Splines is a set of C++ classes 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 oin PCHIP with 4th derivative set to 0 at nodal points
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.
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://www.ing.unitn.it/~bertolaz/4-software/Splines/index.html
Enrico Bertolazzi
Dipartimento di Ingegneria Industriale
Universita` degli Studi di Trento
email: [email protected]