ISSN":["0010-4485"],"issn-type":[{"value":"0010-4485","type":"print"}],"subject":[],"published":{"date-parts":[[1991,4]]}}}