SPLINE
Interpolation and Approximation of Data


SPLINE is a C library which constructs and evaluates spline functions.

These spline functions are typically used to

The most common use of this software is for situations where a set of (X,Y) data points is known, and it is desired to determine a smooth function which passes exactly through those points, and which can be evaluated everywhere. Thus, it is possible to get a formula that allows you to "connect the dots".

Of course, you could could just connect the dots with straight lines, but that would look ugly, and if there really is some function that explains your data, you'd expect it to curve around rather than make sudden angular turns. The functions in SPLINE offer a variety of choices for slinky curves that will make pleasing interpolants of your data.

There are a variety of types of approximation curves available, including:

Also included are a set of routines that return the local "basis matrix", which allows the evaluation of the spline in terms of local function data.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

SPLINE is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

BERNSTEIN_POLYNOMIAL, a C library which evaluates the Bernstein polynomials, useful for uniform approximation of functions;

CHEBYSHEV, a C library which computes the Chebyshev interpolant/approximant to a given function over an interval.

DIVDIF, a C library which uses divided differences to interpolate data.

HERMITE_CUBIC, a C library which can compute the value, derivatives or integral of a Hermite cubic polynomial, or manipulate an interpolating function made up of piecewise Hermite cubic polynomials.

LAGRANGE_INTERP_1D, a C library which defines and evaluates the Lagrange polynomial p(x) which interpolates a set of data, so that p(x(i)) = y(i).

TEST_APPROX, a C library which defines test problems for approximation, provided as a set of (x,y) data.

TEST_INTERP_1D, a C library which defines test problems for interpolation of data y(x), depending on a 1D argument.

Reference:

  1. JA Brewer, DC Anderson,
    Visual Interaction with Overhauser Curves and Surfaces,
    SIGGRAPH 77,
    in Proceedings of the 4th Annual Conference on Computer Graphics and Interactive Techniques,
    ASME, July 1977, pages 132-137.
  2. Edwin Catmull, Raphael Rom,
    A Class of Local Interpolating Splines,
    in Computer Aided Geometric Design,
    edited by Robert Barnhill, Richard Reisenfeld,
    Academic Press, 1974,
    ISBN: 0120790505.
  3. Samuel Conte, Carl deBoor,
    Elementary Numerical Analysis,
    Second Edition,
    McGraw Hill, 1972,
    ISBN: 07-012446-4.
  4. Alan Davies, Philip Samuels,
    An Introduction to Computational Geometry for Curves and Surfaces,
    Clarendon Press, 1996,
    ISBN: 0-19-851478-6,
    LC: QA448.D38.
  5. Carl deBoor,
    A Practical Guide to Splines,
    Springer, 2001,
    ISBN: 0387953663.
  6. Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
    LINPACK User's Guide,
    SIAM, 1979,
    ISBN13: 978-0-898711-72-1.
  7. Gisela Engeln-Muellges, Frank Uhlig,
    Numerical Algorithms with C,
    Springer, 1996,
    ISBN: 3-540-60530-4.
  8. James Foley, Andries vanDam, Steven Feiner, John Hughes,
    Computer Graphics, Principles and Practice,
    Second Edition,
    Addison Wesley, 1995,
    ISBN: 0201848406,
    LC: T385.C5735.
  9. Fred Fritsch, Judy Butland,
    A Method for Constructing Local Monotone Piecewise Cubic Interpolants,
    SIAM Journal on Scientific and Statistical Computing,
    Volume 5, Number 2, 1984, pages 300-304.
  10. Fred Fritsch, Ralph Carlson,
    Monotone Piecewise Cubic Interpolation,
    SIAM Journal on Numerical Analysis,
    Volume 17, Number 2, April 1980, pages 238-246.
  11. David Kahaner, Cleve Moler, Steven Nash,
    Numerical Methods and Software,
    Prentice Hall, 1989,
    ISBN: 0-13-627258-4,
    LC: TA345.K34.
  12. David Rogers, Alan Adams,
    Mathematical Elements of Computer Graphics,
    Second Edition,
    McGraw Hill, 1989,
    ISBN: 0070535299.

Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the C source codes.


Last revised on 10 October 2012.