paella/Code/include/Geometry/Spline.hpp

#ifndef SPLINE_HPP
#define SPLINE_HPP

#include <vector>
#include <tuple>
#include <cmath>
#include <Geometry/Circle.hpp>
#include <Utility/TupleFunctions.hpp>

namespace geo
{

///////////////////////////////////////////////////////////////
/// \brief Utility template class for manipulating B-splines
//////////////////////////////////////////////////////////////
template<typename... Types>
class Spline
{
    public:
        ////////////////////////////////////////////////////////////
        /// \brief Default constructor
        ///
        /// Creates an empty spline (with no control points)
        ///////////////////////////////////////////////////////////
        Spline();

        ///////////////////////////////////////////////////////////
        /// \brief Evaluates the spline at a certain time
        ///
        /// \param t Time at which you want to evaluate the spline. Must be between 0 and 1
        ///
        /// \return Tuple that corresponds to the points of the spline at time t
        ///////////////////////////////////////////////////////////
        std::tuple<Types...> operator()(float t) const;

        ///////////////////////////////////////////////////////////
        /// \brief Evaluates the derivative of the spline at a certain time
        ///
        /// \param t Time at which you want to evaluate the derivative of the
        ///          spline. Must be between 0 and 1
        ///
        /// \return Tuple that corresponds to the derivative of each
        ///         coordinates of the spline at time t
        ///////////////////////////////////////////////////////////
        std::tuple<Types...> prime(float t) const;

        ///////////////////////////////////////////////////////////
        /// \brief Prints the spline to the stream
        ///
        /// \param t Time at which you want to evaluate the derivative of the
        ///          spline. Must be between 0 and 1
        ///
        /// \return Tuple that corresponds to the derivative of each
        ///         coordinates of the spline at time t
        ///
        /// Prints first the degree of the spline, than the nodes and finally
        /// the control points. For example
        /// \code
        /// d 3
        ///
        /// n 0 0 0 0 0.333333 0.666667 1 1 1 1
        ///
        /// p 0.60 0.43 0.51 0.142
        /// p 0.60 0.89 0.36 0.135
        /// p 0.72 1.28 0.24 0.129
        /// p 0.96 1.72 0.14 0.125
        /// p 1.27 2.10 0.06 0.122
        /// p 1.69 2.29 0 0.12
        /// \endcode
        ///////////////////////////////////////////////////////////
        template<typename... T>
        friend std::ostream& operator<<( std::ostream& out, Spline<T...> const& spline);

        geo::Circle<float> computeCircle(float t, unsigned int const nbPoints, geo::Vector3<float>& v, unsigned int const offset = 0) const;

        std::vector<geo::Circle<float>> computeCircles(unsigned int nbCircles, unsigned int const nbPoints, unsigned int const globalOffset = 0) const;

    // private:
        ///////////////////////////////////////////////////////////
        /// \brief Add a control point to the spline
        ///
        /// \param node String representation of the node to be added
        ///////////////////////////////////////////////////////////
        void addControlPoint(std::string const& node);

        std::vector<std::tuple<Types...>> controlPoints; ///< Vector of the control points of the spline
        std::vector<float> nodes;                        ///< Vector of nodes of the spline
        int degree;                                      ///< Degree of the spline
};

namespace detail
{
template<typename... Types>
std::tuple<Types...> evalSpline(std::vector<std::tuple<Types...>> const& controlPoints , std::vector<float> const& nodes, int degree, float f);

template<typename... Types>
std::tuple<Types...> evalDerivativeSpline(std::vector<std::tuple<Types...>> const& controlPoints , std::vector<float> const& nodes, int degree, float f);

} // namespace detail

} // namespace geo

#include "Spline.inl"

#endif // SPLINE_HPP

////////////////////////////////////////////////////////////
/// \class geo::Spline
/// \ingroup geometry
///
/// A class that can manage splines and generates points on the splines
////////////////////////////////////////////////////////////