Interactive Data Interpolation by Rational Bezier Curves

Some interpolation techniques produce curves that the designer considers unsatisfactory. Even when the data points lie on an apparently simple curve, the resulting interpolant may not be the obvious one. This article presents an algorithm that combines interactive techniques with interpolation methods to allow user intervention. Rational Bezier curves are used as local interpolants, and an approach is discussed for exploiting shape parameters.

[1]  Les A. Piegl,et al.  A geometric investigation of the rational bezier scheme of computer aided design , 1986 .

[2]  A. Robin Forrest,et al.  Curves and surfaces for computer-aided design , 1968 .

[3]  Laszlo Piegl,et al.  On the use of infinite control points in CAGD , 1987, Comput. Aided Geom. Des..

[4]  David F. McAllister,et al.  Algorithms for Computing Shape Preserving Spline Interpolations to Data , 1977 .

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

[6]  Gábor Renner,et al.  Method of shape description for mechanical engineering practice , 1982 .

[7]  John A. Roulier Constrained Interpolation , 1980 .

[8]  Les A. Piegl Representation of rational Be´zier curves and surfaces by recursive algorithms , 1986 .

[9]  S. A. Coons SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS , 1967 .

[10]  James Ferguson,et al.  Multivariable Curve Interpolation , 1964, JACM.

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

[12]  Sudhir P. Mudur,et al.  Mathematical Elements for Computer Graphics , 1985, Advances in Computer Graphics.

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

[14]  A. W. Nutbourne A cubic spline package. Part 2-The mathematics , 1973, Comput. Aided Des..

[15]  J. R. Manning Continuity Conditions for Spline Curves , 1974, Comput. J..

[16]  C. R. Deboor,et al.  A practical guide to splines , 1978 .

[17]  Harry McLaughlin,et al.  Shape-Preserving Planar Interpolation: An Algorithm , 1983, IEEE Computer Graphics and Applications.

[18]  A. R. Forrest,et al.  The twisted cubic curve: a computer-aided geometric design approach , 1980 .

[19]  Les A. Piegl The sphere as a rational Bézier surface , 1986, Comput. Aided Geom. Des..

[20]  E. Nakamae,et al.  Application of the Bézier curve to data interpolation , 1982 .

[21]  A. W. Nutbourne,et al.  A cubic spline package. Part 1 - The user's guide , 1972, Comput. Aided Des..