Boost C++ Libraries

Synopsis

#include <boost/math/interpolators/cardinal_quadratic_b_spline.hpp>

namespace boost{ namespace math{ namespace interpolators {

template <class Real>
class cardinal_quadratic_b_spline
{
public:
    // If you don't know the value of the derivative at the endpoints, leave them as nans and the routine will estimate them.
    // y[0] = y(a), y[n - 1] = y(b), step_size = (b - a)/(n -1).
    cardinal_quadratic_b_spline(const Real* const y,
                                size_t n,
                                Real t0 /* initial time, left endpoint */,
                                Real h  /*spacing, stepsize*/,
                                Real left_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN(),
                                Real right_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN())

    cardinal_quadratic_b_spline(std::vector<Real> const & y,
                                Real t0 /* initial time, left endpoint */,
                                Real h  /*spacing, stepsize*/,
                                Real left_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN(),
                                Real right_endpoint_derivative = std::numeric_limits<Real>::quiet_NaN())

    Real operator()(Real t) const;

    Real prime(Real t) const;
};
}}}

Cardinal Quadratic B-Spline Interpolation

The cardinal quadratic B-spline interpolator is very nearly the same as the cubic B-spline interpolator, with the modification that the basis functions are constructed by convolving a box function with itself twice, rather than three times as is done with the cubic B-spline.

Since the basis functions are less smooth than the cubic B-spline, you will nearly always wish to use the cubic B-spline interpolator rather than this. However, this interpolator is occasionally useful for approximating functions of reduced smoothness, as hence finds a uses internally in the Boost.Math library.

It is reasonable to test this interpolator against the cubic b-spline interpolator when you are approximating functions which are two or three times continuously differentiable, but not three or four times differentiable.