externalized helper function to build cubic and quintic splines

include/spline/cubic_spline.h

@@ -33,6 +33,14 @@ T_Point make_cubic_vector(Point const& a, Point const& b, Point const& c, Point
     res.push_back(a);res.push_back(b);res.push_back(c);res.push_back(d);
     return res;
 }
+
+template<typename Time, typename Numeric, std::size_t Dim, bool Safe, typename Point, typename T_Point>
+spline_curve<Time,Numeric,Dim,Safe,Point,T_Point> create_cubic(Point const& a, Point const& b, Point const& c, Point const &d,
+               const Time min, const Time max)
+{
+    T_Point coeffs = make_cubic_vector<Point, T_Point>(a,b,c,d);
+    return spline_curve<Time,Numeric,Dim,Safe,Point,T_Point>(coeffs.begin(),coeffs.end(), min, max);
+}
 }
 #endif //_STRUCT_CUBICSPLINE
 

include/spline/cubic_zero_vel_acc.h

@@ -20,8 +20,7 @@
 #ifndef _CLASS_CUBICZEROVELACC
 #define _CLASS_CUBICZEROVELACC
 
-#include "curve_abc.h"
-#include "cubic_spline.h"
+#include "exact_cubic.h"
 
 #include "MathDefs.h"
 
@@ -30,23 +29,28 @@
 
 namespace spline
 {
-/// \class ExactCubic
+/// \class cubic_zero_vel.
 /// \brief Represents a set of cubic splines defining a continuous function 
-/// crossing each of the waypoint given in its initialization
+/// crossing each of the waypoint given in its initialization. Additional constraints
+/// are used to increase the order of the last and first splines, to start and finish
+/// trajectory with zero velocity and acceleration. Thus the first and last splines
 ///
-template<typename Time= double, typename Numeric=Time, std::size_t Dim=3, bool Safe=false
-, typename Point= Eigen::Matrix<Numeric, Dim, 1> >
-struct exact_cubic : public curve_abc<Time, Numeric, Dim, Safe, Point>
+///
+template<typename Time= double, typename Numeric=Time, std::size_t Dim=3, bool Safe=false,
+         typename Point= Eigen::Matrix<Numeric, Dim, 1>,
+         typename T_Point =std::vector<Point,Eigen::aligned_allocator<Point> > >
+struct cubic_zero_vel : public exact_cubic<Time, Numeric, Dim, Safe, Point, T_Point>
 {
-	typedef Point 	point_t;
-	typedef Eigen::Matrix<Numeric, Eigen::Dynamic, Eigen::Dynamic> MatrixX;
-	typedef Time 	time_t;
-	typedef Numeric	num_t;
-	typedef cubic_spline<time_t, Numeric, Dim, Safe, Point> cubic_spline_t;
-    typedef quintic_spline<time_t, Numeric, Dim, Safe, Point> cubic_spline_t;
-    typedef typename std::vector<cubic_spline_t*> T_cubic;
-	typedef typename T_cubic::iterator IT_cubic;
-	typedef typename T_cubic::const_iterator CIT_cubic;
+    typedef Point 	point_t;
+    typedef T_Point t_point_t;
+    typedef Eigen::Matrix<Numeric, Eigen::Dynamic, Eigen::Dynamic> MatrixX;
+    typedef Time 	time_t;
+    typedef Numeric	num_t;
+    typedef spline_curve<time_t, Numeric, Dim, Safe, point_t, t_point_t> spline_t;
+    typedef exact_cubic<Time, Numeric, Dim, Safe, Point> exact_cubic_t;
+    typedef typename std::vector<spline_t> t_spline_t;
+    typedef typename t_spline_t::iterator it_spline_t;
+    typedef typename t_spline_t::const_iterator cit_spline_t;
 
 	/* Constructors - destructors */
 	public:
@@ -54,119 +58,19 @@ struct exact_cubic : public curve_abc<Time, Numeric, Dim, Safe, Point>
 	///\param wayPointsBegin : an iterator pointing to the first element of a waypoint container
 	///\param wayPointsEns   : an iterator pointing to the end           of a waypoint container
 	template<typename In>
-	exact_cubic(In wayPointsBegin, In wayPointsEnd)
+    cubic_zero_vel(In wayPointsBegin, In wayPointsEnd)
+        : exact_cubic_t(wayPointsBegin, wayPointsEnd)
 	{
-		std::size_t const size(std::distance(wayPointsBegin, wayPointsEnd));
-		if(Safe && size < 1)
-		{
-			throw; // TODO
-		}
-
-		// refer to the paper to understand all this.
-		MatrixX h1 = MatrixX::Zero(size, size);
-		MatrixX h2 = MatrixX::Zero(size, size);
-		MatrixX h3 = MatrixX::Zero(size, size);
-		MatrixX h4 = MatrixX::Zero(size, size);
-		MatrixX h5 = MatrixX::Zero(size, size);
-		MatrixX h6 = MatrixX::Zero(size, size);
-
-		MatrixX a =  MatrixX::Zero(size, Dim);
-		MatrixX b =  MatrixX::Zero(size, Dim);
-		MatrixX c =  MatrixX::Zero(size, Dim);
-		MatrixX d =  MatrixX::Zero(size, Dim);
-		MatrixX x =  MatrixX::Zero(size, Dim);
-
-	
-		In it(wayPointsBegin), next(wayPointsBegin);
-        ++next;
-
-		for(std::size_t i(0); next != wayPointsEnd; ++next, ++it, ++i)
-		{
-			num_t const dTi((*next).first  - (*it).first);
-			num_t const dTi_sqr(dTi * dTi);
-			num_t const dTi_cube(dTi_sqr * dTi);
-			// filling matrices values
-			h3(i,i)   = -3 / dTi_sqr;
-			h3(i,i+1) =  3 / dTi_sqr;
-			h4(i,i)   = -2 / dTi;
-			h4(i,i+1) = -1 / dTi;
-			h5(i,i)   =  2 / dTi_cube;
-			h5(i,i+1) = -2 / dTi_cube;
-			h6(i,i)   =  1 / dTi_sqr;
-			h6(i,i+1) =  1 / dTi_sqr;
-			if( i+2 < size)
-			{
-				In it2(next); ++ it2;
-				num_t const dTi_1((*it2).first - (*next).first);
-				num_t const dTi_1sqr(dTi_1 * dTi_1);
-				// this can be optimized but let's focus on clarity as long as not needed
-				h1(i+1, i)   =  2 / dTi;
-				h1(i+1, i+1) =  4 / dTi + 4 / dTi_1;
-				h1(i+1, i+2) =  2 / dTi_1;
-				h2(i+1, i)   = -6 / dTi_sqr;
-				h2(i+1, i+1) = (6 / dTi_1sqr) - (6 / dTi_sqr);
-				h2(i+1, i+2) =  6 / dTi_1sqr;
-			}
-			x.row(i)= (*it).second.transpose();
-	      	}
-		// adding last x
-		x.row(size-1)= (*it).second.transpose();
-		a= x;
-		PseudoInverse(h1);
-		b = h1 * h2 * x; //h1 * b = h2 * x => b = (h1)^-1 * h2 * x
-		c = h3 * x + h4 * b;
-		d = h5 * x + h6 * b;
-		it= wayPointsBegin, next=wayPointsBegin; ++ next;
-		for(int i=0; next != wayPointsEnd; ++i, ++it, ++next)
-		{
-            subSplines_.push_back(new cubic_spline_t(a.row(i), b.row(i), c.row(i), d.row(i), (*it).first, (*next).first));
-		}
-        subSplines_.push_back(new cubic_spline_t(a.row(size-1), b.row(size-1), c.row(size-1), d.row(size-1), (*it).first, (*it).first));
+        // NOTHING
 	}
 
 	///\brief Destructor
-	~exact_cubic()
-    {
-        for(IT_cubic it = subSplines_.begin(); it != subSplines_.end(); ++ it)
-        {
-            delete(*it);
-        }
-	}
-
-	private:
-	exact_cubic(const exact_cubic&);
-	exact_cubic& operator=(const exact_cubic&);
-	/* Constructors - destructors */
-
-	/*Operations*/
-	public:
-	///  \brief Evaluation of the cubic spline at time t.
-	///  \param t : the time when to evaluate the spine
-	///  \param return : the value x(t)
-	virtual point_t operator()(time_t t) const
-	{
-
-        if(Safe && (t < subSplines_.front()->t_min_ || t > subSplines_.back()->t_max_)){throw std::out_of_range("TODO");}
-		for(CIT_cubic it = subSplines_.begin(); it != subSplines_.end(); ++ it)
-		{
-            if(t >= ((*it)->t_min_) && t <= ((*it)->t_max_))
-			{
-                return (*it)->operator()(t);
-			}
-		}
-	}
-	/*Operations*/
-
-	/*Helpers*/
-	public:
-    num_t virtual min() const{return subSplines_.front()->t_min_;}
-    num_t virtual max() const{return subSplines_.back()->t_max_;}
-	/*Helpers*/
+    ~cubic_zero_vel(){}
 
-	/*Attributes*/
 	private:
-	T_cubic subSplines_;
-	/*Attributes*/
+    cubic_zero_vel(const cubic_zero_vel&);
+    cubic_zero_vel& operator=(const cubic_zero_vel&);
+    /* Constructors - destructors */
 };
 }
 #endif //_CLASS_CUBICZEROVELACC

include/spline/exact_cubic.h

@@ -48,6 +48,7 @@ struct exact_cubic : public curve_abc<Time, Numeric, Dim, Safe, Point>
     typedef typename std::vector<spline_t> t_spline_t;
     typedef typename t_spline_t::iterator it_spline_t;
     typedef typename t_spline_t::const_iterator cit_spline_t;
+    typedef curve_abc<Time, Numeric, Dim, Safe, Point> curve_abc_t;
 
 	/* Constructors - destructors */
 	public:
@@ -56,7 +57,7 @@ struct exact_cubic : public curve_abc<Time, Numeric, Dim, Safe, Point>
 	///\param wayPointsEns   : an iterator pointing to the end           of a waypoint container
 	template<typename In>
 	exact_cubic(In wayPointsBegin, In wayPointsEnd)
-        : subSplines_(computeWayPoints<In>(wayPointsBegin, wayPointsEnd))
+        : curve_abc_t(), subSplines_(computeWayPoints<In>(wayPointsBegin, wayPointsEnd))
     {
 	}
 
@@ -131,19 +132,14 @@ struct exact_cubic : public curve_abc<Time, Numeric, Dim, Safe, Point>
         it= wayPointsBegin, next=wayPointsBegin; ++ next;
         for(int i=0; next != wayPointsEnd; ++i, ++it, ++next)
         {
-            add_cubic(a.row(i), b.row(i), c.row(i), d.row(i),(*it).first, (*next).first, subSplines);
+            subSplines.push_back(
+                create_cubic<Time,Numeric,Dim,Safe,Point,T_Point>(a.row(i), b.row(i), c.row(i), d.row(i),(*it).first, (*next).first));
         }
-        add_cubic(a.row(size-1), b.row(size-1), c.row(size-1), d.row(size-1),(*it).first, (*it).first, subSplines);
+        subSplines.push_back(
+                create_cubic<Time,Numeric,Dim,Safe,Point,T_Point>(a.row(size-1), b.row(size-1), c.row(size-1), d.row(size-1), (*it).first, (*it).first));
         return subSplines;
     }
 
-    void add_cubic(point_t const& a, point_t const& b, point_t const& c, point_t const &d,
-                   const time_t min, const time_t max, t_spline_t& subSplines) const
-    {
-        t_point_t coeffs = make_cubic_vector<point_t, t_point_t>(a,b,c,d);
-        subSplines.push_back(spline_t(coeffs.begin(),coeffs.end(), min, max));
-    }
-
 	private:
 	exact_cubic(const exact_cubic&);
 	exact_cubic& operator=(const exact_cubic&);
@@ -156,10 +152,10 @@ struct exact_cubic : public curve_abc<Time, Numeric, Dim, Safe, Point>
 	///  \param return : the value x(t)
 	virtual point_t operator()(time_t t) const
 	{
-        if(Safe && (t < subSplines_.front().t_min_ || t > subSplines_.back().t_max_)){throw std::out_of_range("TODO");}
+        if(Safe && (t < subSplines_.front().min() || t > subSplines_.back().max())){throw std::out_of_range("TODO");}
         for(cit_spline_t it = subSplines_.begin(); it != subSplines_.end(); ++ it)
 		{
-            if(t >= (it->t_min_) && t <= (it->t_max_))
+            if(t >= (it->min()) && t <= (it->max()))
 			{
                 return it->operator()(t);
 			}
@@ -169,8 +165,8 @@ struct exact_cubic : public curve_abc<Time, Numeric, Dim, Safe, Point>
 
 	/*Helpers*/
 	public:
-    num_t virtual min() const{return subSplines_.front().t_min_;}
-    num_t virtual max() const{return subSplines_.back().t_max_;}
+    num_t virtual min() const{return subSplines_.front().min();}
+    num_t virtual max() const{return subSplines_.back().max();}
 	/*Helpers*/
 
 	/*Attributes*/

include/spline/quintic_spline.h

@@ -35,6 +35,14 @@ T_Point make_quintic_vector(Point const& a, Point const& b, Point const& c,
     res.push_back(d);res.push_back(e);res.push_back(f);
     return res;
 }
+
+template<typename Time, typename Numeric, std::size_t Dim, bool Safe, typename Point, typename T_Point>
+spline_curve<Time,Numeric,Dim,Safe,Point,T_Point> create_quintic(Point const& a, Point const& b, Point const& c, Point const &d, Point const &e, Point const &f,
+               const Time min, const Time max)
+{
+    T_Point coeffs = make_quintic_vector<Point, T_Point>(a,b,c,d,e,f);
+    return spline_curve<Time,Numeric,Dim,Safe,Point,T_Point>(coeffs.begin(),coeffs.end(), min, max);
+}
 }
 #endif //_STRUCT_QUINTIC_SPLINE
 

include/spline/spline_curve.h

@@ -39,6 +39,7 @@ struct spline_curve : public curve_abc<Time, Numeric, Dim, Safe, Point>
     typedef typename t_point_t::const_iterator cit_point_t;
     typedef Time 	time_t;
     typedef Numeric	num_t;
+    typedef curve_abc<Time, Numeric, Dim, Safe, Point> curve_abc_t;
 /* Constructors - destructors */
     public:
     ///\brief Constructor
@@ -48,7 +49,8 @@ struct spline_curve : public curve_abc<Time, Numeric, Dim, Safe, Point>
     ///\param min: LOWER bound on interval definition of the spline
     ///\param max: UPPER bound on interval definition of the spline
     spline_curve(const T_Point& coefficients, const time_t min, const time_t max)
-        :coefficients_(coefficients), t_min_(min), t_max_(max), dim_(Dim), order_(coefficients_.size()+1)
+        : curve_abc_t(),
+          coefficients_(coefficients), t_min_(min), t_max_(max), dim_(Dim), order_(coefficients_.size()+1)
     {
         if(Safe)
         {
@@ -71,7 +73,8 @@ struct spline_curve : public curve_abc<Time, Numeric, Dim, Safe, Point>
     ///\param max: UPPER bound on interval definition of the spline
     template<typename In>
     spline_curve(In zeroOrderCoefficient, In out, const time_t min, const time_t max)
-        :coefficients_(init_coeffs(zeroOrderCoefficient, out)), t_min_(min), t_max_(max), dim_(Dim), order_(coefficients_.size()+1)
+        :coefficients_(init_coeffs(zeroOrderCoefficient, out)), dim_(Dim), order_(coefficients_.size()+1),
+          t_min_(min), t_max_(max)
     {
         if(Safe)
         {
@@ -131,9 +134,11 @@ struct spline_curve : public curve_abc<Time, Numeric, Dim, Safe, Point>
 /*Attributes*/
     public:
     t_point_t coefficients_;
-    time_t t_min_, t_max_;
     std::size_t dim_;
     std::size_t order_;
+
+    private:
+    time_t t_min_, t_max_;
 /*Attributes*/
 
     private:

src/tests/spline_test/Main.cpp

 
 #include "spline/exact_cubic.h"
+#include "spline/cubic_zero_vel_acc.h"
 #include "spline/bezier_curve.h"
 #include "spline/spline_curve.h"
 
@@ -14,7 +15,7 @@ namespace spline
 typedef Eigen::Vector3d point_t;
 typedef std::vector<point_t,Eigen::aligned_allocator<point_t> >  t_point_t;
 typedef spline_curve  <double, double, 3, true, point_t, t_point_t> cubic_function_t;
-typedef exact_cubic   <double, double, 3, true, point_t> exact_cubic_t;
+typedef exact_cubic <double, double, 3, true, point_t> exact_cubic_t;
 typedef bezier_curve  <double, double, 3, true, point_t> bezier_curve_t;
 typedef std::pair<double, point_t> Waypoint;
 typedef std::vector<Waypoint> T_Waypoint;