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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Box Splines (Paperback, Softcover reprint of hardcover 1st ed. 1993)
Loot Price: R1,452
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Box Splines (Paperback, Softcover reprint of hardcover 1st ed. 1993)
Series: Applied Mathematical Sciences, 98
Expected to ship within 18 - 22 working days
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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.
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