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Along with the classical requirements on B-splines bases (minimal support, positivity, normalization) we show that it is natural to introduce an additional “end point property”. When dealing with multiple knots, this additional property is exactly the appropriate requirement to obtain the poles of nondegenerate splines as intersections of osculating flats at consecutive knots.
@article{M2AN_2002__36_6_1177_0,
author = {Mazure, Marie-Laurence},
title = {B-spline bases and osculating flats : one result of {H.-P.} {Seidel} revisited},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1177--1186},
publisher = {EDP-Sciences},
volume = {36},
number = {6},
year = {2002},
doi = {10.1051/m2an:2003010},
mrnumber = {1958664},
zbl = {1027.65020},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2003010/}
}
TY - JOUR AU - Mazure, Marie-Laurence TI - B-spline bases and osculating flats : one result of H.-P. Seidel revisited JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2002 SP - 1177 EP - 1186 VL - 36 IS - 6 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2003010/ DO - 10.1051/m2an:2003010 LA - en ID - M2AN_2002__36_6_1177_0 ER -
%0 Journal Article %A Mazure, Marie-Laurence %T B-spline bases and osculating flats : one result of H.-P. Seidel revisited %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2002 %P 1177-1186 %V 36 %N 6 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2003010/ %R 10.1051/m2an:2003010 %G en %F M2AN_2002__36_6_1177_0
Mazure, Marie-Laurence. B-spline bases and osculating flats : one result of H.-P. Seidel revisited. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 36 (2002) no. 6, pp. 1177-1186. doi: 10.1051/m2an:2003010
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