Shape-Preserving C2 Functional Interpolation via Parametric Cubics

The paper proposes a method for the construction of a shape preserving C2 function interpolating a given set of data. The constructed interpolant is a parametric cubic curve. The shape of the curve can be easily controlled via tension parameters which have an immediate geometric interpretation. The approximation order is investigated and numerical examples are presented.

[1]  R. E. Carlson,et al.  Monotone Piecewise Cubic Interpolation , 1980 .

[2]  G. Nielson.  SOME PIECEWISE POLYNOMIAL ALTERNATIVES TO SPLINES UNDER TENSION , 1974 .

[3]  Josef Hoschek,et al.  Fundamentals of computer aided geometric design , 1996 .

[4]  Paolo Costantini,et al.  On monotone and convex spline interpolation , 1986 .

[5]  B. I. Kvasov,et al.  Algorithms for shape preserving local approximation with automatic selection of tension parameters , 2000, Comput. Aided Geom. Des..

[6]  Carla Manni.  C 1 comonotone Hermite interpolation via parametric cubics , 1996 .

[7]  Carla Manni,et al.  Monotone interpolation of order 3 by C2 cubic splines , 1997 .

[8]  H. Huynh,et al.  Accurate monotone cubic interpolation , 1993 .

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

[10]  Chris Grandison.  Behaviour of Exponential Splines as Tensions Increase without Bound , 1997 .

[11]  Paolo Costantini.  An algorithm for computing shape-preserving interpolating splines of arbitrary degree , 1988 .

[12]  R. J. Walker.  Algebraic curves , 1950 .

[13]  Tim N. T. Goodman,et al.  Total Positivity and the Shape of Curves , 1996 .

[14]  Miljenko Marušić,et al.  Sharp error bounds for interpolating splines in tension , 1995 .

[15]  Hiroshi Akima,et al.  A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures , 1970, JACM.

[16]  D. Schweikert.  An Interpolation Curve Using a Spline in Tension , 1966 .

[17]  Jochen W. Schmidt,et al.  Constructive methods in convexC2 interpolation using quartic splines , 2005, Numerical Algorithms.

[18]  J. Gregory,et al.  C2 Rational Quadratic Spline Interpolation to Monotonic Data , 1983 .

[19]  A. Edelman,et al.  Nonnegativity-, monotonicity-, or convexity-preserving cubic and quintic Hermite interpolation , 1989 .

[20]  Paolo Costantini,et al.  Curve and surface construction using variable degree polynomial splines , 2000, Comput. Aided Geom. Des..

[21]  Panagiotis D. Kaklis,et al.  Convexity-Preserving Polynomial Splines of Non-uniform Degree , 1990 .

[22]  Carla Manni.  On Shape Preserving C2 Hermite Interpolation , 2001 .