linear.h

// Description: Linear interpolation
// Documentation: math_functions.txt

#ifndef PASTELSYS_LINEAR_H
#define PASTELSYS_LINEAR_H

#include "pastel/sys/vector.h"
#include "pastel/sys/tuple.h"
#include "pastel/sys/range.h"

#include <iterator>

namespace Pastel
{

    //! Interpolates linearly between points.
    /*!
   linear(startPoint, endPoint, time) =
   startPoint + time * (endPoint - startPoint)
   */
    template <
        typename PointType,
        typename Real>
    PointType linear(
        const PointType& startPoint,
        const PointType& endPoint,
        const Real& time);

    //! Interpolates linearly between vectors.
    template <typename Real, integer N>
    Vector<Real, N> linear(
        const Vector<Real, N>& startPoint,
        const Vector<Real, N>& endPoint,
        const NoDeduction<Real>& time);

    //! Interpolates linearly in a [0, 1]^n cube.
    /*!
   Preconditions:
   data.size() >= (1 << n)

   Time complexity:
   O(2^n), where n is the dimensionality.

   data:
   The values of the cube vertices 
   in lexicographical order in coordinates.
   */
    template <integer N, typename Vector_Range>
    typename boost::range_value<Vector_Range>::type linear(
        const Vector<real, N>& position,
        const Vector_Range& data);

    //! Return midpoint of two points.
    /*!
   This is a convenience function that calls:

   linear(startPoint, endPoint, (Real)0.5);
   */
    template <typename Real, integer N>
    Vector<Real, N> midpoint(
        const Vector<Real, N>& startPoint,
        const Vector<Real, N>& endPoint);

}

#include "pastel/sys/math/linear.hpp"

#endif