A shape preserving interpolant with tension controls

Abstract The monotonically and convexly constrained (MONCON) weighted v -spline interpolant is presented, which is the C 1 piecewise cubic solution to a constrained optimization problem. In addition to preserving the local monotonicity and local convexity of the data, the method has tension parameters which can be used to modify the shape of the interpolating function. Local monotonicity constraints are given that don't necessarily force the derivatives to be zero where the data changes from increasing to decreasing.

[1]  R. Beatson.  Monotone and Convex Approximation by Splines: Error Estimates and a Curve Fitting Algorithm , 1982 .

[2]  R. Beatson,et al.  Monotonicity Preserving Surface Interpolation , 1985 .

[3]  L. D. Irvine,et al.  Constrained interpolation and smoothing , 1986 .

[4]  Carl de Boor,et al.  Piecewise monotone interpolation , 1977 .

[5]  Panagiotis D. Kaklis,et al.  An algorithm for constructing convexity and monotonicity-preserving splines in tension , 1988, Comput. Aided Geom. Des..

[6]  David F. McAllister,et al.  An Algorithm for Computing a Shape-Preserving Osculatory Quadratic Spline , 1981, TOMS.

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

[8]  Philip E. Gill,et al.  Practical optimization , 1981 .

[9]  J. A. Gregory.  Shape preserving spline interpolation , 1986 .

[10]  K. Salkauskas.  $C^1$ >splines for interpolation of rapidly varying data , 1984 .

[11]  F. Fritsch,et al.  A Method for Constructing Local Monotone Piecewise Cubic Interpolants , 1984 .

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

[13]  Thomas A. Foley,et al.  Interpolation with interval and point tension controls using cubic weighted v-splines , 1987, TOMS.

[14]  J. Hyman.  Accurate Monotonicity Preserving Cubic Interpolation , 1983 .

[15]  D. R. Ferguson.  Construction of curves and surfaces using numerical optimization techniques , 1986 .

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

[17]  E. Polak.  Introduction to linear and nonlinear programming , 1973 .

[18]  J. Gregory,et al.  Piecewise rational quadratic interpola-tion to monotonic data , 1982 .

[19]  Gregory M. Nielson,et al.  Rectangular v-Splines , 1986, IEEE Computer Graphics and Applications.

[20]  David F. McAllister,et al.  Interpolation by convex quadratic splines , 1978 .

[21]  Larry I. Schumaker.  ON SHAPE PRESERVING QUADRATIC SPLINE INTERPOLATION , 1983 .

[22]  C. Micchelli,et al.  Admissible slopes for monotone and convex interpolation , 1987 .

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

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