bezier_curve.h 6.3 KB
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/**
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* \file bezier_curve.h
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* \brief class allowing to create a Bezier curve of dimension 1 <= n <= 3.
* \author Steve T.
* \version 0.1
* \date 06/17/2013
*/


#ifndef _CLASS_BEZIERCURVE
#define _CLASS_BEZIERCURVE

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#include "curve_abc.h"
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#include "bernstein.h"
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#include "MathDefs.h"

#include <vector>
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#include <stdexcept>
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#include <iostream>

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namespace spline
{
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/// \class BezierCurve
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/// \brief Represents a Bezier curve of arbitrary dimension and order.
/// For degree lesser than 4, the evaluation is analitycal.Otherwise
/// the bernstein polynoms are used to evaluate the spline at a given location.
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///
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template<typename Time= double, typename Numeric=Time, std::size_t Dim=3, bool Safe=false
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, typename Point= Eigen::Matrix<Numeric, Dim, 1> >
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struct bezier_curve : public curve_abc<Time, Numeric, Dim, Safe, Point>
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{
	typedef Point 	point_t;
	typedef Time 	time_t;
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    typedef Numeric	num_t;
    typedef std::vector<point_t,Eigen::aligned_allocator<point_t> > t_point_t;
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    typedef bezier_curve<Time, Numeric, Dim, Safe, Point > bezier_curve_t;
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/* Constructors - destructors */
	public:
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	///\brief Constructor
	///\param PointsBegin, PointsEnd : the points parametering the Bezier curve
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    ///
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	template<typename In>
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	bezier_curve(In PointsBegin, In PointsEnd, const time_t minBound=0, const time_t maxBound=1)
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	: minBound_(minBound)
	, maxBound_(maxBound)
	, size_(std::distance(PointsBegin, PointsEnd))
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    , bernstein_(spline::makeBernstein<num_t>(size_-1))
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	{
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        assert(bernstein_.size() == size_);
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		In it(PointsBegin);
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        if(Safe && (size_<1 || minBound >= maxBound))
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		{
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            throw std::out_of_range("can't create bezier min bound is higher than max bound"); // TODO
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		}
		for(; it != PointsEnd; ++it)
		{
			pts_.push_back(*it);
		}
	}
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	///\brief Destructor
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	~bezier_curve()
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	{
		// NOTHING
	}
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	private:
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//	bezier_curve(const bezier_curve&);
//  bezier_curve& operator=(const bezier_curve&);
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/* Constructors - destructors */

/*Operations*/
	public:
	///  \brief Evaluation of the cubic spline at time t.
	///  \param t : the time when to evaluate the spine
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	///  \param return : the value x(t)
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    virtual point_t operator()(const time_t t) const
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	{
		num_t nT = (t - minBound_) / (maxBound_ - minBound_);
		if(Safe &! (0 <= nT && nT <= 1))
		{
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            throw std::out_of_range("can't evaluate bezier curve, out of range"); // TODO
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        }
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		else
		{
			num_t dt = (1 - nT);
			switch(size_)
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            {
                case 1 :
                    return pts_[0];
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				case 2 :
					return pts_[0] * dt +  nT * pts_[1];
				break;
				case 3 :
					return 	pts_[0] * dt * dt 
                       				+ 2 * pts_[1] * nT * dt
						+ pts_[2] * nT * nT;
				break;
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                case 4 :
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					return 	pts_[0] * dt * dt * dt
						+ 3 * pts_[1] * nT * dt * dt 
						+ 3 * pts_[2] * nT * nT * dt 
						+ pts_[3] * nT * nT *nT;
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                default :
                    return evalBernstein(dt);
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				break;
			}
		}
	}
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    ///  \brief Computes the derivative curve at order N.
    ///  \param order : order of the derivative
    ///  \param return : the value x(t)
    bezier_curve_t compute_derivate(const std::size_t order) const
    {
        if(order == 0) return *this;
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        num_t degree = (num_t)(size_-1);
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        t_point_t derived_wp;
        for(typename t_point_t::const_iterator pit =  pts_.begin(); pit != pts_.end()-1; ++pit)
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            derived_wp.push_back(degree * (*(pit+1) - (*pit)));
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        if(derived_wp.empty())
            derived_wp.push_back(point_t::Zero());
        bezier_curve_t deriv(derived_wp.begin(), derived_wp.end(),minBound_,maxBound_);
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        std::cout << "deriv size" << deriv.size_ << std::endl;
        std::cout << "val size" << size_ << std::endl;
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        assert(deriv.size_ +1 == this->size_);
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        return deriv.compute_derivate(order-1);
    }

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    ///  \brief Computes the primitive of the curve at order N.
    ///  \param constant : value of the primitive at t = 0
    ///  \param return : the curve x_1(t) such that d/dt(x_1(t)) = x_1(t)
    bezier_curve_t compute_primitive(const std::size_t order) const
    {
        if(order == 0) return *this;
        num_t new_degree = (num_t)(size_);
        t_point_t n_wp;
        point_t current_sum =  point_t::Zero();
        // recomputing waypoints q_i from derivative waypoints p_i. q_0 is the given constant.
        // then q_i = (sum( j = 0 -> j = i-1) p_j) /n+1
        n_wp.push_back(current_sum);
        for(typename t_point_t::const_iterator pit =  pts_.begin(); pit != pts_.end(); ++pit)
        {
            current_sum += *pit;
            n_wp.push_back(current_sum / new_degree);
        }
        bezier_curve_t integ(n_wp.begin(), n_wp.end(),minBound_,maxBound_);
        assert(integ.size_== this->size_ +1 );
        return integ.compute_primitive(order-1);
    }

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    ///  \brief Evaluates the derivative at order N of the curve.
    ///  If the derivative is to be evaluated several times, it is
    ///  rather recommended to compute the derivative curve using compute_derivate
    ///  \param order : order of the derivative
    ///  \param t : the time when to evaluate the spine
    ///  \param return : the value x(t)
    virtual point_t     derivate(const time_t t, const std::size_t order) const
    {
        bezier_curve_t deriv =compute_derivate(order);
        return deriv(t);
    }

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    ///
    /// \brief Evaluates all Bernstein polynomes for a certain degree
    ///
    point_t evalBernstein(const Numeric u) const
    {
        point_t res = point_t::Zero();
        typename t_point_t::const_iterator pts_it = pts_.begin();
        for(typename std::vector<Bern<Numeric> >::const_iterator cit = bernstein_.begin();
            cit !=bernstein_.end(); ++cit, ++pts_it)
        {
            res += cit->operator()(u) * (*pts_it);
        }
        return res;
    }

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/*Operations*/
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/*Helpers*/
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	virtual time_t min() const{return minBound_;}
	virtual time_t max() const{return maxBound_;}
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/*Helpers*/

	public:
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    const time_t minBound_, maxBound_;
    const std::size_t size_;
    const std::vector<Bern<Numeric> > bernstein_;
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    private:
    t_point_t  pts_;

    //storing bernstein polynoms, even in low dimension
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};
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}
#endif //_CLASS_BEZIERCURVE