A shape-preserving approximation by weighted cubic splines

作者：Kim Tae wan^*; Kvasov Boris

来源：Journal of Computational and Applied Mathematics, 2012, 236(17): 4383-4397.

DOI：10.1016/j.cam.2012.04.001

• Shape-preserving interpolation and approximation
• Differential multipoint boundary value problem
• Weighted cubic splines
• Error bounds
• Adaptive choice of shape control parameters
• Recurrence relations for weighted B-splines

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.

• 出版日期2012-11