LEADER 05649nam 22008175 450 001 9910299972703321 005 20200705010749.0 010 $a3-319-08635-9 024 7 $a10.1007/978-3-319-08635-4 035 $a(CKB)3710000000268422 035 $a(EBL)1968131 035 $a(OCoLC)894509021 035 $a(SSID)ssj0001372775 035 $a(PQKBManifestationID)11888499 035 $a(PQKBTitleCode)TC0001372775 035 $a(PQKBWorkID)11310644 035 $a(PQKB)10536144 035 $a(MiAaPQ)EBC1968131 035 $a(DE-He213)978-3-319-08635-4 035 $a(PPN)182099989 035 $a(EXLCZ)993710000000268422 100 $a20141024d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSAGA ? Advances in ShApes, Geometry, and Algebra $eResults from the Marie Curie Initial Training Network /$fedited by Tor Dokken, Georg Muntingh 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (324 p.) 225 1 $aGeometry and Computing,$x1866-6795 ;$v10 300 $aDescription based upon print version of record. 311 $a3-319-08634-0 320 $aIncludes bibliographical references and index. 327 $a1 Introduction to ShApes, Geometry, and Algebra: Tor Dokken and Georg Muntingh -- Part I Change of Representation: 2 Numerical methods for implicitisation and their applications: Oliver J. D. Barrowclough -- 3 Sparse implicitization via interpolation: Ioannis Z. Emiris, Tatjana Kalinka, and Christos Konaxis -- 4 The intersection problems of parametric curves and surfaces by means of matrix-based implicit representations: Thang Luu Ba -- Part II Geometric Computing ? Algebraic Tools: 5 Singular Zeros of Polynomial Systems: Angelos Mantzaflaris and Bernard Mourrain -- 6 Plane mixed discriminants and toric jacobians: Alicia Dickenstein, Ioannis Z. Emiris and Anna Karasoulou -- 7 Topology of the intersection of two parameterized surfaces, using computations in 4D space: Stéphane Chau and André Galligo --  8 Rational Bézier Formulas with Quaternion and Clifford Algebra Weights: Rimvydas Krasauskas and Severinas Zubé -- Part III Algebraic Geometry for CAD Applications: 9 Algebraic spline geometry ? some remarks: Ragni Piene -- 10 On the dimension of spline spaces on triangulations: Nelly Villamizar and Bernard Mourrain -- 11 Polynomial Interpolation Problems in Projective Spaces and Products of Projective Lines: Elisa Postinghel -- 12 Rational parametrizations of edge and corner blends for isogeometric analysis: Heidi E. I. Dahl -- Part IV Practical Industrial Problems: 13 Bisectors and Vorono¨? diagram of a family of parallel half-lines: I. Adamou, M. Fioravanti, L. Gonzalez-Vega, and B. Mourrain -- 14 Generating an approximate trivariate spline representation for contractible domains: Thien T. Nguyen -- 15 Isogeometric analysis of Navier-Stokes flow using locally refinable B-splines: Peter Nørtoft and Tor Dokken. 330 $aThis book summarizes research carried out in workshops of the SAGA project, an Initial Training Network exploring the interplay of Shapes, Algebra, Geometry and Algorithms. Written by a combination of young and experienced researchers, the book introduces new ideas in an established context. Among the central topics are approximate and sparse implicitization and surface parametrization; algebraic tools for geometric computing; algebraic geometry for computer aided design applications and problems with industrial applications. Readers will encounter new methods for the (approximate) transition between the implicit and parametric representation; new algebraic tools for geometric computing; new applications of isogeometric analysis, and will gain insight into the emerging research field situated between algebraic geometry and computer aided geometric design. 410 0$aGeometry and Computing,$x1866-6795 ;$v10 606 $aGeometry 606 $aAlgebra 606 $aComputer science?Mathematics 606 $aComputer-aided engineering 606 $aMathematical models 606 $aGeometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21006 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 606 $aMathematics of Computing$3https://scigraph.springernature.com/ontologies/product-market-codes/I17001 606 $aComputer-Aided Engineering (CAD, CAE) and Design$3https://scigraph.springernature.com/ontologies/product-market-codes/I23044 606 $aMathematical Modeling and Industrial Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M14068 615 0$aGeometry. 615 0$aAlgebra. 615 0$aComputer science?Mathematics. 615 0$aComputer-aided engineering. 615 0$aMathematical models. 615 14$aGeometry. 615 24$aAlgebra. 615 24$aMathematics of Computing. 615 24$aComputer-Aided Engineering (CAD, CAE) and Design. 615 24$aMathematical Modeling and Industrial Mathematics. 676 $a003.3 676 $a004.0151 676 $a510 676 $a512 702 $aDokken$b Tor$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aMuntingh$b Georg$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299972703321 996 $aSAGA ? Advances in ShApes, Geometry, and Algebra$91409848 997 $aUNINA