[/
Copyright (c) 2019 Nick Thompson
Use, modification and distribution are subject to the
Boost Software License, Version 1.0. (See accompanying file
LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
]

[section:cardinal_quadratic_b Cardinal Quadratic B-spline interpolation]

[heading 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;
    };
    }}}

[heading 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.

[endsect]
[/section:cardinal_quadratic_b]
