43,671 research outputs found
Piecewise Extended Chebyshev Spaces: a numerical test for design
Given a number of Extended Chebyshev (EC) spaces on adjacent intervals, all
of the same dimension, we join them via convenient connection matrices without
increasing the dimension. The global space is called a Piecewise Extended
Chebyshev (PEC) Space. In such a space one can count the total number of zeroes
of any non-zero element, exactly as in each EC-section-space. When this number
is bounded above in the global space the same way as in its section-spaces, we
say that it is an Extended Chebyshev Piecewise (ECP) space. A thorough study of
ECP-spaces has been developed in the last two decades in relation to blossoms,
with a view to design. In particular, extending a classical procedure for
EC-spaces, ECP-spaces were recently proved to all be obtained by means of
piecewise generalised derivatives. This yields an interesting constructive
characterisation of ECP-spaces. Unfortunately, except for low dimensions and
for very few adjacent intervals, this characterisation proved to be rather
difficult to handle in practice. To try to overcome this difficulty, in the
present article we show how to reinterpret the constructive characterisation as
a theoretical procedure to determine whether or not a given PEC-space is an
ECP-space. This procedure is then translated into a numerical test, whose
usefulness is illustrated by relevant examples
Polynomial cubic splines with tension properties
In this paper we present a new class of spline functions with tension properties. These splines are composed by polynomial cubic pieces and therefore are conformal to the standard, NURBS based CAD/CAM systems
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