Applied Mathematical Sciences

Box Splines

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

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About this Textbook

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.

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook 58,84 €
price for Spain (gross)
  • ISBN 978-1-4757-2244-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
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Hardcover 72,79 €
price for Spain (gross)
  • ISBN 978-0-387-94101-1
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 69,63 €
price for Spain (gross)
  • ISBN 978-1-4419-2834-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Box Splines
Authors
Series Title
Applied Mathematical Sciences
Series Volume
98
Copyright
1993
Publisher
Springer-Verlag New York
Copyright Holder
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
Series ISSN
0066-5452
Edition Number
1
Number of Pages
XVII, 201
Number of Illustrations
68 b/w illustrations
Topics