Interproximation: interpolation and approximation using cubic spline curves

Abstract An algorithm for the construction of a cubic spline curve with relatively good shape that interpolates specified data points at some knots and passes through specified regions at some other knots is presented. The curve constructed by the algorithm has minimum energy on each of its components. This algorithm has applications in various fields, such as the reconstruction of natural phenomena where data points cannot be sampled exactly, or computer-aided modeling where some of the fitting points cannot be explicitly specified.

[1]  Donald E. Knuth,et al.  TEX and METAFONT: New directions in typesetting , 1979 .

[2]  I. Faux,et al.  Computational Geometry for Design and Manufacture , 1979 .

[3]  J. Kjellander.  Smoothing of cubic parametric splines , 1983 .

[4]  B. Barsky,et al.  An Introduction to Splines for Use in Computer Graphics and Geometric Modeling , 1987 .

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

[6]  E. T. Y. Lee.  Energy, fairness, and a counterexample , 1990, Comput. Aided Des..

[7]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[8]  Wolfgang Böhm,et al.  A survey of curve and surface methods in CAGD , 1984, Comput. Aided Geom. Des..

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

[10]  Fuhua Cheng,et al.  B-spline curves and surfaces viewed as digital filters , 1990, Comput. Vis. Graph. Image Process..

[11]  C. Reinsch.  Smoothing by spline functions , 1967 .

[12]  B. Barsky,et al.  Determining a set of B-spline control vertices to generate an interpolating surface , 1980 .

[13]  Fuhua Cheng,et al.  A parallel B-spline surface fitting algorithm , 1988, TOGS.

[14]  Thomas A. Foley,et al.  Weighted bicubic spline interpolation to rapidly varying data , 1987, TOGS.

[15]  A. K. Cline.  Scalar- and planar-valued curve fitting using splines under tension , 1974, Commun. ACM.

[16]  Donald P. Greenberg,et al.  Interactive surface representation system using a B-spline formulation with interpolation capability , 1982 .

[17]  Mordecai Avriel,et al.  Nonlinear programming , 1976 .

[18]  Brian A. Barsky.  Exponential and polynomial methods for applying tension to an interpolating spline curve , 1984, Comput. Vis. Graph. Image Process..

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