Applied Mathematical Sciences

Box Splines

Autoren: Boor, Carl de, Höllig, Klaus, Riemenschneider, Sherman

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Über dieses Lehrbuch

Compactly supported smooth piecewise polynomial functions provide an efficient tool for the approximation of curves and surfaces and other smooth functions of one and several arguments. Since they are locally polynomial, they are easy to evaluate. Since they are smooth, they can be used when smoothness is required, as in the numerical solution of partial differential equations (in the Finite Element method) or the modeling of smooth sur­ faces (in Computer Aided Geometric Design). Since they are compactly supported, their linear span has the needed flexibility to approximate at all, and the systems to be solved in the construction of approximations are 'banded'. The construction of compactly supported smooth piecewise polynomials becomes ever more difficult as the dimension, s, of their domain G ~ IRs, i. e. , the number of arguments, increases. In the univariate case, there is only one kind of cell in any useful partition, namely, an interval, and its boundary consists of two separated points, across which polynomial pieces would have to be matched as one constructs a smooth piecewise polynomial function. This can be done easily, with the only limitation that the num­ ber of smoothness conditions across such a breakpoint should not exceed the polynomial degree (since that would force the two joining polynomial pieces to coincide). In particular, on any partition, there are (nontrivial) compactly supported piecewise polynomials of degree ~ k and in C(k-l), of which the univariate B-spline is the most useful example.

Inhaltsverzeichnis (7 Kapitel)

Inhaltsverzeichnis (7 Kapitel)

Dieses Buch kaufen

eBook 58,84 €
Preis für Deutschland (Brutto)
  • ISBN 978-1-4757-2244-4
  • Versehen mit digitalem Wasserzeichen, DRM-frei
  • Erhältliche Formate: PDF
  • eBooks sind auf allen Endgeräten nutzbar
  • Sofortiger eBook Download nach Kauf
Hardcover 74,89 €
Preis für Deutschland (Brutto)
Softcover 71,64 €
Preis für Deutschland (Brutto)
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Bibliografische Information

Bibliographic Information
Buchtitel
Box Splines
Autoren
Titel der Buchreihe
Applied Mathematical Sciences
Buchreihen Band
98
Copyright
1993
Verlag
Springer-Verlag New York
Copyright Inhaber
Springer Science+Business Media New York
eBook ISBN
978-1-4757-2244-4
DOI
10.1007/978-1-4757-2244-4
Hardcover ISBN
978-0-387-94101-1
Softcover ISBN
978-1-4419-2834-4
Buchreihen ISSN
0066-5452
Auflage
1
Seitenzahl
XVII, 201
Anzahl der Bilder
68 schwarz-weiß Abbildungen
Themen