Инд. авторы:	Kim T.W., Kvasov B.
Заглавие:	A shape-preserving approximation by weighted cubic splines
Библ. ссылка:	Kim T.W., Kvasov B. A shape-preserving approximation by weighted cubic splines // Journal of Computational and Applied Mathematics. - 2012. - Vol.236. - Iss. 17. - P.4383-4397. - ISSN 0377-0427. - EISSN 1879-1778.
Внешние системы:	DOI: 10.1016/j.cam.2012.04.001; РИНЦ: 17998899; SCOPUS: 2-s2.0-84862871617; WoS: 000307027700018;
Реферат:	eng: This paper addresses new algorithms for constructing weighted cubic splines that are very effective in interpolation and approximation of sharply changing data. Such spline interpolations are a useful and efficient tool in computer-aided design when control of tension on intervals connecting interpolation points is needed. The error bounds for interpolating weighted splines are obtained. A method for automatic selection of the weights is presented that permits preservation of the monotonicity and convexity of the data. The weighted B-spline basis is also well suited for generation of freeform curves, in the same way as the usual B-splines. By using recurrence relations we derive weighted B-splines and give a three-point local approximation formula that is exact for first-degree polynomials. The resulting curves satisfy the convex hull property, they are piecewise cubics, and the curves can be locally controlled with interval tension in a computationally efficient manner.
Издано:	2012
Физ. характеристика:	с.4383-4397