B-spline bases and osculating flats : one result of H.-P. Seidel revisited
- Volume: 36, Issue: 6, page 1177-1186
- ISSN: 0764-583X
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topMazure, Marie-Laurence. "B-spline bases and osculating flats : one result of H.-P. Seidel revisited." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 36.6 (2002): 1177-1186. <http://eudml.org/doc/245133>.
@article{Mazure2002,
abstract = {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.},
author = {Mazure, Marie-Laurence},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {geometric design; B-spline basis; blossoming; osculating flats},
language = {eng},
number = {6},
pages = {1177-1186},
publisher = {EDP-Sciences},
title = {B-spline bases and osculating flats : one result of H.-P. Seidel revisited},
url = {http://eudml.org/doc/245133},
volume = {36},
year = {2002},
}
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 - Modélisation Mathématique et Analyse Numérique
PY - 2002
PB - EDP-Sciences
VL - 36
IS - 6
SP - 1177
EP - 1186
AB - 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.
LA - eng
KW - geometric design; B-spline basis; blossoming; osculating flats
UR - http://eudml.org/doc/245133
ER -
References
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- [3] M.-L. Mazure, Blossoming: a geometrical approach. Constr. Approx. 15 (1999) 33–68. Zbl0924.65010
- [4] M.-L. Mazure, Quasi-Chebyshev splines with connexion matrices. Application to variable degree polynomial splines. Comput. Aided Geom. Design 18 (2001) 287–298. Zbl0978.41006
- [5] H. Pottmann, The geometry of Tchebycheffian splines. Comput. Aided Geom. Design 10 (1993) 181–210. Zbl0777.41016
- [6] L. Ramshaw, Blossoms are polar forms. Comput. Aided Geom. Design 6 (1989) 323–358. Zbl0705.65008
- [7] H.-P. Seidel, New algorithms and techniques for computing with geometrically continuous spline curves of arbitrary degree. RAIRO Modél. Math. Anal. Numér. 26 (1992) 149–176. Zbl0752.65008
- [8] H.-P. Seidel, Polar forms for geometrically continuous spline curves of arbitrary degree. ACM Trans. Graphics 12 (1993) 1–34. Zbl0770.68116
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