Planar cubic G1 interpolatory splines with small strain energy

In this paper, a classical problem of the construction of a cubic G^1 continuous interpolatory spline curve is considered. The only data prescribed are interpolation points, while tangent directions are unknown. They are constructed automatically in such a way that a particular minimization of the strain energy of the spline curve is applied. The resulting spline curve is constructed locally and is regular, cusp-, loop- and fold-free. Numerical examples demonstrate that it is satisfactory as far as the shape of the curve is concerned.

[1]  J. Koch,et al.  Geometric Hermite interpolation with maximal orderand smoothness , 1996, Comput. Aided Geom. Des..

[2]  E. T. Y. Lee,et al.  Choosing nodes in parametric curve interpolation , 1989 .

[3]  Jun-Hai Yong,et al.  Geometric Hermite curves with minimum strain energy , 2004, Comput. Aided Geom. Des..

[4]  Steven Pruess.  Shape preserving C2 cubic spline interpolation , 1993 .

[5]  Costanza Conti,et al.  PiecewiseC1-shape-preserving Hermite interpolation , 2005, Computing.

[6]  T. Goodman,et al.  Shape preserving interpolation by parametrically defined curves , 1988 .

[7]  Paolo Costantini,et al.  A General Scheme for Shape Preserving Planar Interpolating Curves , 2003 .

[8]  Gasper Jaklic,et al.  On geometric interpolation of circle-like curves , 2007, Comput. Aided Geom. Des..

[9]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[10]  Carla Manni,et al.  Shape-preserving interpolants with high smoothness , 2003 .

[11]  Johannes Wallner.  Note on curve and surface energies , 2007, Comput. Aided Geom. Des..

[12]  Panagiotis D. Kaklis,et al.  Convexity-preserving interpolatory parametric splines of non-uniform polynomial degree , 1995, Comput. Aided Geom. Des..

[13]  Abedallah Rababah.  High order approximation method for curves , 1995, Comput. Aided Geom. Des..

[14]  Jernej Kozak,et al.  Geometric interpolation by planar cubic G1 splines , 2007 .

[15]  Michael S. Floater.  On the deviation of a parametric cubic spline interpolant from its data polygon , 2008, Comput. Aided Geom. Des..

[16]  Gasper Jaklic,et al.  On geometric interpolation by planar parametric polynomial curves , 2007, Math. Comput..

[17]  Knut Mørken,et al.  A general framework for high-accuracy parametric interpolation , 1997, Math. Comput..

[18]  Jernej Kozak,et al.  On Geometric Interpolation by Polynomial Curves , 2004, SIAM J. Numer. Anal..

[19]  Malcolm A. Sabin,et al.  High accuracy geometric Hermite interpolation , 1987, Comput. Aided Geom. Des..