Splines is a set of C++ classes (with MATLAB mex interface) which implements varios spline interpolation.
The classes are the following:
- ConstantSpline, for piecewise constants functions
- LinearSpline, for piecewise linear interpolation
- CubicSpline, for classical cubic spline interpolation
- AkimaSpline, for Akima "non oscillatory" spline interpolation
- BesselSpline, for Bessel "non oscillatory" spline interpolation
- PchipSpline,
- QuinticSpline, Simple quintic spline based on PCHIP
References
- F.N. Fritsch and R.E. Carlson, Monotone Piecewise Cubic Interpolation, SIAM Journal of Numerical Analysis, Vol. 17, No. 2, pp. 238-246, April 1980.
Matlab
To use in MATLAB install the toolbox Splines.mltbx then compile the files running CompileSplinesLib.
C++ Usage
The usage is simple:
#include "Splines.hh"
using namespace SplinesLoad;
....
CubicSpline spline;
double x[] = {1,2,3,4};
double y[] = {3,1,1,3};
spline.build(x,y,4); // build a cubic spline with 4 points
cout << spline(1.1) << '\n'; // spline at x = 1.1
cout << spline.D(1.1) << '\n'; // spline first derivative at x = 1.1
cout << spline.DD(1.1) << '\n'; // spline second derivative at x = 1.1
cout << spline.DDD(1.1) << '\n'; // spline third derivative at x = 1.1
splines can be built incrementally
#include "Splines.hh"
using namespace SplinesLoad;
....
CubicSpline spline;
spline . pushBack( 1, 3 );
spline . pushBack( 2, 1 );
spline . pushBack( 3, 1 );
spline . pushBack( 4, 3 );
spline . build();
cout << spline(1.1) << '\n'; // spline at x = 1.1
cout << spline.D(1.1) << '\n'; // spline first derivative at x = 1.1
cout << spline.DD(1.1) << '\n'; // spline second derivative at x = 1.1
cout << spline.DDD(1.1) << '\n'; // spline third derivative at x = 1.1
or by using standard vector
#include "Splines.hh"
#include <vector>
using namespace SplinesLoad;
using namespace std;
....
CubicSpline spline;
std::vector x, y;
x.push_back(1); y.push_back(3);
x.push_back(2); y.push_back(1);
x.push_back(3); y.push_back(1);
x.push_back(4); y.push_back(3);
spline . build(x,y);
cout << spline(1.1) << '\n'; // spline at x = 1.1
cout << spline.D(1.1) << '\n'; // spline first derivative at x = 1.1
cout << spline.DD(1.1) << '\n'; // spline second derivative at x = 1.1
cout << spline.DDD(1.1) << '\n'; // spline third derivative at x = 1.1
Compile and tests
Edit makefile file to match compiler of your OS and do:
make
To run the test
make run
To generate documentation (using DOXYGEN: http://www.stack.nl/~dimitri/doxygen/index.html)
make doc
DOXYGEN documentation
Available at: http://ebertolazzi.github.io/Splines/html/index.html
Enrico Bertolazzi
Dipartimento di Ingegneria Industriale
Universita` degli Studi di Trento
email: [email protected]