LEADER 02748nam 2200409 450 001 9910795157003321 005 20230803043726.0 010 $a3-8325-9165-6 035 $a(CKB)4910000000017334 035 $a(MiAaPQ)EBC5850421 035 $a5a8e86f0-aa04-4848-925e-66c5b0dd2d03 035 $a(EXLCZ)994910000000017334 100 $a20190917d2013 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aModeling with ambient B-Splines /$fNicole Lehmann 210 1$aBerlin :$cLogos Verlag,$d[2013] 210 4$d©2013 215 $a1 online resource (126 pages) $cillustrations 300 $aPublicationDate: 20140117 311 $a3-8325-3602-7 320 $aIncludes bibliographical references. 330 $aLong description: The present thesis introduces a new approach for the generation of C^k-approximants of functions defined on closed submanifolds for arbitrary k in N. In case a function on a surface resembles the three coordinates of a topologically equivalent surface in R³, we even obtain C^k-approximants of closed surfaces of arbitrary topology. The key idea of our method is a constant extension of the target function into the submanifold's ambient space. In case the reference submanifolds are embedded and C^k, the usage of standard tensor product B-splines for the approximation of the extended function is straightforward. We obtain a C^k-approximation of the target function by restricting the approximant to the reference submanifold. We illustrate our method by an easy example in R² and verify its practicality by application-oriented examples in R³. The first treats the approximation of the geoid, an important reference magnitude within geodesy and geophysics. The second and third example treat the approximation of geometric models. The usage of B-splines not only guarantees full approximation power but also allows a canonical access to adaptive refinement strategies. We elaborate on two hierarchical techniques and successfully apply them to the introduced examples. Concerning the modeling of surfaces by the new approach, we derive numerically robust formulas for the determination of normal vectors and curvature information of a target surface which only need the spline approximant as well as the normal vectors and curvature information of the reference surface. 606 $aSpline theory 615 0$aSpline theory. 676 $a511.42 700 $aLehmann$b Nicole$01561688 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910795157003321 996 $aModeling with ambient B-Splines$93828658 997 $aUNINA