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Article Dans Une Revue Computer Aided Geometric Design Année : 2016

Design with Quasi Extended Chebyshev Piecewise Spaces

Marie-Laurence Mazure
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Résumé

A Quasi Extended Chebyshev (QEC) space is a space of sufficiently differentiable functions in which any Hermite interpolation problem which is a not a Taylor problem is unisolvent. On a given interval the class of all spaces which contains constants and for which the space obtained by differentiation is a QEC-space has been identified as the largest class of spaces (under ordinary differentiability assumptions) which can be used for design. As a first step towards determining the largest class of splines for design, we consider a sequence of QEC-spaces on adjacent intervals, all of the same dimension, we join them via connection matrices, so as to maintain both the dimension and the unisolvence. The resulting space is called a Quasi Extended Chebyshev Piecewise (QECP) space. We show that all QECP-spaces are inverse images of two-dimensional Chebyshev spaces under piecewise generalised derivatives associated with systems of piecewise weight functions. We show illustrations proving that QECP-spaces can produce interesting shape effects.
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Dates et versions

hal-01219653 , version 1 (23-10-2015)

Identifiants

Citer

Marie-Laurence Mazure. Design with Quasi Extended Chebyshev Piecewise Spaces. Computer Aided Geometric Design, 2016, SI: New Developments Geometry, 47, pp.3-28. ⟨10.1016/j.cagd.2016.03.002⟩. ⟨hal-01219653⟩
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