{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,30]],"date-time":"2025-05-30T15:40:02Z","timestamp":1748619602643,"version":"3.41.0"},"publisher-location":"Cham","reference-count":24,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319243689"},{"type":"electronic","value":"9783319243696"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-319-24369-6_35","type":"book-chapter","created":{"date-parts":[[2015,9,10]],"date-time":"2015-09-10T22:46:37Z","timestamp":1441925197000},"page":"423-434","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Lagrange Piecewise-Quadratic Interpolation Based on Planar Unordered Reduced Data"],"prefix":"10.1007","author":[{"given":"Ryszard","family":"Kozera","sequence":"first","affiliation":[]},{"given":"Piotr","family":"Szmielew","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,10,30]]},"reference":[{"key":"35_CR1","doi-asserted-by":"publisher","DOI":"10.1142\/9789812813381","volume-title":"Methods of Shape-Preserving Spline Approximation","author":"BI Kvasov","year":"2000","unstructured":"Kvasov, B.I.: Methods of Shape-Preserving Spline Approximation. World Scientific Publishing Company, Singapore (2000)"},{"issue":"18","key":"35_CR2","first-page":"28","volume":"7","author":"M Janik","year":"2013","unstructured":"Janik, M., Kozera, R., Kozio\u0142, P.: Reduced data for curve modeling - applications in graphics, computer vision and physics. Advances in Science and Technology 7(18), 28\u201335 (2013)","journal-title":"Advances in Science and Technology"},{"key":"35_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-59223-2","volume-title":"The NURBS Book","author":"L Piegl","year":"1997","unstructured":"Piegl, L., Tiller, W.: The NURBS Book. Springer, Heidelberg (1997)"},{"unstructured":"Ross, K.A., Wright, C.R.B.: Discrete Mathematics. Pearson (2002)","key":"35_CR4"},{"issue":"4B\u201361","key":"35_CR5","first-page":"1","volume":"25","author":"R Kozera","year":"2004","unstructured":"Kozera, R.: Curve modeling via interpolation based on multidimensional reduced data. Studia Informatica 25(4B\u201361), 1\u2013140 (2004)","journal-title":"Studia Informatica"},{"key":"35_CR6","volume-title":"A Practical Guide to Splines","author":"C Boor De","year":"2001","unstructured":"De Boor, C.: A Practical Guide to Splines. Springer, Heidelberg (2001)"},{"key":"35_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"430","DOI":"10.1007\/978-3-642-40925-7_40","volume-title":"Computer Information Systems and Industrial Management","author":"R Kozera","year":"2013","unstructured":"Kozera, R., Noakes, L., Szmielew, P.: Trajectory estimation for exponential parameterization and different samplings. In: Saeed, K., Chaki, R., Cortesi, A., Wierzcho\u0144, S. (eds.) CISIM 2013. LNCS, vol. 8104, pp. 430\u2013441. Springer, Heidelberg (2013)"},{"key":"35_CR8","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1588-2","volume-title":"Handbook of Complex Variables","author":"SG Krantz","year":"1999","unstructured":"Krantz, S.G.: Handbook of Complex Variables. Springer Science+Business Media, New York (1999)"},{"doi-asserted-by":"crossref","unstructured":"Noakes, L., Kozera, R.: Cumulative chord piecewise quadratics and piecewise cubics. In: Klette, R., Kozera, R., Noakes, L., Weickert, J. (eds.) Geometric Properties for Incomplete Data Computational Imaging and Vision, vol. 31, pp. 59\u201376. Springer (2006)","key":"35_CR9","DOI":"10.1007\/1-4020-3858-8_4"},{"doi-asserted-by":"crossref","unstructured":"Kozera, R., Noakes, L.: Piecewise-quadratics and reparameterizations for interpolating reduced data. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds.) CASC 2015. LNCS, vol. 9301, pp. 260\u2013274. Springer Int. Pub. Switzerland (2015)","key":"35_CR10","DOI":"10.1007\/978-3-319-24021-3_20"},{"unstructured":"Wolfram Mathematica 9, Documentation Center. http:\/\/reference.wolfram.com\/mathematica\/guide\/Mathematica.html","key":"35_CR11"},{"key":"35_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1007\/3-540-36586-9_26","volume-title":"Geometry, Morphology, and Computational Imaging","author":"R Kozera","year":"2003","unstructured":"Kozera, R., Noakes, L., Klette, R.: External versus internal parameterizations for lengths of curves with nonuniform samplings. In: Asano, T., Klette, R., Ronse, C. (eds.) Geometry, Morphology, and Computational Imaging. LNCS, vol. 2616, pp. 403\u2013418. Springer, Heidelberg (2003)"},{"issue":"3","key":"35_CR13","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1090\/qam\/1999832","volume":"61","author":"L Noakes","year":"2003","unstructured":"Noakes, L., Kozera, R.: More-or-less uniform sampling and lengths of curves. Quarterly of Applied Mathematics 61(3), 475\u2013484 (2003)","journal-title":"Quarterly of Applied Mathematics"},{"issue":"4","key":"35_CR14","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1007\/s10044-008-0134-x","volume":"12","author":"M Bator","year":"2009","unstructured":"Bator, M., Chmielewski, L.: Finding regions of interest for cancerous masses enhanced by elimination of linear structures and considerations on detection correctness measures in mammography. Pattern Analysis and Applications 12(4), 377\u2013390 (2009)","journal-title":"Pattern Analysis and Applications"},{"key":"35_CR15","doi-asserted-by":"publisher","first-page":"620","DOI":"10.1016\/j.amc.2013.06.060","volume":"221","author":"R Kozera","year":"2013","unstructured":"Kozera, R., Noakes, L.: Piecewise-quadratics and exponential parameterization for reduced data. Applied Mathematics and Computation 221, 620\u2013638 (2013)","journal-title":"Applied Mathematics and Computation"},{"key":"35_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/978-3-642-53926-8_4","volume-title":"Image and Video Technology \u2013 PSIVT 2013 Workshops","author":"R Kozera","year":"2014","unstructured":"Kozera, R., Noakes, L., Szmielew, P.: Length estimation for exponential parameterization and $$\\epsilon $$ -uniform samplings. In: Huang, F., Sugimoto, A. (eds.) PSIVT 2013. LNCS, vol. 8334, pp. 33\u201346. Springer, Heidelberg (2014)"},{"key":"35_CR17","volume-title":"Curves and Surfaces for Computer Aided Geometric Design","author":"G Farin","year":"1993","unstructured":"Farin, G.: Curves and Surfaces for Computer Aided Geometric Design, 3rd edn. Academic Press, San Diego (1993)","edition":"3"},{"key":"35_CR18","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1137\/0713025","volume":"13","author":"MP Epstein","year":"1976","unstructured":"Epstein, M.P.: On the influence of parameterization in parametric interpolation. SIAM Journal of Numerical Analysis. 13, 261\u2013268 (1976)","journal-title":"SIAM Journal of Numerical Analysis."},{"issue":"3\u20134","key":"35_CR19","doi-asserted-by":"crossref","first-page":"285","DOI":"10.3233\/FUN-2004-613-406","volume":"61","author":"R Kozera","year":"2004","unstructured":"Kozera, R., Noakes, L.: $$C^1$$ interpolation with cumulative chord cubics. Fundamenta Informaticae 61(3\u20134), 285\u2013301 (2004)","journal-title":"Fundamenta Informaticae"},{"issue":"2","key":"35_CR20","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1016\/0165-0114(91)90002-8","volume":"44","author":"W Homenda","year":"1991","unstructured":"Homenda, W., Pedrycz, W.: Processing uncertain information in the linear space of fuzzy sets. Fuzzy Sets and Systems 44(2), 187\u2013198 (1991)","journal-title":"Fuzzy Sets and Systems"},{"issue":"2","key":"35_CR21","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1134\/S0361768813020035","volume":"39","author":"DA Budzko","year":"2013","unstructured":"Budzko, D.A., Prokopenya, A.N.: Symbolic numerical methods for searching equilibrium states in a restricted four-body problem. Programming and Computer Software 39(2), 74\u201380 (2013)","journal-title":"Programming and Computer Software"},{"issue":"217","key":"35_CR22","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1090\/S0025-5718-97-00796-5","volume":"66","author":"K M\u00f8rken","year":"1997","unstructured":"M\u00f8rken, K., Scherer, K.: A general framework for high-accuracy parametric interpolation. Mathematics of Computation 66(217), 237\u2013260 (1997)","journal-title":"Mathematics of Computation"},{"key":"35_CR23","first-page":"95","volume":"5","author":"LM Koci\u0107","year":"1990","unstructured":"Koci\u0107, L.M., Simoncelli, A.C., Della Vecchia, B.: Blending parameterization of polynomial and spline interpolants, Facta Universitatis (NI\u0160). Series Mathematics and Informatics 5, 95\u2013107 (1990)","journal-title":"Series Mathematics and Informatics"},{"issue":"6","key":"35_CR24","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1016\/0010-4485(89)90003-1","volume":"21","author":"ETY Lee","year":"1987","unstructured":"Lee, E.T.Y.: Choosing nodes in parametric curve interpolation. Computer-Aided Design 21(6), 363\u2013370 (1987)","journal-title":"Computer-Aided Design"}],"container-title":["Lecture Notes in Computer Science","Computer Information Systems and Industrial Management"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-24369-6_35","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,30]],"date-time":"2025-05-30T15:08:56Z","timestamp":1748617736000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-24369-6_35"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319243689","9783319243696"],"references-count":24,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-24369-6_35","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2015]]},"assertion":[{"value":"30 October 2015","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}