{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T07:07:01Z","timestamp":1751872021317},"reference-count":42,"publisher":"Elsevier","isbn-type":[{"value":"9780121745851","type":"print"}],"license":[{"start":{"date-parts":[[1987,1,1]],"date-time":"1987-01-01T00:00:00Z","timestamp":536457600000},"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":[],"published-print":{"date-parts":[[1987]]},"DOI":"10.1016\/b978-0-12-174585-1.50022-1","type":"book-chapter","created":{"date-parts":[[2014,7,1]],"date-time":"2014-07-01T19:28:07Z","timestamp":1404242887000},"page":"219-232","source":"Crossref","is-referenced-by-count":33,"title":["TRIANGULATION METHODS"],"prefix":"10.1016","author":[{"given":"Larry L.","family":"Schumaker","sequence":"first","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib1","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1145\/355780.355786","article-title":"A method of bivariate interpolation and smooth surface fitting for values given at irregularly distributed points","volume":"4","author":"Akima","year":"1978","journal-title":"ACM TOMS"},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib2","series-title":"Mathematical Software III","first-page":"68","article-title":"Representation and approximation of surfaces","author":"Barnhill","year":"1977"},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib3","series-title":"Surfaces in Computer Aided Design","first-page":"1","article-title":"Computer aided surface representation and design","author":"Barnhill","year":"1983"},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib4","series-title":"Surfaces in CAGD '84","first-page":"1","article-title":"Surfaces in computer-aided geometric design: a survey with new results","author":"Barnhill","year":"1985"},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib5","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1216\/RMJ-1984-14-1-77","article-title":"Three- and four-dimensional surfaces","volume":"14","author":"Barnhill","year":"1984","journal-title":"Rocky Mt. J. Math."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib6","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/BF01939851","article-title":"Construction of isarithms and isarithmic maps by computers","volume":"4","author":"Bengtsson","year":"1964","journal-title":"BIT"},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib7","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1093\/comjnl\/24.2.162","article-title":"Computing Dirichlet tessellations","volume":"24","author":"Bowyer","year":"1981","journal-title":"Computer J."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib8","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1111\/j.1538-4632.1979.tb00695.x","article-title":"Procedure to generate Thiessen polygons","volume":"11","author":"Brassel","year":"1979","journal-title":"Geograph. Anal."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib9","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1002\/nme.1620080402","article-title":"Automatic triangulation of arbitrary planar domains for the finite element method","volume":"8","author":"Cavendish","year":"1974","journal-title":"Int. J. for Numer. Methods in Engr."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib10","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1216\/RMJ-1984-14-1-119","article-title":"A storage-efficient method for construction of a Thiessen triangulation","volume":"14","author":"Cline","year":"1984","journal-title":"Rocky Mt. J. Math."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib11","unstructured":"Correc, Y., Generation automatique d'une triangulation sur des point donnes, 1980."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib12","unstructured":"Correc, Y. and E. Chapuis, Fast computation of Delaunay triangulations, 1985."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib13","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1002\/nme.1620020411","article-title":"Rules governing the numbers of nodes and elements in a finite element mesh","volume":"2","author":"Ewing","year":"1970","journal-title":"Int. J. Numer. Meth. Eng."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib14","first-page":"56","article-title":"An algorithm for contouring random data without gridding","volume":"24","author":"Frenkel","year":"1975","journal-title":"Israeli J. Earth Sciences"},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib15","unstructured":"Fowler, R. J., DELTRI: A program for inductively computing Delaunay triangulations, Rpt. 18, Dept. Geology, Simon Fraser Univ., 1981."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib16","article-title":"Triangulierung und Interpolation von im IR2 unregelm\u00e4ssig verteilten Daten","volume":"357","author":"Gleue","year":"1981","journal-title":"HMI B"},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib17","doi-asserted-by":"crossref","unstructured":"Gold, C. M., Automated contour mapping using triangular element data structures and an interpolant over each irregular triangular domain, Siggraph. Proc. (1977), 170\u2013175.","DOI":"10.1145\/965141.563887"},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib18","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1145\/965141.563887","article-title":"Automated contour mapping using triangular element data structures and an interpolant over each irregular triangular domain","volume":"11","author":"Gold","year":"1977","journal-title":"Computer Graphics"},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib19","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1093\/comjnl\/21.2.168","article-title":"Computing Dirichlet tesselations in the plane","volume":"21","author":"Green","year":"1978","journal-title":"Computer J."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib20","series-title":"The Mathematics of Finite Elements and Application II","first-page":"163","article-title":"Error bounds for linear interpolation on triangles","author":"Gregory","year":"1975"},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib21","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1051\/m2an\/1982160302111","article-title":"Triangulation automatique d'un polyedre in dimension n","volume":"76","author":"Hermeline","year":"1982","journal-title":"RAIRO Anal. Numer."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib22","unstructured":"Lafranche, Y., Application de l'interpolation polynomiale au d\u00e9pouillement graphique de valeurs de IR3, Dissertation, Univ. Rennes, 1984."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib23","article-title":"Generation of a triangular grid with application to contour plotting","volume":"299","author":"Lawson","year":"1972","journal-title":"JPL"},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib24","series-title":"Mathematical Software III","first-page":"161","article-title":"Software for C1 surface interpolation","author":"Lawson","year":"1977"},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib25","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1216\/RMJ-1984-14-1-177","article-title":"C1 surface interpolation for scattered data on a sphere","volume":"14","author":"Lawson","year":"1984","journal-title":"Rocky Mt. J."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib26","unstructured":"Lawson, C. L., Some properties of n-dimensional triangulations, JPL Rpt. 85\u201342, Cal. Tech, 1985."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib27","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/BF00977785","article-title":"Two algorithms for constructing a Delaunay triangulation","volume":"9","author":"Lee","year":"1980","journal-title":"Int. J. Comp. Inf. Sci."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib28","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1093\/comjnl\/21.4.324","article-title":"Triangulation of planar regions with applications","volume":"21","author":"Lewis","year":"1978","journal-title":"Computer J."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib29","unstructured":"Little, F. F., Triangular interpolants for computer aided geometric design and scattered data fitting, Dissertation, Univ. of Utah, 1981."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib30","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1093\/comjnl\/19.2.178","article-title":"Two dimensional interpolation from random data","volume":"19","author":"McLain","year":"1976","journal-title":"Comput. J."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib31","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/0307-904X(78)90002-1","article-title":"A triangulation algorithm for arbitrary planar domains","volume":"2","author":"Nelson","year":"1978","journal-title":"Appl. Math. Modelling"},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib32","unstructured":"Pitteway, N. L. K., Computer-graphics research in an academic environment, Datafair 73 Conference Proceedings Vol. 2, 1973, 471\u2013478."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib33","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1145\/2701.2703","article-title":"Interpolation of data on the surface of a sphere","volume":"10","author":"Renka","year":"1984","journal-title":"ACM TOMS"},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib34","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1145\/2701.356108","article-title":"Algorithm 624: Triangulation and interpolation of arbitrarily distributed points in the plane","volume":"10","author":"Renka","year":"1984","journal-title":"ACM TOMS"},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib35","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1111\/j.1538-4632.1973.tb01003.x","article-title":"Analytic delineation of Thiessen polygons","volume":"5","author":"Rhynsburger","year":"1973","journal-title":"Geograph. Anal."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib36","series-title":"Algorithms for the approximation of functions and data","article-title":"Numerical aspects of piecewise polynomials on triangulations","author":"Schumaker","year":"1987"},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib37","unstructured":"Sewell, E. G., Automatic generation of triangulations for piecewise polynomial approximation, Dissertation, Purdue Univ., 1972."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib38","doi-asserted-by":"crossref","unstructured":"Shamos, M.I. and D. Hoey, Closest point problems, in Proc. 16th Ann. Symp. on Foundations of Computer Science, 1975, 151\u2013162.","DOI":"10.1109\/SFCS.1975.8"},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib39","doi-asserted-by":"crossref","unstructured":"Shamos, M.I., Geometric complexity, in Proc. 7th ACM Symp. of Theory of Computing, 1975, 224\u2013233.","DOI":"10.1145\/800116.803772"},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib40","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1093\/comjnl\/21.3.243","article-title":"Locally equiangular triangulations","volume":"21","author":"Sibson","year":"1978","journal-title":"Computer J."},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib41","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/0098-3004(82)90039-5","article-title":"ACORD = Automatic contouring of raw data","volume":"8","author":"Watson","year":"1981","journal-title":"Computer & Geoscience"},{"key":"10.1016\/B978-0-12-174585-1.50022-1_bib42","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1093\/comjnl\/24.2.167","article-title":"Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes","volume":"24","author":"Watson","year":"1981","journal-title":"Comp. J."}],"container-title":["Topics in Multivariate Approximation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:B9780121745851500221?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:B9780121745851500221?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,8,12]],"date-time":"2019-08-12T08:47:50Z","timestamp":1565599670000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/B9780121745851500221"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1987]]},"ISBN":["9780121745851"],"references-count":42,"URL":"https:\/\/doi.org\/10.1016\/b978-0-12-174585-1.50022-1","relation":{},"subject":[],"published":{"date-parts":[[1987]]}}}